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Adventist Youth Honors Answer Book/Nature/Weather

a. Fog
Relative humidity is a measure of how much water is in the air compared to how much water can be in the air. As the temperature rises, the air can hold more water, and as it drops, it can hold less. When the humidity is 100% and the temperature drops, the air can no longer hold all the water that is in it. Fog is moisture that gets squeezed out of the air when the temperature drops. This moisture, a fog bank, can be thought of as a cloud near ground level.

b. Rain
Rain forms when separate drops of water fall to the Earth's surface from clouds.

For rain to fall, moist air needs to cool, resulting in condensation of vapor. This is commonly achieved by something which forces the air to rise. Air rises because of: hills and mountains (orographic lift), irregularities on the earth surface, causing mechanical or frictional turbulence, air pressure systems colliding (such as cold fronts undercutting warmer air), hot air uplift (convection), low pressure systems in which there is a general area of upward movement.

If there is sufficient moisture and the air rises enough to form dense clouds there could be rain from any of these.

c. Dew
Dew is water in the form of droplets that appears on thin, exposed objects in the morning or evening. As the exposed surface cools by radiating its heat to the sky, atmospheric moisture condenses at a rate greater than that of which it can evaporate, resulting in the formation of water droplets.

d. Snow
Snow is precipitation in the form of crystalline water ice, consisting of a multitude of snowflakes. Since it is composed of small rough particles it is a granular material. It has an open and therefore soft structure, unless packed by external pressure.

Snow is commonly formed when water vapor undergoes deposition high in the atmosphere at a temperature of less than 0 °C (32 °F). It can also be produced by falling particles of ice fog formed when the humidity in surface air freezes at very low temperatures.

e. Sleet
In Britain and other Commonwealth countries, sleet refers to snow that has partially melted on its fall to the ground, due to surrounding air that is sufficiently warm to partially melt it while falling, but not warm enough to fully melt it into rain. Thus it refers to partially melted droplets, a mixture of snow and rain. It does not tend to form a layer on the ground, unless the ground has a temperature that is below freezing, when it can form a dangerous layer of invisible ice on surfaces known as 'black ice'.

In American usage, sleet is a form of precipitation consisting of tiny frozen raindrops, or ice pellets. This is often mistaken for hail, but forms in a different fashion and is usually (but not always) smaller. This occurs when snow flakes falling through a small layer of warmer air in the atmosphere will begin to melt. They can then refreeze if they pass back into a layer of colder, sub-freezing air closer to the ground, resulting in little balls of ice. These ice balls may bounce when they hit the ground, and do not freeze into a solid mass unless mixed with freezing rain.

f. Hail
Hail forms on condensation nuclei such as dust, insects, or ice crystals, when super cooled water freezes on contact. Hailstones are usually from the size of a pea to the size of a golf ball.

g. Frost
If solid surfaces in contact with the air are chilled below the frost point, then structures of ice grow out from the solid surface. The size of the crystals depends on time and the amount of water vapor available.

2. Identify either in the sky or from pictures the following types of clouds: cirrus, cumulus, stratus, nimbus. What kind of weather is associated with each.

 * Cirrus: Cirrus clouds are at the highest altitudes. They often appear thin and wispy.  They are associated with fair weather.

 * Cumulus: Cumulus clouds are usually puffy and often have very distinct edges and usually a noticeable vertical development. They often have a popcorn-like appearance. Cells can be rather isolated or they can be grouped together in clusters. The first rain to fall out of the base of a cumulus cloud evaporates into the air beneath, cooling the air - often by several degrees. This cooled air descends, and the more it is cooled the more rapidly it descends. Thus instead of air rising into a cloud we have not only rain falling out the cloud, but air as well.  This is why cool and rainy weather is associated with cumulus clouds.

 * Stratus: Stratus clouds belong to a class characterized by horizontal layering with a uniform base, as opposed to convective clouds that are as tall or taller than wide (these are termed cumulus clouds). More specifically, the term stratus is used to describe flat, featureless clouds of low altitude varying in color from dark gray to nearly white. These clouds are essentially fog that is above ground level and are formed either through the lifting of morning fog or when cold air moves at low altitudes over a region. These clouds do not usually bring precipitation, although if sufficiently low in altitude to become fog, drizzle or mist may result.

 * Nimbus: Nimbus clouds are dark, precipitous clouds. Nimbus is a Latin word meaning cloud or rain storm. These are commonly called "thunderclouds."

Spirit thermometer
A spirit thermometer and a mercury thermometer work on the same principles. The "spirit" in a spirit thermometer is alcohol, and both alcohol and mercury expand and contract with temperature changes. When it's cold, they contract, and when it's hot, they expand. A thermometer can be built to exploit and amplify these properties. A glass tube with a bulb at the bottom is filled with alcohol. The tube allows for a greater volume of alcohol, so there is more of it to expand. When it expands, the only place it can go is into the narrow tube. The temperature is read based on how high up the tube the expansion sends the alcohol.

Mercury barometer
A standard mercury barometer has a glass column of 76 cm (30 inches) in height, closed at one end, with an open mercury-filled reservoir at the base. Mercury in the tube adjusts until the weight of the mercury column balances the atmospheric force exerted on the reservoir. High atmospheric pressure places more downward force on the reservoir, forcing mercury higher in the column. Low pressure allows the mercury to drop to a lower level in the column by lowering the downward force placed on the reservoir.

Aneroid barometer
The purpose of a barometer is to measure the weight of the atmosphere, or the pressure exerted by the air. An aneroid barometer is similar to a balloon, in that it has a cell filled with air. When the outside air pressure increases, the air pressure inside the cell is also increased. The only way it can do that is by decreasing the volume of the cell - in other words, the outside air pressure squishes the cell. Going back to the balloon analogy, the balloon would get smaller. When the outside air pressure decreases, the air inside the cell follows by decreasing its pressure as well. The only way it can do this is by expanding, taking up more volume, and making the cell containing it larger. In the balloon analogy, the balloon gets larger. An aneroid barometer basically measures the thickness of the cell.

An aneroid barometer uses a small, flexible metal box called an aneroid cell. This aneroid capsule (cell) is made from an alloy of beryllium and copper. The evacuated capsule (or usually more capsules) is prevented from collapsing by a strong spring. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer. Many models include a manually set needle which is used to mark the current measurement so a change can be seen. In addition, the mechanism is made deliberately 'stiff' so that tapping the barometer reveals whether the pressure is rising or falling as the pointer moves.

Rain gauge
The standard rain gauge consists of a funnel attached to a graduated cylinder that fits into a larger container. If the water overflows from the graduated cylinder the outside container will catch it. So when it is measured the cylinder will be measured and then the excess will be put in another cylinder and measured. In most cases the cylinder is marked in mm and in the picture above will measure up to 25 mm (0.98 in) of rainfall. Each horizontal line on the cylinder is 0.2 mm (0.007 in). The larger container collects any rainfall amounts over 25 mm that flows from a small hole near the top of the cylinder. A metal pipe is attached to the container and can be adjusted to ensure the rain gauge is level. This pipe then fits over a metal rod that has been placed in the ground.

==4. Why is it possible to be rainy on one side of the mountain range and dry on the other? Give an illustration for your country or region. a. Why is it cooler and more moist in the mountains than in the lowlands? b. From which direction do rain and clear weather usually come in your locality?== Orographic lift occurs when an air mass is forced from a low elevation to a higher elevation as it moves over rising terrain. As the air mass gains altitude it expands and cools. This cooler air cannot hold the moisture as well as warm air and this effectively raises the relative humidity to 100%, creating clouds and frequently precipitation.

Precipitation induced by orographic lift occurs in many places throughout the world. Examples include:
 * The eastern seaboard of Australia, which faces prevailing easterly winds,
 * The mountains of New Zealand, which face a prevailing westerly flow off the Tasman Sea.
 * The southern Andes, which face a prevailing westerly flow off the Pacific Ocean.
 * The Northwestern United States and Canada (Oregon, Washington and British Columbia) see prevailing westerly flow off the northern Pacific Ocean. Places on the sea-facing side of coastal mountains see over 100 inches (over 2.5 m) of precipitation per year. These locales are on the side of the mountains which are in the path of storm systems, and therefore receive the moisture which is effectively squeezed from the clouds.

5. Show with the help of a diagram how the earth's relationship to the sun produces the seasons.

The Earth's tilt on its axis causes the seasons. When the axial tilt points a hemisphere away from the sun, it is winter, and when it points it towards the sun it is summer. This is not because the distance between that part of the Earth and the Sun varies, but rather, it is because the angle of the sunlight is either more direct, or less direct. The Earth's elliptical orbit about the sun causes its distance from the Sun to vary by a lot more than the axial tilt does, and it does not affect the seasons.

It is better to think of it this way: shine a flashlight on a piece of paper or cardboard. When the rays from the flashlight are parallel to the paper, the spot is circular. If you tilt the paper, the spot becomes elongated. The same amount of light strikes the paper in both cases, but the light is more concentrated in the circular spot verses the elongated spot. The area illuminated by the elongated spot is greater, so less light hits each square inch in the elongated "light spot". Less light means less heat, and in the case of the Earth, that means "winter".

How lightning is formed and what causes thunderstorms and lightning
Lightning is caused when electrical charges build up in clouds. Scientists are still unsure exactly why that happens, but it is plausible that water droplets and ice travelling up and down within the cloud separate electrons from one another and transport them to the lower portions of the cloud. However this happens, it causes the cloud to have an electric field. When this field becomes strong enough, the electrons in the cloud begin to repel electrons on the ground, causing the ground to have a positive charge. When the voltage difference between the ground and the cloud becomes great enough, the air breaks down and actually conducts electricity. The air actually turns into plasma. When it conducts, the result is a lightning strike. The charge lowers toward earth usually splitting into filaments; these attract an upward plasma charge from objects on the earth such as trees, poles, towers, animals, blades of grass. These filaments are visible to the eye. Many of these charges will travel upwards but usually only one will contact the filaments in the air completing the circuit. Once this happens, lightning strikes with a gigantic release of energy.

Many people mistakenly believe that the reason a car is a good place to be during a lightning storm is because the rubber in the tires insulates the riders from the ground. But considering the fact that a lightning bolt may have just travelled a mile though the air, how much do you think a quarter inch of rubber is going to slow it down? Not at all! The reason you are safe in a car is because you are surrounded by a metal shell that will carry the electrical current around you instead of through you.

Thunder
Thunder is, even today, not completely understood by modern science. The word usually describes a sonic shock wave caused by the rapid heating and expansion of the air surrounding and within a bolt of lightning. The bolt changes the air into plasma and it instantly explodes, causing the sound known as a thunder clap.

This phenomenon occurs at the same time as a lightning flash, but a thunder clap is usually heard after lightning is seen because light travels faster (300,000,000 meters per second) than sound (around 300 meters per second). In very close proximity to the lightning strike, sound and light can be heard and seen almost simultaneously.

Kinds of Lightning
Some lightning strikes take on particular characteristics; scientists and the public have given names to these various types of lightning.

Intracloud lightning, sheet lightning, anvil crawlers
Intracloud lightning is the most common type of lightning, and occurs completely inside one cumulonimbus cloud; it is termed sheet lightning because the bolt is not seen, instead one sees the whole cloud light up from inside. Lightning that appears to travel extensively along the cloud anvil or its base is commonly called a crawler, or sometimes 'spider lightning'. Discharges of electricity in anvil crawlers travel up the sides of the cumulonimbus cloud branching out at the anvil top.

Cloud-to-ground lightning, anvil-to-ground lightning
Cloud-to-ground lightning is a great lightning discharge between a cumulonimbus cloud and the ground initiated by the downward-moving leader stroke. This is the second most common type of lightning. One special type of cloud-to-ground lightning is anvil-to-ground lightning, a form of positive lightning, since it emanates from the anvil top of a cumulonimbus cloud where the ice crystals are positively charged. In anvil-to-ground lightning, the leader stroke issues forth in a nearly horizontal direction until it veers toward the ground. These usually occur miles ahead of the main storm and will strike without warning on a sunny day. They are signs of an approaching storm and are known colloquially as "bolts out of the blue".

Cloud-to-cloud lightning
Cloud-to-cloud or intercloud lightning is a somewhat rare type of discharge lightning between two or more completely separate cumulonimbus clouds.

Ground-to-cloud lightning
Ground-to-cloud lightning is a lightning discharge between the ground and a cumulonimbus cloud from an upward-moving leader stroke. These thunderstorm clouds are formed wherever there is enough upward motion, instability in the vertical, and moisture to produce a deep cloud that reaches up to levels somewhat colder than freezing. These conditions are most often met in summer.

Heat lightning or summer lightning
Heat lightning (or, in the UK, "summer lightning") is nothing more than the faint flashes of lightning on the horizon or other clouds from distant thunderstorms. Heat lightning was named because it often occurs on hot summer nights. Heat lightning can be an early warning sign that thunderstorms are approaching. In Florida, heat lightning is often seen out over the water at night, the remnants of storms that formed during the day along a sea breeze front coming in from the opposite coast. In some cases, the thunderstorm may be too distant to hear the associated thunder from the lightning discharge.

Ball lightning
Ball lightning is described as a floating, illuminated ball that occurs during thunderstorms. They can be fast moving, slow moving or nearly stationary. Some make hissing or crackling noises or no noise at all. Some have been known to pass through windows and even dissipate with a bang. Ball lightning has been described by eyewitnesses but rarely, if ever, recorded by meteorologists.

7. Show with the help of a diagram what a convection is. What is its relation to winds?

A rising body of air typically loses heat because it radiates heat. At some point the air becomes denser than the air underneath it, which is still rising. Since it cannot descend through the rising air, it moves to one side. At some distance its downward force overcomes the rising force beneath it and the air begins to descend. As it descends, it warms again through surface contact, conductivity, or compression, and the cycle repeats itself. (The heating through compression of descending air is what is responsible for such welcome winter phenomena as what is known in Western North America as a Chinook wind or in the Alps as a Föhn wind.)

Radar
A weather radar is a type of radar used to locate precipitation, calculate its motion, estimate its type (rain, snow, hail, etc.), and forecast its future position and intensity. Modern weather radars are mostly doppler radars, capable of detecting the motion of rain droplets in addition to intensity of the precipitation. Both types of data can be analyzed to determine the structure of storms and their potential to cause severe weather.

Satellites
A weather satellite is a type of satellite that is primarily used to monitor the weather and climate of the Earth. These meteorological satellites, however, see more than clouds and cloud systems. City lights, fires, effects of pollution, auroras, sand and dust storms, snow cover, ice mapping, boundaries of ocean currents, energy flows, etc., are other environmental information collected from weather satellites.

El Niño and its effects on weather are monitored daily from satellite images. The Antarctic ozone hole is mapped from weather satellite data. Collectively, weather satellites flown by the U.S., Europe, India, China, Russia, and Japan provide nearly continuous observations for a global weather watch.

Visible-light images from weather satellites during local daylight hours are easy to interpret even by the average person; clouds, cloud systems such as fronts and tropical storms, lakes, forests, mountains, snow ice, fires, and pollution such as smoke, smog, dust and haze are readily apparent. Even wind can be determined by cloud patterns, alignments and movement from successive photos.

Computers
Computers are largely responsible for the accuracy of today's weather forecasts. Various computers are used not only to collect weather data from thousands of sensors around the world, but also for running weather simulations, and for presenting the information to the public on television news broadcasts.

Of these tasks, running weather simulations is certainly the most demanding. Numerical weather prediction models are computer simulations of the atmosphere. They take the analysis as the starting point and project the state of the atmosphere forward in time using an understanding of physics and fluid dynamics. The complicated equations which govern how the state of a fluid changes with time require supercomputers to solve them. The output from the model provides the basis of the weather forecast. There are a number of models that are used in forecasting, and each of them is a little different. Meteorologists look at the output of several and form their forecasts based on this.

a. Jet stream
Jet streams are fast flowing, relatively narrow air currents found in the atmosphere at around 11 kilometers (36,000 ft) above the surface of the Earth. They form at the boundaries of adjacent air masses with significant differences in temperature, such as of the polar region and the warmer air to the south. For this reason, areas between the pole and the jet stream are cold, and area between the equator and the jet stream are warm. As the jet stream shifts along the north-south direction, the weather shifts as well.

Meteorologists now understand that the path of the jet stream steers cyclonic storm systems at lower levels in the atmosphere, and so knowledge of their course has become an important part of weather forecasting. Jet streams also play an important part in the creation of super cells, the storm systems which create tornadoes.

The jet stream, a narrow band of fast moving wind, generally above 9 km (30,000 feet) has three dimensional regions or pockets of maximum winds along the jet. Where the winds enter these max regions it is appropriately called an entrance region and where it exits, an exit region. As the wind accelerates going into a jet max it produces an area of divergence. This divergence aloft helps generate areas of convergence near the surface. These latter areas are called low pressure centers. And from them we get lots of weather. Besides helping to produce storm centers in the lower atmosphere, the jet stream then helps to steer these storms which are like pieces of wood caught in a fast moving stream of water.

b. Volcano eruption
When a volcano erupts, it sends incredible amounts of volcanic ash into the atmosphere. This is enough to decrease the amount of sunlight that reaches the earth, causing a temporary (though sometimes devastating) global cooling. It also affects the intensity of the colors in the sunset for years.

The main effect on weather right near a volcano is that there is often a lot of rain, lightning, and thunder during an eruption. This is because all the ash particles that are thrown up into the atmosphere are good at attracting/collecting water droplets. We don’t quite know exactly how the lightning is caused but it probably involves the particles moving through the air and separating positively and negatively charged particles

10. Make a drawing showing the water cycle in weather.
The water cycle is the continuous movement of water over, above, and beneath the Earth's surface. It is powered by solar energy, and because it is a cycle, there is no beginning or end. As water moves around in the hydrosphere, it changes state among liquid, vapour, and ice. The time taken for water to move from one place to another varies from seconds to thousands of years, and the amount of water stored in different parts of the hydrosphere ranges up to 1.37 billion km³, which is contained in the oceans. Despite continual movement within the hydrosphere, the total amount of water at any one time remains essentially constant.

Wind Vane
A simple wind van can be made by fastening two sides of a strip of heavy paper around a short section of drinking straw. First, bend the strip in half. Place the straw in the bend and then glue the strip to itself. Drive a dowel, broom stick, or some similar item into the ground where you wish to measure the wind direction, and drive a finish nail into the top end. Then place the straw over the nail so that it may swing freely. When the wind blows, the vane (strip of paper and straw) will swivel on the nail indicating the wind direction.

Rain Gauge
A rain gauge is very simple to make. You will need a small, transparent vessel with constant diameter from top to bottom. If you have difficulty finding a vessel with constant diameter, you may opt to use a two-liter soda bottle. Strip off the label. Cut the top off the bottle, and fill it with plaster to a depth of 4 to 5 cm (this will provide a smooth bottom instead of the knobby bottom with which a two-liter bottle is typically endowed). You may wish to use epoxy instead of plaster - it is more expensive, but is more water proof. Plaster will work fine unless you plan to use the rain gauge for extended periods. You can also improve the water-resistance of the plaster by varnishing it.

Mark the sides of the vessel with a ruler, indicating millimeters and centimeters, with the 0 mark coinciding with the bottom of the vessel's inside. Then set it outside where it can collect rain. When the rain ends, a quick comparison of the water level to the indicators will tell you how much rain fell. Empty the rain gauge between storms.

12. Keep a weather chart for one week and record readings at 12-hour intervals. Include the following: a. Temperature b. Moisture (dew, fog, rain, frost, or snow) c. Cloud formation d. Wind direction
You may need to call your Pathfinders every day to get them to do this. It may help to build the weather instruments from requirement 11 first to build some excitement about weather. It may also help to work on this honor during the season in your area that has the most extreme weather. You can download a tracking chart here and give one to each of your students. http://www.pathfindersonline.org/pdf/resources/weather_tracking_chart.pdf

If you are teaching this honor to a class of Explorers, there is a chart they can fill out in their diaries.


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User talk:63.229.121.32

You have been blocked from editing Wikibooks for a period of 6 months for writing racist material in IB Biology Option D - Evolution and IB Biology/Cells. --Jomegat 04:41, 15 May 2007 (UTC)

title: User talk:63.229.121.32


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Template talk:Korean/Question-answer

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User talk:61.9.75.189

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 08:46, 15 May 2007 (UTC)

title: User talk:61.9.75.189


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Wikibooks:Requests for deletion/Binding Io to C++

Binding Io to C++
This was marked as qr-em and became speedy but the magic isn't working at present so it didn't make it to the category. However I am not happy deleting this as a speedy anyway. Over to you folk -- Herby talk thyme 12:48, 22 February 2007 (UTC)

* Move: I think something like this would do well as an example in the C++ book, though I'm not sure if it's a legit program or not, someone who knows something about programming would need to check that. But I'm not sure if this topic is already covered in the existing C++ book, and/or if it has any examples of how to do it. Mattb112885 13:28, 22 February 2007 (UTC)

 * Move : Will take a look if some content is fit for the C+++ Programming book, Is there a book on Io ? I'll give you some info later if so a merge would be good solution. --Panic 20:46, 14 March 2007 (UTC)
 * As Darklama points out there is a similarity in the page Binding Io to C++(more code) and Programming:Io/Binding Io to C++ on the Io Programming book, the page content would fit to both books, but mostly useful to the Io, I propose it should be moved to that book namespace the contributors informed and let them chose how to go about it. --Panic 02:17, 15 March 2007 (UTC)

 * Comment: to me it looks like something intended to be part of Io Programming. I suppose that sort of answers the question of is there a book on Io. However that book looks like its more intended to be a tutorial from what it says. --dark [[Image:Yin yang.svg|12px]] lama 02:07, 15 March 2007 (UTC)

 * Merge and Move, or Delete. : After looking at the edit history of Programming:Io/Binding Io to C++ and Binding Io to C++, I noticed they were both started by the same IP address on the same day with little difference in time, there is a good chance that both were created by the same individual. I think either both pages should be merged and moved into the Io Programming book or this copy deleted since it was created before the other copy and Programming:Io/Binding Io to C++ moved to Io Programming/Binding Io to C++ to fix the naming convention. --dark [[Image:Yin yang.svg|12px]] lama 02:32, 15 March 2007 (UTC)

 * Merge: I was completely unaware of this, but if it is essentially the same content there's no point to having it twice, and yeah I think it makes more sense in a book on IO than one on C++ (not sure though, how relevant is it, for all the computer programmers out there?) Mattb112885 (talk) 03:28, 15 March 2007 (UTC)

 * Comment - a Merge in this situation is not as easy, merge will require tagging and waiting, since the content seems to be at least some kind o duplication (it is about the same topic but the content is not equal and it is from the same editor it seems) a move to the IO book would address its "orphan" state, people on the book can then take care of the page or select what best fits their needs. --Panic 05:20, 18 March 2007 (UTC)

 * Why don't we say we move it to IO then, this discussion's been dead for over a month! If there's no objections of course, do you think the current title would be fine? Mattb112885 (talk) 00:48, 2 May 2007 (UTC)


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Wikibooks:Requests for deletion/Uniform Investment Adviser Law Exam

Uniform Investment Adviser Law Exam
Same as above --dark lama  16:04, 25 February 2007 (UTC)

 * Keep - Ditto my remarks about Uniform Securities Agent State Law Exam, as this is essentially the same kind of Wikibook in stub form at the moment. Hopefully even having something like this as a stub may inspire somebody in the future to create a Wikibook on this topic that is much more comprehensive.  --Rob Horning 22:54, 27 February 2007 (UTC)
 * Delete - accepting the "maybe a stub might bring someone" there really is nothing worthwhile here and it has not been actively edited for a year (barely then). It really is just "headings" - anyone wanting to write this will almost certainly start again -- Herby  talk thyme 10:29, 3 March 2007 (UTC)
 * To note here, there is value to having stubs, and really no real benefit in getting rid of them. This merely becomes a slightly more elaborate "suggested idea for a new Wikibook" instead.  Pressing the "delete" button does not really remove the content from the Wikimedia servers, it only hides it from "ordinary Wikibookians".  Clearly this is something that would be useful on Wikibooks if we could but have somebody willing to extend this book.  It should be clearly marked as a stub and left alone as a backwater part of Wikibooks.  Besides, there is no policy about deleting stubs on Wikibooks either, and indeed the Deletion Policy specifically states "In general, keep stubs."  I think this clearly applies here.  --Rob Horning 20:07, 6 March 2007 (UTC)
 * Keep - As per my comment for the above vfd. Xania [[Image:Flag_of_Poland_2.svg|15px]]talk 19:31, 11 March 2007 (UTC)
 * Delete per my reasons re above vfd —The preceding unsigned comment was added by Archolman (talk • contribs) 23:12, 17 Mar 2007  (UTC)
 * Keep - stubs as in book plans should not be targets of VfD, a good enough reason would be someone starting a similar book and then requesting a delete. --Panic 18:11, 22 March 2007 (UTC)
 * Delete as per my comments above. --Whiteknight (talk) (projects) 19:14, 22 March 2007 (UTC)
 * Keep or, at most, user-fy / scrapbook. Stubs are an excellent way to start a book; an outline is even better because it lays down your ideas for the reader. --Iamunknown 00:40, 26 March 2007 (UTC)


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Logic for Computer Scientists

Table of Contents

 * 1) /Preface/
 * 2) /Introduction/
 * 3) /Induction/
 * 4) /Propositional Logic/
 * 5) /Predicate Logic/
 * 6) /Modal Logic/

Authors

 * Uli Furbach

title: Logic for Computer Scientists


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User talk:Nouveau roues de willy

Hi, I see you've moved the Template:Interpreted code. Could you change the documentation at http://en.wikibooks.org/wiki/Template:Code#Code:Interpreted if you want this to be permanent

Thanks

Yan

title: User talk:Nouveau roues de willy


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User talk:74.104.224.214

Dora Nichov 11:03, 15 May 2007 (UTC)

title: User talk:74.104.224.214


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Template talk:Code:Interpreted

Name changes here can cause problems elsewhere. I have reverted one already. A standardized name should be chosen and documentation updated at Template:Code. Yan 11:49, 15 May 2007 (UTC)

I would like to find a way to mark the box title as an H3 header. Is this a good idea? Ideally this would provide an "edit" link to edit just the section inside the  box. Is this possible? Yan 11:49, 15 May 2007 (UTC)

title: Template talk:Code:Interpreted


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User talk:SarahGb

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You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add this page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! -- Herby talk thyme 11:25, 15 May 2007 (UTC)

Naming
Thanks for the contribution. Can you look at the naming policy as your new subpage does not comply? Simple to rename though - just use the "move" tab and give it the new name - thanks -- Herby talk thyme 11:25, 15 May 2007 (UTC)
 * Again - can you look at the naming of Logic for Computer Scientists: 2. Introduction, it should be named either Logic for Computer Scientists/2. Introduction or Logic for Computer Scientists/Introduction (numbering can be easily done on the main page) -- Herby talk thyme 11:38, 15 May 2007 (UTC)

Image copyright
You forgot about the license here: Image:Example1.png. Please select one from WB:ICT.

By the way, are you the author of Logic for Computer Scientists text? I see attribution for "Uli Furbach" there. --Derbeth talk 09:42, 16 May 2007 (UTC)

Logic for Computer Scientists
Hi SarahGb,

the Book you are working on looks great - im currently working on a similar one Computer_Science:Logic. I picked it up from other people that have worked on it before.

what would think about a merge? You can deal with chapter 1&2 as you like, I'm mainly interested in model theory (ch 4 & 5) and we could think about how to structure the rest?

--Sterling 21:57, 8 September 2007 (UTC)

title: User talk:SarahGb


text:
Logic for Computer Scientists/Introduction

Introduction
Although logic was developed and researched since Aristotle and Megara (430 - 360 b.c.) we want to focus to the development of mathematical logic, for which Gottfried Frege can be seen as the founder (Begriffsschrift, 1879). That was the first time, logic was introduced in a totally formal language; of course there have been others like Leibniz and Boole who contributed to the formalisation of logic, but it was Frege who radically introduced the idea of formalisation and deduction. This aspect is of particular interest for computer science, because there, the automation of the deduction process is investigated. The development of modern mathematical logic came along with a deep crisis in mathematics: At the end of the 19th and the beginning of the 20th century axiomatisation of set theory and of arithmetic have been a focus of mathematical research and in 1910 -1913 Whitehead and Rusell published their Principia Mathematica, an attempt to formalise the entire mathematics on the grounds of a formal logic, which was essentially the one given by Frege. This formalisation made it possible to avoid a number of antinomies, which have been discussed at that time. However it was in 1931, that Kurt Goedel proved in his famous incompleteness theorems, that an approach to formalise arithmetic cannot be complete given its consistency. It is important to note that during this period in the 1930th the foundation of theoretical computer science was laid: Alan Turing published his work on theoretical machines and on computability, Alonso Church developed his $$\lambda$$-calculus and Stephen Kleene developed the foundations of recursion theory.

For the rest of this introduction we will directly jump into the use of logic for modern computer science. The reader who is interested in history of logic is referred to the bibliographic section at the end of this introduction.

Programming
Within the last decade it turned out that computerised systems are the very base of advanced technology. Software is present in nearly all devices of modern houses, in our cars, not to speak about aircrafts or weapons. Without going into details, it is immediately obvious that for most, if not all applications, robust, safe and correct behaviour of a system is mandatory. To achieve this it is widely accepted that it is only possible if formal methods are applied during the entire process of hard- and software-development. In the following we shortly depict some tasks where the use of logic has proved to be extremely helpful.

Abstract Datatypes
In order to define datatypes and to derive efficient implementations for it, the concept of abstract datatype definitions is central. The idea is to define the abstract properties of a datatype, instead of giving special realisations. A very trivial example is the definition of a stack: Let $$\Sigma$$ be an alphabet. In order to define a stack $$S$$ over $$\Sigma$$ we assume $$clear$$ to be a nullary function and we define the following properties of stacks: $$\begin{matrix} clear \in S \\

\forall s \in S \;  \forall x \in \Sigma \;(push(s,x)\in S)\\

\forall s \in S \; (s \neq clear \Rightarrow pop(s) \in S)\\

\forall s \in S \; (s \neq clear \Rightarrow top(s) \in\Sigma)\\

\forall s \in S \; (empty(s) \in \{true, false\})\\ \end{matrix}$$ Hence, we have the functions $$clear, push$$ and $$pop$$, which yield stacks and the predicate $$empty$$, furthermore we need the following properties with respect to the $$push$$-operation.

$$\begin{matrix} \forall s \in S \; \forall x \in \Sigma   \; (push(s,x)  \neq  clear) \\

\forall s \in S \; \forall x,y \in \Sigma \; (push(s,x) = push(s,y) \Rightarrow  x=y)\\

\forall s,t\in S \; \forall x \in \Sigma  \; (push(s,x) = push(t,x)& \Rightarrow  s=t)\\ \end{matrix}$$

And we have to give properties with respect of the combinations of functions:

$$\begin{matrix} \forall s \in S \; \forall x \in \Sigma &( top(push(s,x)) = x \land pop(push(s,x)) = s)\\

\forall s \in S \; \forall x \in \Sigma & ( empty(push(s,x))= false)\\

& empty(clear) = true\\ \end{matrix}$$

The above formulae state what properties we expect stacks to have. Obviously it contains no hints how to implement such a data type. And indeed this specification is aiming to solve other problems, e.g. The reader may have already noticed, that the axioms are nothing else than formulas in predicate logic, i.e. all logic where variables like $$x$$ or $$s$$ together with so called quantifiers $$\forall$$ and $$\exists$$ are used. The above two questions, namely correctness and completeness, are very central topics for the design of formal systems in logic. The proof of these properties often is difficult and costly, but on the other hand it is one of the clear advantages of logical systems, that these properties can be proved formally. In the main part of this course we will deal with these questions explicitly.
 * Is the specification correct? I.e. is there a set $$S$$ together   with the given operations, such that the axioms above hold?
 * Is the specification complete. I.e. do the axioms imply all the  properties we intuitively assume a  stack to have? Are there sets   $$S$$ which do not meet our expectations?

Program Developments
There are a number of attempts to define methods, which allow the development of a program together with a formal argument of its correctness. We will give a very rough idea with a toy example. Assume the following simple program contains a loop, and assume that it has an array of integers: max := a(1); do i = 2,n if a(i) > max then max := a(i) end In order to understand what is going on if this program is executed, the following so called loop invariant is helpful: $$ \forall j : 1 \leq j \leq i \Rightarrow max \geq a(j) $$ This means, that for every value of $$i$$, i.e. before and after every execution of the if-statement within the do-loop the above formula is valid. Now assume that the loop is executed the last time, hence the value of $$i$$ after executing of the loop-body is $$n$$, one can conclude that max contains the maximum value of the array: $$ \forall j : 1 \leq j \leq n \Rightarrow max \geq a(j) $$ Another important issue for program development is the specification of programs. In order to give a formal specification of the above program for finding the maximum of an array the following logical formula can be used: $$ \forall S \; \forall m \; max(S, m) \Leftrightarrow (S \neq \emptyset \Rightarrow ( m \in S \land \forall x \; (x \in S \Rightarrow m \geq x))) $$ Note that in this specification $$S$$ is assumed to be a set. There is no decision yet made, that this has to be implemented by means of an array.

On the other hand logic can be used not only for the specification but also as programs itself. The following is a logic program which computes the maximum value of a list of values. Lists are represented as [ head.tail ], where head denotes the front element of a list, tail the rest of the list and nil the empty list.

max([m.nil], m) <-. max([head.tail], m)   <-  max([tail], m), head < m.   max([head.tail], head) <-  max([tail], m), head >= m.

Artificial Intelligence
One of the oldest sub-disciplines of Artificial Intelligence (AI) research is automated theorem proving. In the early days some were very optimistic about using theorem provers as general problem solvers for various different tasks, like action planning, knowledge representation or program verification. Now it is clear, that for special tasks tailored reasoning systems are necessary. We will comment in this subsection on theorem proving, aiming at proving mathematical theorems and on knowledge representation. This idea can be seen as going back to the ideas of Gottfried Wilhelm Leibnitz (1646 - 1716), who already at this time had a dream of formalisation, and even automatisation of mathematics.

A recent success is the proof of Robbins conjecture, which even reached the New York Times. For details see http://www-unix.mcs.anl.gov/~mccune/papers/robbins/. In 1933, E. V. Huntington presented the following basis for Boolean algebra: x + y = y + x.                                           [commutativity] (x + y) + z = x + (y + z). [associativity] n(n(x) + y) + n(n(x) + n(y)) = x.                        [Huntington equation] Shortly thereafter, Herbert Robbins conjectured that the Huntington equation can be replaced with a simpler one: n(n(x + y) + n(x + n(y))) = x.                           [Robbins equation] Robbins and Huntington could not find a proof, and the problem was later studied by Tarski and his students. The proof that solves the Robbins problem was found October 10, 1996, by the theorem prover EQP. EQP is similar in many ways to the more well known program http://www.mcs.anl.gov/AR/otter/. The main differences are that EQP has associative-commutative (AC) unification, is restricted to equational logic, and offers more paramodulation strategies. See the http://www.mcs.anl.gov/~mccune/papers/33-basic-test-problems/ for details.

Knowledge Representation
In many Artificial Intelligence the representation and manipulation of knowledge is a central task. To this end numerous graphic-oriented formalisms have been invented.

An informal semantics of this graphical notation states, that both, man and animal  are mammal  and that man  have a nationality  and an age, whereas an animal  has age and no nationality. A closer investigation of the semantics of such a formalism would show, that this is nothing than a pictorial representation of the following set of predicate logic formulae: $$ \forall x (man(x) \Rightarrow mammal(x)) $$ $$ \forall x (animal(x) \Rightarrow mammal(x)) $$ $$ \forall x (man(x) \Rightarrow \exists y\; age(x, y)) $$ $$ \forall x (man(x) \Rightarrow \exists y\; nationality(x, y)) $$ $$ \forall x (mammal(x) \Rightarrow \exists y\; age(x)) $$

See also: Gellrich/Gellrich: Mathematik (1) - Schaltalgebra Example:

Problem 1 (Introduction)
In a criminal case the following facts are proved: These circumstances are not sufficient to accuse one of them but it can be said for certain that at least one of two persons must be guilty. Which two are these?
 * 1) At least one of the three persons X,Y,Z is guilty.
 * 2) If X is guilty and Y is innocent, then Z is guilty.

Problem 2 (Introduction)
Which of the following syllogisms are valid? Give a reason for your answer or give a counterexample.
 * 1) All $$M$$ are $$P$$, some $$S$$ are not $$M$$ then: Some $$S$$ are $$P$$.
 * 2) All $$M$$ are $$P$$, some $$S$$ are not $$M$$ then: Some $$S$$ are not $$P$$
 * 3) All $$P$$ are $$M$$, some $$S$$ are not $$M$$ then: Some $$S$$ are not $$P$$.

Problem 3 (Introduction)
In a meeting there are 100 politicians discussing with each other. Everyone of them is either corrupted or uncorrupted. The Following facts are known:
 * 1) at least one politician is uncorrupted.
 * 2) In each pair of two politicians is at least one corrupted .  How Many of the politicians are corrupt, how many are uncorrupted?

Problem 4 (Introduction)
The anthropologist Abercrombie entered the island of the knights and the mucker with a slack feeling he have never had before. He knew that very wondrous people lived on this island: The knights made only true propositions the mucker false propositions every time. Abercrombie knew also that he had to find a friend before he could experience something. He had to find someone whose propositions he can trust. So he asked the first three people of the island he met to find a knight. Abercrombie asked Arthur at first: Are Bernard and Charles both knights? Arthur answered: Yes they are! Abercrombie asked then: Is Bernard a knight? With a big surprise he get the answer: No! Is Charles a knight or a mucker? Deduce your answer and give a reason for it.

Problem 5 (Introduction)
A little island had exactly 100 inhabitants. Every inhabitant either always told the truth or always lied. One Researcher came one day on the island and questioned the inhabitants sequentially. The first told: "There is at least one liar with us." The second said: "At least two liars live among us." etc.. The last finally claimed: "There are 100 liars on this Island." How many liars were there really? The researcher went to another island with 99 Inhabitants a year later. In an interview the inhabitants of these island spoke completely corresponding like on the first island, i.e. the $$n$$th inhabitants said: "There are at least $$n$$ liars here." What can you say about this island?

Problem 6 (Introduction)
In a village the priest explained one Sunday: "It was confessed to me that there are men who are unfaithful in our village. However, the confessing secret forbids it to me to call the names. It will you nevertheless learn all of them, if we proceed as follows: Any woman who for certain knows that her husband is unfaithful shall throw him in the following night out of the house." However, the problem was that every woman knows all about every other husband but nothing about her husband. In the next morning the priest went through the streets; not one single man was turned adrift. Also on the next day he saw nobody. But at 100th acre he saw men, who had been thrown out of the house by their wifes. How many?

Problem 7 (Introduction)
There is a hotel with countable infinitely many rooms 0, 1, 2,.... All rooms are vacant. Now, a $$\omega$$-decker bus comes with $$\omega$$ many seats on every deck. How can all of the passengers be accommodated in the hotel?

Up to Logic for Computer Scientists


text:
Logic for Computer Scientists/Preface

This is all about Computer science and technology of computers

Preface
This logic course is intended for computer scientists and it assumes practically no previous knowledge except some basic mathematical notions like relations and orderings. The material presented here can, of course, be printed and used as an ordinary textbook. However, it should be pointed out; that this is not the intention of the author; the aim was to create an electronic, interactive script where logics can be experienced by interaction and experimentation. The reader who is interested in more traditional forms of a textbook is referred to the following sources: Further bibliographic information will be given at the end of each section. Up to Logic for Computer Scientists
 * Uwe Schöning: Logik für Informatiker. BI-Wissenschaftsverlag, Mannheim, 1987. The chapter on propositional logics is based on the treatment in this book. Some definitions and proofs are given in the same way Schöning does.
 * Chin-Liang Chang; Richard Char-Tung Lee: Symbolic Logic and Mechanical Theorem Proving. Academic Press, London, 1973. The chapter on predicate logics is based on this standard textbook on mechanical theorem proving.
 * Melvin Fitting: First-Order Logic and Automated Theorem Proving. Springer-Verlag, Berlin, Heidelberg, New York, 1990. This is a modern computer science oriented treatment of analytic tableaux, which inspired the sections on tableaux of this course.

title: Logic for Computer Scientists/Preface


text:
User talk:YanWong

Hello, and welcome to Wikibooks!

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You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add this page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! -- Herby talk thyme 12:08, 15 May 2007 (UTC)

Template move
That was vandalism and sorted now I hope - regards -- Herby talk thyme 12:08, 15 May 2007 (UTC)

Thanks a lot. Quick work. I'll carry on padding out my book. Nice to know there is a helpful community. Yan 12:11, 15 May 2007 (UTC)
 * Folks are pretty friendly - ask around if you need any help -- Herby talk thyme 12:17, 15 May 2007 (UTC)

title: User talk:YanWong


text:
Talk:Statistical Analysis: an Introduction using R

New Book
I'm filling in this text in order to teach my partner some statistics before she starts medical school. A brief intro is on the Cover page. Feel free to add stuff: this is my first wikibook, and I hope I've started this in the right way. Discuss stuff here if you aren't sure. Yan 12:17, 15 May 2007 (UTC)

R code
If you want to add stuff, note that a lot of use is made of Template:Code, in particular Template:Code:Interpreted. Some notes on usage are at Template:Code. HYanWong (talk) 23:01, 16 November 2008 (UTC)

To do

 * Ask in new users forum about uploading text files, to use titanic data
 * Ask about toggling sections (to globally hide R topics)
 * Correct links in /R folder

 * Get in fit state for contributions (comments on each chapter)!

General points
Try to use "classic data sets" in the main text: these usually make good examples and are not software dependent. R-specific datasets can be used in topic boxes. Here are some suggestions: please add any you think fit. Many are in the R package "HistData".
 * von Bortkiewicz's deaths by horse kicks in the Prussian army ("prussian" in R package "pscl")
 * Titanic death/survival ("titanic" in R "datasets", or (better), titanic3 in "PASWR")
 * Student's criminal data ("crimtab" in R "datasets")
 * Fisher's iris data ("iris" in R "datasets")
 * Bumpus' sparrow data
 * Michelson's speed of light data ("morley" in R "datasets")
 * John Snow's cholera spatial data
 * Richard Doll's smoking in doctors dataset (try "breslow" in R "boot")
 * Anscombe's quartet ("anscombe" in R "datasets")
 * ?old Faithful data
 * ? data from Gosset, "The Probable Error of a Mean,"

General points

 * Aim to introduce the "why" behind statistics - this is not a book of statistical recipes.
 * Should aim to introduce the idea of statistical models asap

Chapter ideas

 * Intro Basic principles of data analysis, plus plots
 * Chapter 0 We should provide a "getting started in R" to allow users to install R, and see how it works etc. Since this is not statistics-specific, it is considered a pre-chapter
 * Chapter 1 To provide the background to statistics, have a "philosophy of analysis" type chapter at the very start
 * Chapter 2 We cannot advance into modelling without some prior knowledge about what it is that we are trying to model - the atoms of the system, as it were. Hence next chapter has to be to introduce data types
 * Now we can introduce modelling. There are two distinct parts to this
 * What is a statistical model (examples, etc.)
 * How can we come up with statistical models
 * What order should these be done in? On this principle that it is useful to have an example in one's mind when discussing a topic, (1) has been taken first. Hence
 * Chapter 3 Statistical models
 * Chapter 4 IDA/EDA data exploration

Conventions for markup used in this book
Some general suggestions for formatting. Are these sensible?

 * Variables in italics.
 * Factor levels in 'single quotes' (reserve double quotes for clarifying prose)
 * Topic boxes
 * No R code outside topic boxes
 * R code that is interspersed with discussion text within a topic box should be on its own line with an indent, to give <pre>-type formatting
 * Named R objects in discussion text should be surrounded by <code> tags. Functions should have braces.
 * Headings etc
 * TOC on each page shows header levels down to h4 (but not h5 or h6)
 * Main text uses header levels h2, h3, and h4.
 * Figures and tables labelled with <h5> (so they are not put in the TOC)
 * Topic boxes are titled using <h4>-level tags (to be included in the TOC)


text:
Statistical Analysis: an Introduction using R/Chapter 2

Data is the life blood of statistical analysis. A recurring theme in this book is that most analysis consists of constructing sensible statistical models to explain the data that has been observed. This requires a clear understanding of the data and where it came from. It is therefore important to know the different types of data that are likely to be encountered. Thus in this chapter we focus on different types of data, including simple ways in which they can be examined, and how data can organised into coherent datasets.

Variables
The simplest sort of data is just a collection of measurements, each measurement being a single "data point". In statistics, a collection of single measurements of the same sort is commonly known as a variable, and these are often given a name. Variables usually have a reasonable amount of background context associated with them: what the measurements represent, why and how they were collected, whether there are any known omissions or exceptional points, and so forth. Knowing or finding out this associated information is an essential part of any analysis, along with examination of the variables (e.g. by plotting or other means).

Measurement values
One important feature of any variable is the values it is allowed to have. For example, a variable such as sex can only take a limited number of values ('Male' and 'Female' in this instance), whereas a variable such as humanHeight can take any numerical value between about 0 and 3 metres. This is the sort of obvious background information that cannot necessarily be inferred from the data, but which can be vital for analysis. Only a limited amount of this information is usually fed directly into statistical analysis software. As always, it's very important to take account of such background information. This can be usually done using that commodity - unavailable to a computer - known as common sense. For example, a computer could be used to perform an analysis of human height without realising that one person has been recorded as (say) 175, rather than 1.75, metres tall. A computer can blindly perform analysis on this variable without noticing the error, even though it is glaringly obvious to a human. That's one of the primary reasons that it is important to plot data before analysis.

Categorical versus quantitative variables
Nevertheless, a few bits of information about a variable can (indeed, often must) be given to analysis software. Nearly all statistical software packages require you, at a minimum, to distinguish between categorical variables (e.g. sex) in which each data point takes one of a fixed number of pre-defined "levels", and quantitative variables (e.g. humanHeight) in which each data point is a number on a well-defined scale. Further examples are given in Table 2.1. This distinction is important even for such simple analyses as taking an average: a procedure which is meaningful for a quantitative variable, but rarely for a categorical variable (what is the "average" sex of a 'male' and a 'female'?).

It is not always immediately obvious from the plain data whether a variable is categorical or quantitative: often this judgement must be made by careful consideration of the context of the data. For example, a variable containing numbers 1, 2, and 3 might seem to be a numerical quantity, but it could just as easily be a categorical variable describing (say) a medical treatment using either drug 1, drug 2, or drug 3. More rarely, a seemingly categorical variable such as colour (levels 'blue', 'green', 'yellow', 'red') might be better represented as a numerical quantity such as the wavelength of light emitted in an experiment. Again, it's your job to make this sort of judgement, on the basis of what you are trying to do.

Borderline categorical/quantitative variables
Despite the importance of the categorical/quantitative distinction (and its prominence in many textbooks), reality is not always so clear-cut. It can sometimes be reasonable to treat categorical variables as quantitative, or vice versa. Perhaps the commonest case is when the levels of a categorical variable seem to have a natural order, such as the class variable in Table 2.1, or the Likert scale often used in questionnaires.

In rare and specific circumstances, and depending on the nature of the question being asked, there may be rough numerical values that can be allocated to each level. For example, maybe a survey question is accompanied by a visual scale on which the Likert categories are marked, from 'absolutely agree' to 'absolutely disagree'. In this case it may be justifiable to convert the categorical variable straight into to a quantitative one.

More commonly, the order of levels is known, but exact values cannot be generally agreed upon. Such categorical variables can be described as ordinal or ranked, as opposed ones such as gender or professedReligion which are purely nominal. Hence we can recognise two major types of categorical variable: ordered ("ordinal") and unordered ("nominal"), as illustrated by the two examples in Table 2.1.

Classification of quantitative variables
Although the categorical/quantitative division is the most important one, we can further subdivide each type (as we have already seen when discussing categorical variables). The most commonly taught classification is due to Stevens (1946). As well as dividing categorical variables into ordinal and nominal types, he classified quantitative variables into two types, interval or ratio, depending on the nature of the scale that was used. To this classification can be added circular variables. Hence classifying quantitative variables on the basis of the measurement scale leads to three subdivision (as illustrated by the subdivisions in Table 2.1):
 * Ratio data is the most commonly encountered. Examples include distances, lengths of time, numbers of items, etc. These variables are measured on a scale with a natural zero point; because we can work with exclusively positive integers.
 * Interval data is measured on a scale where there is no natural zero point. The most common examples are temperature (in degrees Centigrade or Fahrenheit) and calendar date. Since the zero point on the scale is essentially arbitrary, The name comes from the fact that while ratios are not meaningful, intervals are. E.g. means that ****
 * Circular data is measured on a scale which "wraps around", such as Direction, TimeOfDay, Logitude etc. ***

The Stevens classification is not the only way to categorise quantitative variables. Another sensible division recognises the difference between continuous and discrete measurements. Specifically, quantitative variables can represent either In practice, discrete data are often treated as continuous, especially when the units into which they are divided are relatively small. For example, the population size of different countries is theoretically discrete (you can't have half a person), but the values are so huge that it may be reasonable to treat such data as continuous. However, for small values, such as the number of people in a household, the data are rather "granular", and the discrete nature of values becomes very apparent. One common result of this is the presence of multiple repeated values (e.g. there will be a lot of 2 person households in most data sets).
 * Continuous data, in which it makes sense to talk about intermediate values (e.g. 1.2 hours, 12.5%, etc.). This includes cases where data have been rounded ***.
 * "Discrete data", where intermediate values are nonsensical (e.g. doesn't make much sense to talk about 1.2 deaths, or 2.6 cancer cases in a group of 10 people). Often these are counts of things: this is sometime known as meristic data.

A third way of classifying quantitative variables depends on whether the scale has upper or lower bounds, or even both.
 * bounded at one end (e.g. landArea cannot be below 0),
 * at both ends (e.g. percentages cannot be less then 0 or greater than 100). Also see censored data ***
 * unbounded (weightLoss).

Most important is circular - often requires very different analytical tools. Often best to make linear in some way (e.g. difference from a fixed direction).

Interval data cannot use ratios (division). Rather rare

Bounds: very common to have lower bound. Unusual to have only an upper bound. Both often indicates a percentage. - often treated by transformation (e.g. log)

Count data: if multiple identical values, can affect plotting etc. If true independent counts, indicates error function.

The distinctions between the different types of variables are summarised in Figure ***. Note that it is also common to

Independence of data points
Does the actual value cause correllations in "surrounding" values (e.g. time series), or do both reflect some common association (e.g. blocks/heterogeneity).

Time series Spatial data Blocks

Incorporating information
Time series, other sources of non-independence

Visualising a single variable
Before carrying out a formal analysis, you should always perform an Initial Data Analysis, part of which is to inspect the variables that are to be analysed. If there are only a few data points, the numbers can be scanned by eye, but normally it is easier to inspect data by plotting.

Scatter plots, such as those in Chapter 1, are perhaps the most familiar sort of plot, and are useful for showing patterns of association between two variables. These are discussed later in this chapter, but in this section we first examine the various ways of visualising a single variable.

Plots of a single variable, or univariate plots are particularly used to explore the distribution of a variable; that is its shape and position. Apart from initial inspection of data, one very common use of these plots is to look at the residuals (see Figure 1.2): the unexplained part of the data that remains after fitting a statistical model. Assumptions about the distribution of these residuals are often checked by plotting them.

The plots which follow illustrate a few of the more common types of univariate plot. The classic text is Tufte (cite: the visual display of quantitative information).

Categorical variables
For categorical variables, the choice of plots is quite simple. The most basic plots simply involve counting up the data points at each level.

Figure 2.1(a) displays these counts as a bar chart; another possibility is to use points as in Figure 2.1(b). In the case of gender, the order of the levels is not important: either 'male' or 'female' could come first. In the case of class, the natural order of the levels is used in the plot. In the extreme case, where intermediate levels might be meaningful, or where you wish to emphasise the pattern between levels, it may be reasonable to connect points by lines. For illustrative purposes, this has been done in Figure 2.1(b), although the reader may question whether it is appropriate in this instance. plot(1:length(Gender), Gender, yaxs="n"); axis(2, 1:2, levels(Gender), las=1) In some cases we may be interested in the actual sequence of data points. This is particularly so for time series data, but may also be relevant elsewhere. For instance, in the case of gender, the data was recorded in the order that each child was born. If we think that the preceeding birth influences the following birth (unlikely in this case, but just within the realm of possibility if pheremones are involved), then we might want to do Symbol-by-Symbol plot. If we are looking for associations with time, however, then a bivariate plot may be more appropriate ***, or there are particular features of the data that we are interested in (e.g. repeat rate), then other possibilities exist (doi:10.1016/j.stamet.2007.05.001).See chapter on time series

Quantitative variables
A quantitative variable can be plotted in many more ways than a categorical variable. Some of the most common single-variable plots are discussed below, using the land area of the 50 US states as our example of a continuous variable, and a famous data set of the number of deaths by horse kick as our example of a discrete variable. These data are tabulated in Tables 2.2 and 2.3

Some sorts of data consist of many data points with identical values. This is particularly true for count data where there are low numbers of counts (e.g. number of offspring).

There are 3 things we might want to look for in these sorts of plots
 * points that seem extreme in some way (these are known as outliers). Outliers often reveal mistakes in data collection, and even if they don't, they can have a disproportionate effect on further analysis. If it turns out that they aren't due to an obvious mistake, one option is to remove them from the analysis, but this causes problems of its own/
 * shape & position of the distribution (e.g. normal, bimodal, etc.)
 * similarity to known distributions (QQ)

We'll keep the focus mostly on the variable "landArea" ***

The simplest way to represent quantitative data is to plot the points on a line, as in Figure 2.3(a). This is often called a 'dot plot, although this is also sometimes used to describe a number of other types of plot (e.g. Figure 2.7). To avoid confusion, it may be best to call it a one-dimensional scatterplot. As well as simplicity, there are two advantages to a 1D scatterplot
 * 1) All the information present in the data is retained.
 * 2) Outliers are easily identified. Indeed, it is often useful to be able to identify which data points are outliers. Some software packages allow you to identify points interactively (e.g. by clicking points on the plot). Otherwise, points can be labelled, as has been done for some outlying points in Figure 2.3a.

One dimensional scatterplots do not work so well for large datasets. Figure 2.3(a) consists of only 50 points. Even so, it is difficult to get an overall impression of the data, to (as the saying goes) "see the wood for the trees". This is partly because some points lie almost on top of each other, but also because of the sheer number of closely placed points. It is often the case that features of the data are best explored by summarising it in some way.

Figure 2.3(b) shows a step on the way to a better plot. To alleviate the problem of points obscuring each other, they have been displaced, or jittered sideways by a small, random amount. More importantly, the data have been summarised by dividing into quartiles (and coloured accordingly, for ease of explanation). The quarter of states with the largest area have been coloured red. The smallest quarter of states have been coloured green.

More generally, we can talk about the quantiles of our data. The red line represents the 75% quantile: 75% of the points lie below it. The green line represents the 25% quantile: 25% of the points lie below it. The distance between these lines is known as the Interquartile Range (IQR), and is a measure of the spread of the data. The thick black line has a special name: the median. It marks the middle of the data, the 50% quantile: 50% of the points lie above, and 50% lie below. A major advantage of quantiles over other summary measures is that they are relatively insensitive to outliers, or changes in scale ****.

Figure 2.3(c) is a coloured version of a widely used statistical summary plot: the boxplot. Here it has been coloured to show the correspondence to Figure 2.3(b). The box marks the quartiles of the data, with the median marked within the box. If the median is not positioned centrally within the box, this is often an indicator that the data are skewed in some way. The lines on either side of the box are known as "whiskers", and summarise the data which lies outside of the upper and lower quartiles. In this case, the whiskers have simply been extended to the maximum and minimum observed values.

Figure 2.3(d) is a more sophisticated boxplot of the same data. Here, notches have been drawn on the box: these are useful for comparing the medians in different boxplots. The whiskers have been shortened so that they do not include points considered as outliers. There are various ways of defining these outliers automatically. This figure is based on a convention that considers outlying points as those more than one and a half times the IQR from either side of the box. However it is often more informative to identify and inspect interesting points (including outliers) by visual inspection. For example, in Figure 2.1a it is clear that Alaska and (to a lesser extent) Texas are unusually large states, but that California (identified as an outlier by this automatic procedure) is not so set-apart from the rest.

One problem with plotting on a single line is that, if points are repeated, there ***. This is particularly problematic for discrete data. NB, there is no particular reason (or established convention) for these plots to be vertical. Figure 2.2 shows. The stacked plot (Figure 2.4d) is similar to a histogram (Figure 2.5).

This gives another way of picturing the median & other quantiles: as dividing the area into sections ***

We can space out the points along the other axis. For example, if the order of points in the dataset is meaningful, we can just plot each point in turn. This is true for whatsit's horse-kick data. The data by year are plotted in Figure 2.6.

One thing we can always do is to sort the data points by their value, plotting the smallest first, etc. This is seen in Figure 2.3b. If all the data points were equally spaced (and excluded each other****), we would see a straight line. The plot for the logged variables shows that this transformation has evened out the spacing somewhat. This is called a quantile plot, for the following reason

when the axes are swapped, this is called the empirical cumulative distribution function. The unswapped data is useful for understanding qq plots. Also for understanding quantiles. median, etc.

Transformations
We could put a scale break in, but a better option is usually to transform the variable.

Sometimes, plotting on a different scale (e.g. a logarithmic scale) can be more informative. We can visualise this either as a plot with a non-linear (e.g. logarithmic) axis, or as a conventional plot of a transformed variable (e.g. a plot of log(my.variable) on a standard, linear axis). Figure 2.1(b) illustrates this point: the left axis marks the state areas, the right axis marks the logarithm of the state areas. This sort of rescaling can highlight quite different features of a variable. In this case, it seems clear that there are a batch of nine states which seem distinctly smaller than most, and while Alaska still seems extraordinarily large, Texas does not seem so unusual in that respect. This is also reflected by the automatic labelling of outliers in the log-transformed variable.

It is particularly common for smaller numbers to have greater resolution. As discussed in later chapters ***, logarithmic scales are particularly useful for multiplicative data ***.

There are other common transformations, for example, the square-root transformation (often used for count data). This may be more appropriate for state areas, if the limiting factor for state size is (e.g.) the distance across the state, or factors associated with it (e.g. the length of time to cross from one side to another). Figure 2.1c shows a sqrt rescaling of the data. You can see that in some sense this is less extreme than the log transformation...

Datasets
Multiple variables in a table. Notation. most packages do this.

 * Statistical_Analysis:_an_Introduction_using_R/R/Data frames

 * Statistical_Analysis:_an_Introduction_using_R/R/Reading in data

Quantitative versus quantitative
Scatter plots problems with overplotting? Sunflowerplots etc.

Quantitative versus categorical
Vioplots (&boxplots)

Categorical versus categorical
Mosaicplots

 * Statistical_Analysis:_an_Introduction_using_R/R/Bivariate plots


text:
User talk:BadgerOfDarkness

Hello, and welcome to Wikibooks!

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Good luck! -- Herby talk thyme 13:02, 15 May 2007 (UTC)

title: User talk:BadgerOfDarkness


text:
User talk:Lithran

Nuclear war as an example?
Sounds good to me. I've added it to the contents page. Should be an interesting addition to the book. --AdRiley 15:19, 15 May 2007 (UTC)

title: User talk:Lithran


text:
User:Lithran

This will be updated soon

title: User:Lithran


text:
User:Camila PrincessXOXO

Hi.I'm writing an article on how to write a good book for children.Hope the techniques and stuff I say helps you to write a great and interresting book for children!

title: User:Camila PrincessXOXO


text:
User talk:Coolgirl3000

hello

Hello, welcome to Wikibooks!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add this page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck! -- Herby talk thyme 12:44, 26 May 2007 (UTC)

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 12:44, 26 May 2007 (UTC)

title: User talk:Coolgirl3000


text:
User talk:Sunshine 12

HI SYD WAT IS UP!!! OMG!!!! HIHI

 * --LRainbowz,x 13:30, 15 May 2007 (UTC)

title: User talk:Sunshine 12


text:
User:Starz11

hi, how are you gO AWAY--98.223.85.20 (discuss) 22:33, 2 December 2012 (UTC)UR UGLY

title: User:Starz11


text:
User:Whiteknight/Book

This template is used for displaying the name of a book, all relevant links, and transcluding the Notes page for that book. This is mostly used at User:Whiteknight/All Books.

This template makes heavy use of ParserFunctions, and may only be transcluded into one of my user pages. Attempts to edit this template by other people besides myself will likely be reverted. Plus, this template is very complex and convoluted, so any attempts to edit it will probably fail. I can't even do it right every time, and I know what's supposed to be happening.

 * Parameters:
 * 1: Name of the book
 * title: Alternative name of the book, if it should be displayed differently from how the various pages are named.
 * code: The status code of the book.
 * pc: Alternative name of the personal collection, if any
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 * state: the state of the book on a sliding scale: bad, stub, expand, revise, review, candidate, featured.

title: User:Whiteknight/Book


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User:Tigerpeach

Hey! It's me, Tigerpeach! I haven't been here for a long time! Leave a message after the smiley face! :)

title: User:Tigerpeach


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User:Milkyway 120

hey!! Me and my class is woking on a project called "how to write a good book for children"

title: User:Milkyway 120


text:
User:DragonRider~enwikibooks

A good book for kids

 * Relations to children
 * Interesting, but true facts
 * Use Pictures children can relate to
 * Use bold letters so children can read

By the way i am a student in grade 6 writing a good book for children... Thanks for reading

title: User:DragonRider~enwikibooks


text:
User:Whiteknight/Notes

This page is going to serve as a hub for my layout and design notes on various books. Notes are all transcluded into my Book Foundry.

title: User:Whiteknight/Notes


text:
User:Whiteknight/Notes/Circuit Theory

< Book Foundry — All Books
 * 9 November 2008:Expand to include 3-phase systems. Create and include more images, integrate images better into the text. General Expansion and Cleanup, especially of later chapters.
 * 24 December 2004:Reviewed all existing pages.

title: User:Whiteknight/Notes/Circuit Theory


text:
User:Whiteknight/Notes/Communication Systems

Book Foundry | All Books
 * 9 Nov 2008: User:Jugandi appears to have done a lot of work on this book recently. Some chapters need expansion, but many are in very good condition. Needs a public collection and maybe a PDF version.
 * 24 December 2008: Reviewed all pages in this book. Downgraded from review to expand considering the number of stubbish pages in the book. Needs serious formatting help too.


text:
User:Whiteknight/Notes/Control Systems

< Book Foundry — Dormant Books
 * 9 Nov 2008:Rename the "System Identification" chapter to a new name (it doesnt strictly deal with "system identification"), and create a new page about system identification. Expand later chapters and units. Verify the public collection is good, and all templates render correctly.
 * 15 December 2008: Reviewed all existing pages

title: User:Whiteknight/Notes/Control Systems


text:
User:Whiteknight/Notes/Electrodynamics

< Book Foundry | All Books
 * 19 November 2008: TOC is only about half full with existing pages. Most pages are stubby and need more content. Needs more images, and better integration of existing images. Mostly, needs to be adopted by an active author.

title: User:Whiteknight/Notes/Electrodynamics


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User:Whiteknight/Book2

This template is used to display a link to a book and all relevant pages inline with other text. Does not transclude any information, and does not create edit links. Books that currently exist are displayed in bold, books that do not yet exist are displayed in italics. This template makes heavy use of ParserFunctions, and may not be transcluded into any page out side of my user namespace.

title: User:Whiteknight/Book2


text:
User:Whiteknight/Notes/Microprocessor Design

< Book Foundry | All Books
 * 4 December 2008:TOC is mostly filled-out, but many pages need more content. There are lots of images that aren't integrated into the text well enough, and more images can probably be found on commons. Mostly just needs content expansion.
 * 29 December 2008:Started reviewing pages in this book. Am dropping it down from "Review" to "Expand" state considering the large number of stubbish pages in the book.
 * 02 January 2008:Finished reviewing pages.


text:
User:Whiteknight/Notes/The Scientific Method

< Book Foundry | All Books
 * 12 December 2008:Book is a stub, many pages have zero content. Needs massive expansion.


text:
Horticulture/Erigeron

Erigeron (syn. Stenactis) is a genus of about 200 species of flowering plants in the family Asteraceae. The genus has a cosmopolitan distribution with the highest species diversity in North America.

The most widely used common name, fleabane, is shared with related plants in several other genera; another common name is summer starwort. The common name is derived from the belief that the dried plants repelled fleas.

Many species are used as ornamental plants, with numerous named cultivars such as 'Wayne Roderick', 'Charity', 'Dunkelste Aller' and 'Foersters Liebling'.

Description
The species are annuals, biennials or perennials. They are well-branched plants with erect stems, characterized by their numerous white, lavender or pink ray flowers and yellow disc flowers. Some members of this group have no ray flowers. The pappus (= modified calyx, forming a crown) is shorter than in Aster, and consists of bristles. The ray florets are narrower than in Aster, but are clearly longer than the involucre (= whorled bracts).

Pests and diseases
Bucculatrix angustata, Coleophora squamosella (which feeds exclusively on E. acris), Schinia intermontana, Schinia obscurata (both of which also feed exclusively on Erigeron), Schinia sexata (which feeds exclusively on E. glabellus) and Schinia villosa.

title: Horticulture/Erigeron


text:
Talk:Horticulture/Erigeron

Wikipedian species list

 * Erigeron abajoensis - Abajo fleabane
 * Erigeron accedens
 * Erigeron acer (syn. E. acris) : Blue Fleabane
 * Erigeron acomanus - Bluewater Fleabane
 * Erigeron acutatus
 * Erigeron aequifolius - Hall's Fleabane, Hall's Daisy
 * Erigeron alaskanus
 * Erigeron alcicornutus
 * Erigeron algidus - Stalked Fleabane
 * Erigeron aliceae - Alice Eastwood's Fleabane
 * Erigeron allocotus - Big Horn Fleabane
 * Erigeron alpinus - Alpine Erigeron
 * Erigeron anchana - Sierra Ancha Fleabane
 * Erigeron angustatus
 * Erigeron annuus - Eastern Daisy Fleabane
 * Erigeron aphanactis - Rayless Shaggy Fleabane
 * Erigeron aphanactis var. aphanactis
 * Erigeron aphanactis var. congestus
 * Erigeron arenarioides - Sand Fleabane
 * Erigeron argentatus - Silver Fleabane
 * Erigeron arisolius - Arid Throne Fleabane
 * Erigeron arizonicus - Arizona Fleabane
 * Erigeron asperugineus - Idaho Fleabane
 * Erigeron atticus
 * Erigeron aurantiacus - Orange Daisy
 * Erigeron aureus - Alpine Yellow Fleabane
 * Erigeron austiniae
 * Erigeron awapensis - Awapa Fleabane
 * Erigeron barbellatus - Shining Fleabane
 * Erigeron basalticus - Basalt Fleabane
 * Erigeron bellidiastrum - Western Daisy Fleabane
 * Erigeron bellidiastrum var. arenarius
 * Erigeron bellidiastrum var. bellidiastrum
 * Erigeron bellidiastrum var. robustus
 * Erigeron bellioides
 * Erigeron bigelovii - Bigelow's Fleabane
 * Erigeron biolettii - Biolett's Erigeron
 * Erigeron bistiensis
 * Erigeron blochmaniae - Blochman's Erigeron
 * Erigeron bloomeri - Scabland Fleabane
 * Erigeron bloomeri var. blloomeri
 * Erigeron bloomeri var. nudatus
 * Erigeron bloomeri var. pubens
 * Erigeron borealis - Alpine Fleabane
 * Erigeron breweri - Brewer's Fleabane
 * Erigeron breweri var. bisanctus
 * Erigeron breweri var. breweri
 * Erigeron breweri var. covilei
 * Erigeron breweri var. jacinteus
 * Erigeron breweri var. klamathensis
 * Erigeron breweri var. porphyreticus
 * Erigeron caespitosus (syn. E. hyperboreus) - Tufted Fleabane
 * Erigeron calvus
 * Erigeron canus - Hoary Fleabane
 * Erigeron cascadensis - Cascade Fleabane
 * Erigeron caucasicus
 * Erigeron cervinus - Siskiyou Fleabane
 * Erigeron chrysopsidis - Dwarf Yellow Fleabane, Golden Daisy/Fleabane (yellow ray flowers).
 * Erigeron cinereus
 * Erigeron clokeyi - Clokey's Fleabane
 * Erigeron colomexicanus - Running Fleabane
 * Erigeron compactus - Fern-leaf Fleabane
 * Erigeron compositus - Cut-leaf Fleabane, Dwarf Mountain Fleabane (with or without ray flowers)
 * Erigeron concinnus - Navajo Fleabane
 * Erigeron concinnus var. concinnus
 * Erigeron concinnus var. condensatus
 * Erigeron concinnus var. subglaber
 * Erigeron consimilis - Foothill Fleabane
 * Erigeron corymbosus - Long-leaf Fleabane
 * Erigeron coulteri - Large Mountain Fleabane
 * Erigeron cronquistii - Cronquist's Fleabane
 * Erigeron cuneifolius - Wedge-leaf Fleabane
 * Erigeron decumbens - Willamette Fleabane
 * Erigeron decumbens var. decumbens
 * Erigeron decumbens var. robustior
 * Erigeron delicatus
 * Erigeron delphinifolius
 * Erigeron disparipilus - White Cushion Fleabane
 * Erigeron divergens - Spreading Fleabane
 * Erigeron eatonii - Eaton's Fleabane
 * Erigeron eatonii var. eatonii
 * Erigeron eatonii var. lavandulus
 * Erigeron eatonii var. nevandicola
 * Erigeron eatonii var. plantagineus
 * Erigeron eatonii var. sonnei
 * Erigeron eatonii var. villosus
 * Erigeron elatior - Tall Fleabane
 * Erigeron elatus
 * Erigeron elegantulus - Blue Dwarf Fleabane.
 * Erigeron elmeri
 * Erigeron engelmannii - Engelmann's Fleabane
 * Erigeron engelmannii var. davisii
 * Erigeron engelmannii var. engelmannii
 * Erigeron evermannii - Evermann's Fleabane
 * Erigeron eximius - Spruce-fir Fleabane
 * Erigeron filifolius - Thread-leaf Fleabane.
 * Erigeron filifolius var. filifolius
 * Erigeron filifolius var. robustior
 * Erigeron filifolius var. typicus
 * Erigeron flabellifolius - Fan-leaf Fleabane.
 * Erigeron flagellaris - Trailing Fleabane
 * Erigeron flettii - Flett's Fleabane
 * Erigeron foliosus - Leafy Fleabane
 * Erigeron foliosus var. confinis
 * Erigeron foliosus var. foliosus
 * Erigeron foliosus var. franciscensis
 * Erigeron foliosus var. mendocinus
 * Erigeron foliosus var. hartwegii
 * Erigeron formosissimus - Beautiful Fleabane
 * Erigeron formosissimus var. formosissimus
 * Erigeron formosissimus var. viscidus
 * Erigeron fragilis
 * Erigeron frigidus
 * Erigeron frondeus
 * Erigeron fruticetorum
 * Erigeron fuertesii
 * Erigeron furcatus
 * Erigeron garrettii - Garrett's Fleabane
 * Erigeron geiseri - Geiser's Fleabane
 * Erigeron glabellus - Streamside Fleabane
 * Erigeron glabellus var. glabellus
 * Erigeron glabellus var. pubescens
 * Erigeron glabratus
 * Erigeron glaucus - Beach Aster, Beach Daisy, Seaside Daisy
 * Erigeron goodrichii - Uinta Mountain Fleabane
 * Erigeron gracilis - Quill Fleabane
 * Erigeron grandiflorus - Large-flower Fleabane
 * Erigeron grandiflorus var. arcticus
 * Erigeron grandiflorus var. grandiflorus
 * Erigeron heliographis - Heliograph Peak Fleabane
 * Erigeron hessii - Hess' Fleabane
 * Erigeron howellii - Howell's Fleabane
 * Erigeron hultenii - Hulten's Fleabane
 * Erigeron humilis - Arctic-alpine Fleabane
 * Erigeron hybridus
 * Erigeron hyssopifolius - Hyssop-leaf Fleabane.
 * Erigeron inornatus - California Rayless Fleabane.
 * Erigeron inornatus var. calidipetris
 * Erigeron inornatus var. inornatus
 * Erigeron inornatus var. keilii
 * Erigeron jamaicensis - Jamaica Fleabane
 * Erigeron jonesii - Jones' Fleabane
 * Erigeron kachinensis - Kachina Fleabane
 * Erigeron karvinskianus - Latin American Fleabane
 * Erigeron kuschei - Chiricahua Fleabane
 * Erigeron lackschewitzii
 * Erigeron lanatus - Woolly Fleaban
 * Erigeron lassenianus - Mt. Lassen Fleabane
 * Erigeron lassenianus var. deficiens
 * Erigeron lassenianus var. lassenianus
 * Erigeron latus - Broad Fleabane
 * Erigeron leibergii - Leiberg's Fleabane
 * Erigeron leiomerus - Rockslide Yellow Fleabane
 * Erigeron lemmonii - Lemmon's Fleabane
 * Erigeron linearis - Desert Yellow Fleabane
 * Erigeron lobatus - Lobed Fleabane
 * Erigeron lonchophyllus
 * Erigeron maguirei - Maguire's Fleabane
 * Erigeron mairei - Atlas Mountains Fleabane
 * Erigeron mancus - Depauperate Fleabane
 * Erigeron mariposanus
 * Erigeron melanocephalus - Black-head Fleabane
 * Erigeron mexiae - Mex's Fleabane
 * Erigeron miser - Starved Fleabane
 * Erigeron miyabeanus - Japanese Fleabane
 * Erigeron modestus - Plains Fleabane
 * Erigeron muirii - Muir's Fleabane
 * Erigeron multiceps - Kern River Fleabane
 * Erigeron multiradiatus - Himalayan Fleabane
 * Erigeron myosotis
 * Erigeron nanus - Dwarf Fleabane
 * Erigeron nauseosus - Marysvale Fleabane
 * Erigeron neglectus
 * Erigeron nematophyllus - Needle-leaf Fleabane
 * Erigeron neomexicanus - New Mexico Fleabane
 * Erigeron ochroleucus - Buff Fleabane
 * Erigeron ochroleucus var. ochroleucus
 * Erigeron ochroleucus var. scribneri
 * Erigeron oharai
 * Erigeron oreganus - Gorge Fleabane
 * Erigeron oreophilus - Chaparral Fleabane
 * Erigeron ovinus - Sheep Fleabane
 * Erigeron oxyphyllus - Wand Fleabane
 * Erigeron parishii - Parish's Fleabane
 * Erigeron peregrinus - Wandering Fleabane, Subalpine Fleabane, Foreign Fleabane
 * Erigeron peregrinus subsp. callianthemus
 * Erigeron peregrinus subsp. peregrinus
 * Erigeron petrophilus - Cliff Fleabane, Rock daisy (no ray flowers)
 * Erigeron petrophilus var. petrophilus
 * Erigeron petrophilus var. sierrensis
 * Erigeron petrophilus var. viscidulus
 * Erigeron philadelphicus - Philadelphia Fleabane/Daisy
 * Erigeron philadelphicus var. philadelphicus
 * Erigeron philadelphicus var. provancheri
 * Erigeron pinnatisectus - Feather-leaf Fleabane
 * Erigeron piperianus - Piper's Fleabane
 * Erigeron piscaticus - Fish Creek Fleabane
 * Erigeron poliospermus - Purple Cushion Fleabane
 * Erigeron poliospermus var. cereus
 * Erigeron poliospermus var. poliospermus
 * Erigeron pringlei - Pringle's Fleabane
 * Erigeron procumbens - Corpus Christi Fleabane
 * Erigeron proselyticus - Professor's Fleabane
 * Erigeron pubescens - Hairy Fleabane
 * Erigeron pulchellus - Robin's Plantain
 * Erigeron pulchellus var. brauniae
 * Erigeron pulchellus var. pulchellus
 * Erigeron pulchellus var; tolsteadii
 * Erigeron pulcherrimus - Basin Fleabane
 * Erigeron pumilus - Shaggy Fleabane
 * Erigeron pumilus ssp. intermedius
 * Erigeron pumilus var. pumilus
 * Erigeron purpuratus - Purple Fleabane
 * Erigeron pygmaeus - Pygmy Fleabane
 * Erigeron quercifolius - Oak-leaf Fleabane
 * Erigeron radicatus - Tap-root Fleabane
 * Erigeron reductus
 * Erigeron reductus var. angustatus
 * Erigeron reductus var. reductus
 * Erigeron religiosus - Clear Creek Fleabane
 * Erigeron rhizomatous - Rhizome Fleabane
 * Erigeron roylei - Royle's Fleabane
 * Erigeron rybius - Royal Fleabane
 * Erigeron rydbergii - Rydberg's Fleabane
 * Erigeron salishii - Star Peak Fleabane
 * Erigeron salmonensis - Salmon River Fleabane
 * Erigeron sanctarum - Saints Fleabane
 * Erigeron saxatilis - Rock Fleabane
 * Erigeron sceptrifer - Scepter-bearing Fleabane
 * Erigeron scopulinus - Winn Falls Fleabane
 * Erigeron serpentinus
 * Erigeron simplex - One-stem Fleabane
 * Erigeron sionis - Zion Fleabane
 * Erigeron sivinskii
 * Erigeron speciosus - Aspen Fleabane
 * Erigeron speciosus var. macranthus
 * Erigeron speciosus var. speciosus
 * Erigeron strigosus - Prairie Fleabane
 * Erigeron strigosus var. beyrichii
 * Erigeron strigosus var. septentrionalis
 * Erigeron strigosus var. strigosus
 * Erigeron subglaber - Hairless Fleabane
 * Erigeron subtrinervis - Three-nerve Fleabane
 * Erigeron subtrinervis var. conspicuus
 * Erigeron subtrinervis var. trinervis
 * Erigeron supplex - Supple Fleabane
 * Erigeron tenellus - Rio Grande Fleabane
 * Erigeron tener - Slender Fleabane
 * Erigeron tenuis - Slender-leaf Fleabane
 * Erigeron thunbergii - Thunberg's Fleabane
 * Erigeron tweedyi - Tweedy's Fleabane
 * Erigeron uintahensis - Uinta Fleabane
 * Erigeron uncialis - Lone Fleabane
 * Erigeron uncialis subsp. conjugans
 * Erigeron uncialis subsp. uncialis
 * Erigeron uniflorus - One-flowered Fleabane
 * Erigeron untermannii - Indian Canyon Fleabane
 * Erigeron ursinus - Bear River Fleabane
 * Erigeron utahensis - Utah Fleabane
 * Erigeron utahensis var. sparsifolius
 * Erigeron utahensis var. utahensis
 * Erigeron vagus - Rambling Fleabane
 * Erigeron velutipes
 * Erigeron vernus - Early White-top Fleabane
 * Erigeron versicolor - Sonora Fleabane
 * Erigeron vetensis - Early Blue-top Fleabane
 * Erigeron vreelandii
 * Erigeron watsonii - Watson's Fleabane
 * Erigeron wilkenii - Wilken's Fleabane
 * Erigeron yukonensis - Yukon Fleabane
 * Erigeron zothecinus - Lake Powell Fleabane

title: Talk:Horticulture/Erigeron