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User:Thuvack/Quote Thuvack

'''Thank you for visiting my user page, I am known as Thuvack here at Wikiversity. This page holds some basic facts about me and my involvement with Wikiverstiy.' This Page/sub-page and all other pages related to me are part of Wikiversity and are released under GNU Licence''.

Who am I?
We are who we think we are, and hence what we let others perceive us as. I am simply Thuvack. I live and work in South Africa. I was born there and that I guess makes me South African. I am black and I speak Xitsonga/Shangaan. I am married to my beautiful wife and we have a lovely daughter and a handsome son.

Why I joined Wikiversity
It all started about the end of 2006, when I had just received my Varsity Results ( I had Failed! ). In my depression and anxiety I surfed the net for on-line courses in Electrical Engineering, that is when I stumbbled across Wikiversity ( The Free University! ). After following a link from the main page to the Engineering Portal, I got to The school of Electrical engineering. To my frustration the page was partly developed with a single department news that said: "Department started!".

I was disappointed to say the least, for I really hoped that I had finally found a place where I could supplement my studies. I did not visit Wikiversity for a while, yet at the same time at the back of my mind was an annoying little voice, that kept saying: The next student like you does not have to find such an empty department. It was not until 2007 March 9that I decided to create a Wikiversity account and signed myself up to participate in Developing The school of Electrical engineering.

The whole concerpt of a wiki became very daunting that I did a lot of mistakes at first only to come back the next day and find a fixed page that I thought I had messed-up and a kind remark on my talk page to take a basic wikiversity tour and help page on basics of wiki editing. After a few acceptable edits I disappeared after 2007 March 26 for about ±12months in 2007 due to the internet access policy at work. Things changed recently and I got my internet access back with Wikiversity as one of the accepted sites. I started being active again in 2008 March 31 .As they say the rest is history.

So in summary to this question: I joined Wikiversity to help improve the material/resource for the benefit of many.

What I hope to achieve with Wikiversity

I have come to understand and cherish the idea of Wikiversity and Open Learning as this seemed very much parallel to Open Source and Linux, and obviously appealing to me.

I hope to be part of this Learning Community for as long as I am able to make meaning full contributions. Little efforts stacked upon each other make a very huge difference. I guess I have been looking for something meaningful that I can get involved with and Wikiversity seems to have filled that void.

My Activist Affiliation:

 * Cape Town Open Education Declaration signatory

What is Open Source Software?
Open Source software, is software that is released complete with the source code. Why would anyone want to release a sofware program with its source code? well simply because the author realises that the more people there are working on the same software the greater the chances of the software being functional with minimum bugs in it. You can find more about this topic here.

Why I Started Using Linux

I got my first desktop computer when I started varsity some time ago. It was a PII with an Intel CPU. I had Windows 95 installed [ It was a gift from my sponsoring company ]. The computer kept crashing on me and was simply not adequate for my Varsity programing needs. Then One day when I went to do Student Vaccation work, I saw a similar PC used as the Internet and mail machine. It was running Open SuSe 9.4. I started wondering about this strange operating system.

I decided to read about it, and I found "The Cathedral and the Bazaar" by By Eric S. Raymond. It was very comprehensive and clarified most of my questions about this new animal Open Source Software called Linux. I requested a copy of SuSe 9.x and I loaded it in My PII at home and decided to test drive it on a dual boot mode. I have not looked back to this day.

My Distribution of Choice
I got myself a pre-owned Laptop early this year and I installed SuSe 10.1 and the 10.3 later. I am impressed at the economy of Linux and the efficiency and stability it affords me. By the way my laptop hardly crashes ever since I installed SuSe 10.3. I am patiently awaiting SuSe 11 and KDE4.

OS Information

Enjoy your day and I hope to see you around wikiversity! Thuvack

title: User:Thuvack/Quote Thuvack


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User:Thuvack/Contribute Thuvack

Here are some of the Courses I am Actively involved with.

 * EE-PRE: Electrical Engineering Orientation - ±70% [[Image:75%25.svg|20px|]]

 * Electric Circuit Analysis - completed! [[Image:Emblem-star.svg|20px|]]

 * Electrical Machines II - ±10% [[Image:SYawning.gif|20px|]]
 * Electrical Protection - ±10% [[Image:SYawning.gif|20px|]]

 * Generation of Electrical Power - ±70% [[Image:75%25.svg|20px|]]
 * Transmission of Electrical Power - ±10% [[Image:SYawning.gif|20px|]]
 * Distribution of Electrical Power - ±10% [[Image:SYawning.gif|20px|]]
 * Electrical Power Economics - ±10% [[Image:SYawning.gif|20px|]]

Books:

 * EE102-CIRCUIT ANALYSIS

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Thuvack/Contribute Thuvack


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User:Opensourcejunkie/home

Hey Nate, welcome to the internet! :-D Here's a few useful links for ya:
 * google
 * gmail
 * Wikipedia
 * Wikiversity
 * Your User Page
 * Your Talk Page

title: User:Opensourcejunkie/home


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User:Thuvack/Os-Thuvack

I am a Linux User for about two years now.  Unfortunately my company has'nt caught up as yet.  I'm sure they will as sure as the rest of the world  One day some day soon.
 * Desktop: KDE

title: User:Thuvack/Os-Thuvack


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User:Thuvack/Activist Thuvack

Project Task List.

 * EE-PRE :Engineering Orientation - List for Content Addition / Revamp

 * Do/Finish Lesson #1: Introduction to Electrical Engineering

 * Do/Finish Lesson #2: Introduction to Electronic Engineering

 * Do/Finish Quiz Test 1: Algebra and pre-calculus - ✅

 * Do/Finish Quiz Test 2: Geometry and data representation - ✅

 * Do/Finish Quiz Test 3: Physics Science laws  - ✅

 * Do/Finish Quiz Test 4: chemical Science Processes  - ✅

 * Do/Finish Entrance Courses: Introduction to Engineering Maths

 * EE ??? Electrical Machines II
 * Start Lesson Page Skeletons for Future developments - ✅

 * EE ??? Electrical Power Generation
 * Start Course Page Skeletons for Future developments - ✅
 * To merge with: Generation_of_Electrical_Power - ✅
 * Start Lesson Page Skeletons for Future developments

 * EE ??? Electrical Transmission
 * Start Course Page Skeletons for Future developments - ✅
 * To merge with: Transmission_and_Distribution_of_Electrical_Power - ✅
 * Start Lesson Page Skeletons for Future developments

 * EE ??? Electrical Distribution
 * Start Course Page Skeletons for Future developments - ✅
 * Start Lesson Page Skeletons for Future developments

 * EE ??? Electrical Protection
 * Start Course Page Skeletons for Future developments - ✅
 * To merge with: Protective Relays?
 * Start Lesson Page Skeletons for Future developments

 * EE ??? ELECTRICAL POWER ECONOMICS
 * Start Course Page Skeletons for Future developments - ✅
 * Start Lesson Page Skeletons for Future developments

Weekly Task List.

 * Start Topic in Wikiversity Qolloqium about proposed catergorisation in School and Departments (% system). - ✅

 * School of Electrical Engineering
 * Add catergorization to courses by completion status and Education level etc - ✅
 * Mark pages for deletion when updating page.

 * School of Electronic Engineering:
 * Create School page similar in style to School of Electrical Engineering.  - ✅

 * Edit School Intro page, by adding school emblem/logo: "The Digital Edge". - ✅

 * Create Selected Biography:- The three Gentlemen & the Transistor.  - ✅

 * Suggest Moving of requested courses to Department course wish list. - ✅

 * Start catergorization of courses in Department  - ✅

 * Create User Box: "This User contributes to the school of Electronic Engineering"  - ✅

 * My User Page.
 * Edit About me page: from Text  - ✅
 * Create and Edit Open Source Software & Me: from Text  - ✅
 * Use Top Text on all user pages  - ✅

 * My User Boxes.
 * Remove Male User Box and add Crontribute to school of Electronic Engineering  - ✅

 * Images:
 * Download image in Introduction Electrical Engineering for Editing with Gimp and for use in Transmission and Distribution course.  - ✅

title: User:Thuvack/Activist Thuvack


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Template:Content warning

Purpose
This template was designed to help demarcate potentially offensive material on Wikiversity. The template should be placed at the top of any page or section that contains such material, and should not be removed without ample discussion on the resource's talk page.

Usage
To use this template, place the following wiki code above the questionable material:

The template requires a single parameter - the group(s) who would be offended by the resource/section. Below is the result of the previous code:

title: Template:Content warning


text: Template:The Shootin Barnstar

title: Template:The Shootin Barnstar


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Template:Electrical engineering/RelatDep ELE

You will find that most topics in this Department are linked to the following Schools/Departments:

 * School of Electronic Engineering

 * School of Mathematics .

 * F ACULTY OF P HYSICAL S CIENCES .


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School:Electrical engineering/Projects ELE

Are you busy with some Electrical Engineering Project? List it here. More than one Wikiversity department can 'contain' (link to) the same learning project, As this encourages co-operation.

See: Learning Projects and the Learning model.

 * Design and implementation of PLC systems


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School:Electrical engineering/External ELE

 * How to build the 1000 dollar laser spectrograph.
 * 3D circuit animations very good for learning
 * MIT OpenCourseWare Electronics/Electrical Engineering section
 * Homebrew vacuum tubes
 * CHINA'S QUEST TO BUILD THE BIGGEST & TALLEST


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School:Electrical engineering/Files ELE

 * SPICE Schematics
 * SPICE Parts

title: School:Electrical engineering/Files ELE


text: School talk:Electrical engineering/box-header


text: School talk:Electrical engineering/box-footer


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File:ALE S-3.png

ALE image

title: File:ALE S-3.png


text: School:Electronic engineering/Disciplines ELEC


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South Africa Workshop for Social Entrepreneurship - 2008/Reflections/Community Site Visits - Bus 2

Bus 2 delivered two groups to two schools: Bokgoni Technical High School and Laerskool Die Heuwel...

Insights shared

 * The principal is the epitome of social entrepreneurship: achieving a significant impact in the community under challenging circumstances through determination and perseverance.
 * This does not match my idea of social entrepreneurship.


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School:Electronic engineering/External ELEC

 * A blog dedicated to introductory and advanced topics in digital electronics.
 * An excellent site for the introduction of electronics with an online book. It also includes a forum.


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School:Electronic engineering/Research ELEC

List Research Projects done by this school here.


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School:Electronic engineering/Projects ELEC

See: Learning Projects and the Learning model.

 * Design and implementation of PLC systems


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School:Electronic engineering/Files ELEC

 * SPICE Schematics
 * SPICE Parts


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School:Electronic engineering/RelatDep ELEC

 * School of Electrical Engineering.

 * School of Mathematics .

 * F ACULTY OF P HYSICAL S CIENCES .


text: File:SSE-DelegatesSpeedDating.jpg

title: File:SSE-DelegatesSpeedDating.jpg


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South Africa Workshop for Social Entrepreneurship - 2008/Reflections/Welcome Address

Ms Marjorie Pyoos, Group Executive – Socio-Economic partnerships, Department of Science and Technology:

Ms Pyoos put forward Government’s view on social entrepreneurship. Because Government is aware of the effects of social prejudice born as a result of poverty and lack of access to basic services, it is also acutely aware of the pressing need for social entrepreneurship within South African communities. Government has stated categorically that it is sincerely committed to achieving its millennium goals with positive results having been achieved in the areas of improved school nutrition schemes, basic infrastructure to poor communities, access to education and the lowering of child mortality rates.

However, Government is also aware that often the mechanisms it uses to devise and implement social programmes fail due to bureaucracy and a lack of funds.

The Complexity of Engaging with Society by Government:

Government is, by nature, a bureaucratic institution with high levels of accountability. It therefore requires that society itself be organised accordingly so that Government is able to interact with it. Society organises itself when its activities are geared toward a particular goal i.e. political change. However, communities only seem to mobilise their interaction with Government on social issues when a social entrepreneur takes up the baton of marshalling society into understanding its problems and then motivating Government for change or intervention.

The South African Government is willing to interact with communities and implement programmes to address social problems but it wants to be guided by successful examples. Recent Government initiatives, which have been used to address social change, have all but failed. Only one, the Expanded Public Works Programme (EPWP) has had an impact on communities by providing labour-intensive work opportunities to local communities but once the work is complete the questions remain: “What then….?” “What now…?”

Whilst government is willing to devise and implement programmes geared to addressing society’s problems, society must in turn examine how it uses available resources. Whilst government has committed itself to ensuring better access to clean water, sanitation and housing, society in return must ensure a more responsible attitude towards the use of these resources. Additionally, Government has realised the value of traditional knowledge, particularly in the area of rural health care where traditional medicine has, in the main, been the first choice of rural dwellers when treating basic illnesses. Government is actively engaged in harnessing traditional knowledge across a variety of community activities. This knowledge is being nurtured and harvested to empower communities to find solutions to their particular social problems.

“Rather than leaving societal needs to the government or business sectors, social entrepreneurs find what is not working and solve the problem by changing the system, spreading the solution, and persuading entire societies to take new leaps.” (Ashoka)


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South Africa Workshop for Social Entrepreneurship - 2008/Reflections/Setting the Tone

Kim outlined how we would be spending our time together during these two days.

The event is about:

 * Community building.
 * Taking the opportunity to get to know each other.
 * Interaction and sharing by all, rather than presentation by a few.
 * Collaborative creative thinking
 * ... towards co-creation of a social entrepreneurship network of students, educators and community workers.
 * Sowing the seeds of collaborative action
 * defining the objectives of this community.

The structure of these interactions is indicated in the structure of the Reflections page.

The initiative as a whole is about:

 * developing social entrepreneurs through networks of people in learning institutions, community based organisations, etc., incorporating practical experience in community-led initiatives in the context of a technology enhanced and increasingly connected world.

Some words, phrases and concepts to add to your vocabulary and incorporate in our modus operandum:

 * commons-based peer production
 * free culture
 * libre knowledge, the libre knowledge vision and manifesto.
 * democratising innovation
 * Strength in Diversity.
 * Appreciative.


text: Category:Design templates

title: Category:Design templates


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Multiple linear regression

This learning resource summarises the main teaching points about multiple linear regression (MLR), including key concepts, principles, assumptions, and how to conduct and interpret MLR analyses.

Prerequisites:
 * 1) Correlation
 * 2) Linear regression

What is MLR?

 * Multiple linear regression (MLR) is a multivariate statistical technique for examining the linear correlations between two or more independent variables (IVs) and a single dependent variable (DV).
 * Research questions suitable for MLR can be of the form "To what extent do X1, X2, and X3 (IVs) predict Y (DV)?" e.g., "To what extent does people's age and gender (IVs) predict their levels of blood cholesterol (DV)?"
 * MLR analyses can be visualised as path diagrams and/or venn diagrams

Results

 * MLR analyses produce several diagnostic and outcome statistics which are summarised below and are important to understand.
 * Make sure that you can learn how to find and interpret these statistics from statistical software output.

Correlations
Examine the linear correlations between (usually as a correlation matrix, but also view the scatterplots):
 * IVs
 * each IV and the DV
 * DVs (if there is more than 1)

R

 * 1) (Big) R is the multiple correlation coefficient for the relationship between the predictor and outcome variables.
 * 2) Interpretation is similar to that for little r (the linear correlation between two variables), however R can only range from 0 to 1, with 0 indicating no relationship and 1 a perfect relationship. Large values of R indicate more variance explained in the DV.
 * 3) R can be squared and interpreted as for r2, with a rough rule of thumb being .1 (small), .3 (medium), and .5 (large). These R2 values would indicate 10%, 30%, and 50% of the variance in the DV explained respectively.
 * 4) When generalising findings to the population, the R2 for a sample tends to overestimate the R2 of the population. Thus, adjusted R2 is recommended when generalising from a sample, and this value will be adjusted downward based on the sample size; the smaller the sample size, the greater the reduction.
 * 5) The statistical significance of R can be examined using an F test and its corresponding p level.
 * 6) Reporting example: R2 = .32, F(6, 217) = 19.50, p = .001
 * 7) "6, 217" refers to the degrees of freedom - for more information, see about half-down this page

Cohen's ƒ2

 * Cohen's ƒ2 is based on the R2 and is an alternate indicator of effect size for MLR.

Coefficients
An MLR analysis produces several useful statistics about each of the predictors. These regression coefficients are usually presented in a Results table (example) which may include:
 * Constant (or Intercept) - the starting value for DV when the IVs are 0
 * B (unstandardised) - used for building a prediction equation
 * Confidence intervals for B - the probable range of population values for the Bs
 * β (standardised) - the direction and relative strength of the predictors on a scale ranging from -1 to 1
 * Zero-order correlation (r) - the correlation between a predictor and the outcome variable
 * Partial correlations (pr) - the unique correlations between each IV and the DV (i.e., without the influence of other IVs) (labelled "partial" in SPSS output)
 * Semi-partial correlations (sr) - similar to partial correlations (labelled "part" in SPSS output); squaring this value provides the percentage of variance in the DV uniquely explained by each IV (sr2)
 * t, p - indicates the statistical significance of each predictor. Degrees of freedom for t is n - p - 1.

Equation
$$\hat{Y} = bx + a$$ (for predicted values) or $$Y = bx + a + e$$ (for observed values)
 * A prediction equation can be derived from the regression coefficients in a MLR analysis.
 * The equation is of the form

Residuals
A residual is the difference between the actual value of a DV and its predicted value. Each case will have a residual for each MLR analysis. Three key assumptions can be tested using plots of residuals:
 * 1) Linearity: IVs are linearly related to DV
 * 2) Normality of residuals
 * 3) Equal variances (Homoscedasticity)

Power

 * Post-hoc statistical power calculator for MLR (danielsoper.com)

Advanced concepts

 * Partial correlations
 * Use of hierarchical regression to partial out or remove the effect of 'control' variables
 * Interactions between IVs
 * Moderation and mediation

Writing up
When writing up the results of an MLR, consider describing:
 * Assumptions: How were they tested? To what extent were the assumptions met?
 * Correlations: What are they? Consider correlations between the IVs and the DV separately to the correlations between the IVs.
 * Regression coefficients: Report a table and interpret
 * Causality: Be aware of the limitations of the analysis - it may be consistent with a causal relationship, but it is unlikely to prove causality
 * See also: Sample write-ups

What if there are univariate outliers?
Basically, explore and consider what the implications might be - do these "outliers" impact on the assumptions? A lot depends on how "outliers" are defined. It is probably better to consider distributions in terms of the shape of the histogram and skewness and kurtosis, and whether these values are unduely impacting on the estimates of linear relations between variables. In other words, what are the implications? Ultimately, the researcher needs to decide whether the outliers are so severe that they are unduely influencing results of analyses or whether they are relatively benign. If unsure, explore, test, try the analyses with and without these values etc. If still unsure, be conservative and remove the data points or recode the data.

title: Multiple linear regression


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Linear regression

The first step to understanding linear regression is to make sure you understand linear correlation.

Regression examines the relationship between two variables by determining the line of best fit (on a scatterplot). The properties of this line of best fit are determined as the slope (b) and where it touches the Y-axis (a).

Regression involves:

 * A predictor (X) variable, or an independent variable (IV), shown on the X-axis
 * An outcome (Y) variables, or a dependent variable (DV), shown on the Y-axis

The generic equation for a simple linear regression is:
 * $$\hat Y = bX + a$$

title: Linear regression


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Analysis of variance

ANOVA stands for Analysis of Variance. ANOVA is a family of multivariate statistical technique for helping to infer whether there are real differences between the means of three or more groups or variables in a population, based on sample data. Before tackling this topic, you should be familiar with normal distribution and testing differences.

Interactions
When two or more IVs combine to have synergistic effects on the DV, an interaction is said to occur. This means that the effect of one IV on the DV is moderated by another IV.
 * Notes on understanding interaction

Effect size
Effect sizes should be reported in addition to significance test results for ANOVA. Of note are eta-squared, partial eta-squared and Cohen's d:
 * 1) Partial eta-squared for each of the main effects and interaction(s) (e.g., via SS formula or SPSS - ANOVA - Options)
 * 2) (Total) eta-squared (e.g., via SS formula (SS between groups / Total SS); equivalent to R2 (total variance explained), i.e., provides % of variance in the dependent variable explained by the independent variables.
 * 3) Cohen's d can be calculated, this is for the differences between two means; i.e., pairwise contrasts. So, you might just want to focus on some contrasts e.g., if there's a significant main effect for gender, then compute the Cohen's d for overall motivation for males and females. You can use the spreadsheet from Tutorial 5 or calculate yourself, using http://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d

Recommended further reading: Measures of Effect Size (Strength of Association) for Analysis of Variance (Becker, 1999).

 * FAQ
 * Should I report effect sizes even when the F tests are not significant?

 * ✅ Effect size and statistical significance are two different, important pieces of information about an ANOVA. In a high power study, the results may be statistically significant but the size of the effect may be trivial. On the other hand, in a low power study, the results may not statistically significant, but the size of the effects may be small, medium, or even large. Thus, both are important.

Power
Power for ANOVAs can usually be calculated as part of the analysis using statistical software (e.g., SPSS).

Data analysis exercises

 * ANOVA data analysis tutorial (3rd year tutorial)

title: Analysis of variance


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User:Opensourcejunkie/sandbox

hey, Sylvia! Here's the current policy draft,
 * Draft policy on religious content

and here are links to the important parts of the debate:
 * User talk:Opensourcejunkie
 * User talk:Opensourcejunkie
 * User talk:Opensourcejunkie

the important characters in the debate are myself (Opensourcejunkie), McCormack (my Socratic mentor), and JWSchmidt (some guy with really good insights). Essentially, the debate is over whether or not some religions should be censored. McCormack believes some should, and I believe that none should.

Thanks for reading this, and letting me know what you think!
 * --Opensourcejunkie 13:05, 3 April 2008 (UTC)

title: User:Opensourcejunkie/sandbox


text: Category:Multiple linear regression

title: Category:Multiple linear regression


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Qualitative analysis

Qualitative analysis involves systematic coding, organisation, and analysis of non-numerical data.

title: Qualitative analysis


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Statistical power

Statistical power is the likelihood that a statistical test will:
 * 1) return a significant result based on a sample from a population in which there is a real effect.
 * 2) reject the null hypothesis when the alternative hypothesis is true (i.e. that it will not make a Type II error).

Power can range between 0 and 1, with higher values indicating a greater likelihood of detecting an effect.

What is statistical power?
Statistical power is the probability of correctly rejecting a false H0 (i.e., getting a significant result when there is a real difference in the population).

Desirable power

 * 1) Power ≥ .80 generally considered desirable
 * 2) Power ≥ .60 is typical of studies published in major psychology journals

Increasing power
Power will be higher when the:
 * 1) effect size (ES) is larger
 * 2) sample size (N) is larger
 * 3) critical value (α) is larger

Jacob Cohen published the “bible” of power analysis, which has remained one of the definitive works on statistical power. In this book, he provides some guidelines for what are typically considered “small,” “medium,” and “large” effect sizes. Cohen did not intend these numbers to be set in stone. They were meant to be suggestions, based on his experience with results published on various topics in major journals. However, Cohen believed that they should be ignored or replaced when more appropriate values were known for a specific research area. For better or worse, Cohen’s suggestions have been widely adopted, becoming as conventional as the “p < .05” rule for statistical significance, although unfortunately with little improvement in the power of typical published psychology research.

Estimating power
Statistical power can be calculated prospectively and retrospectively.

If possible, calculate expected power before conducting a study, based on:
 * 1) Estimated N, the sample size needed to achieve a specified power level
 * 2) Critical α, the value below which a p value would be considered "significant" (i.e., rejecting the null hypothesis)
 * 3) Expected or minimum ES (e.g., from related research)

It is possible to solve for necessary sample size, if the effect size, alpha, and desired power are known. This is often called an "a priori" power analysis. Ideally it would be done when planning a study, and often is done in grant proposals, which use 80% power as a common convention.

It also is possible to solve for power after a study is done (when the N, effect size, and critical α all are determined). This is a "post hoc" power analysis, and generally is considered the least helpful, since the study is already completed.

More helpfully, we can solve for the critical effect size that we would have had a set power to detect, given the critical α and a set N. This is sometimes referred to as a "sensitivity" power analysis.

Power calculators
Try searching using terms such as "statistical power calculator" and maybe also the type of test, and you should turn up links to useful pages such as:
 * 1) The GPower program, which is free software available for Windows and Macintosh. This software was sponsored by grants from the German government, and it is available in English as well as German language versions. Examples that go through estimating power for several commonly used statistical tests using the GPower software are hosted on the UCLA website here.
 * 2) Statistical power calculators
 * 3) One Sample Test Using Average Values
 * 4) Post-hoc Statistical Power Calculator for Multiple Regression

title: Statistical power


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Effect size

In statistical inference, an effect size is a measure of the strength of the relationship between two variables. Effect sizes are a useful descriptive statistic. Effect sizes provide a standard metric for comparing across studies and thus are critical to meta-analysis.

When reporting statistical significance for an inferential test, effect size(s) should also be reported. This is emphasized by the American Psychological Association (APA) Task Force on Statistical Inference (Wilkinson & APA Task Force on Statistical Inference, 1999), "reporting and interpreting effect sizes in the context of previously reported effects is essential to good research" (p. 599, emphasis added).

This page provides an undergraduate-level introduction to effect sizes and their usage.

Why use effect sizes?
An inferential test may be statistically significant (i.e., unlikely to have occurred by chance), but this doesn’t necessarily indicate how large the effect is.

There may be non-significant, notable effects especially in low powered tests.

Effect sizes are influenced by sample size, and by the number of groups/conditions (e.g. see Murray and Dosser, 1987). Therefore, caution must be taken when interpreting effect sizes, and when comparing them between different studies! Effect sizes can give additional information about the effects of independent variables within the same study, but should not be applied to compare effects between studies. Unless, sample size and study design are carefully taken into account.

Types
Some commonly used effect size are:

Correlational

 * All correlations are effect sizes
 * r or r2 (bivariate linear correlation or correlation squared)
 * R or R2 (multiple correlation or coefficient of determination)

Mean difference

 * Cohen's d, Hedges' g, or other forms of standard deviation unit effect size which provide the difference between two means in standard deviation units:
 * A standardised measure of the difference between two Means:
 * Cohen's d = (M2 – M1) / σ
 * Cohen's d = (M2 – M1) / SDpooled
 * Not readily available in SPSS, so use a separate calculator e.g., Cohensd.xls
 * Interpreting:
 * -ve  = negative difference/effect
 * 0    = no difference/effect
 * +ve = positive difference/effect
 * $$\eta^2$$ and $$\eta$$$$_p^2$$ (total variance explained and partial variance explained in ANOVA; each IV will have a $$\eta$$$$_p^2$$; total $$\eta^2$$ is equivalent to R2). See also: Eta-squared

Interpreting standardised mean differences
There are no agreed standards for how to interpret an ES. Interpretation is ultimately subjective.
 * Cohen (1977):
 * .2    = small
 * .5    = moderate
 * .8    = large
 * Wolf (1986):
 * .25  = educationally significant
 * .50  = practically significant (therapeutic)
 * Standardised Mean ESs are proportional, e.g., .40 is twice as much change as .20
 * The meaning of effect size depends on context:
 * A small ES can be impressive if, e.g., a variable is difficult to change (e.g. a personality construct) and/or very valuable (e.g. an increase in life expectancy).
 * A large ES doesn’t necessarily mean that there is any practical value e.g. if it isn’t related to the aims of the investigation (e.g. religious orientation).

Equating d and r
For equal and large sample sizes the following formulae are appropriate:

 * $$    $$r = \sqrt{\frac{d^2}{d^2 + 4}}$$

and conversely,
 * $$    $$d = \frac{2r}{\sqrt{1-r^2}}$$

as discussed by Cohen (1965, 1988), Friedman (1968), Glass, McGraw, and Smith(1981), Rosenthal (1984), and Wolf (1986).

The correct formula for unequal or small sample sizes is given by (see ):

 * $$    $$r^2 = \frac{d^2}{d^2+(n_1+n_2-2)(\frac{1}{n_1}+\frac{1}{n_2}))}$$

In the case that  $$n_1 \approx n_2$$  and both are large enough that  $$\frac{n_i+1}{n_i}\approx 1$$,  this reduces to $$

Expressing d as a %

 * 1) Look up a standard normal table (or use an auto-calculator such as ) for the area under the curve for a given d value. e.g., a d of .5 corresponds to 0.6915 which indicates that 69% of people were better off after treatment.
 * 2) "Effect size can also be thought of as the average percentile standing of the average treatment (or experimental) participant relative to the average untreated (or control) participant. A d of 0.0 indicates that the mean of the treatment group is at the 50th percentile of the control group. A d of 0.8 indicates that the mean of the treatment group is at the 79th percentile of the control group. An effect size of 1.7 indicates that the mean of the treatment group is at the 95.5 percentile of the untreated group."
 * 3) "Effect sizes can also be interpreted in terms of the percent of nonoverlap of the treatment group's scores with those of the untreated group. A d of 0.0 indicates that the distribution of scores for the treatment group overlaps completely with the distribution of scores for the control group, there is 0% of nonoverlap. A d of 0.8 indicates a nonoverlap of 47.4% in the two distributions. A d of 1.7 indicates a nonoverlap of 75.4% in the two distributions."

Exercise
Q: 20 athletes rate their personal playing ability, M = 3.4 (SD = .6) (on a scale of 1 to 5). After an intensive training program, the players rate their personal playing ability again, M = 3.8 (SD = .6) What is the ES? How good was the intervention? (For simplicity, this example uses the same SD for both occasions.)

A: Standardised mean effect size = (M2 - M1) / SDpooled = (3.8 - 3.4) / .6 = .4 / .6 = .67 = a moderate-large change over time

(Partial) Eta-squared vs. Cohen's d
In ANOVA, is reporting partial eta-squared sufficient, or should Cohen's d also be reported?

Partial eta-squared and Cohen's d provide two different types of effect size and both may be appropriate and useful in reporting the results of ANOVA.

Partial eta-squared indicates the % of the variance in the Dependent Variable (DV) attributable to a particular Independent Variable (IV). If the model has more than one IV, then report the partial eta-squared for each.

Cohen's d indicates the size of the difference between two means in standard deviation units.

To be thorough, one should report partial eta-squared for each IV and Cohen's ds for each pairwise comparison of interest (e.g., if posthoc tests or planned comparisons were conducted, then Cohen's d should be provided for each contrast).

If F is non-significant for an IV, then reporting the partial eta-squared is sufficient and appropriate. If F is significant and you go on to do planned contrasts or posthoc tests, then each of these pairwise comparisons should also be accompanied by Cohen's d effect sizes.

Note that if the IV of interest only has two levels, then the partial eta-squared and the Cohen's d will communicate similar information but do so using different scales of measurement (% and SD units respectively).

Power and effect sizes in psychology
Ward (2002) examined articles in 3 psychology journals to assess the current status of statistical power and effect size measures:
 * Journal of Personality and Social Psychology
 * Journal of Consulting and Clinical Psychology
 * Journal of Abnormal Psychology

Ward (2002) found that:
 * 7% of studies estimate or discuss statistical power.
 * 30% calculate ES measures.
 * A medium ES was discovered as the average ES across studies
 * Current research designs typically do not have sufficient power to detect such an ES.

Summary
Effect sizes indicate the amount of difference or strength of relationship. They have historically been underutilized. Inferential tests should be accompanied by effect sizes and confidence intervals.

Commonly used effect sizes include Cohen’s d, r.

Whilst rules of thumb for interpreting effect sizes are available, it is best to compare effect sizes with similar or related studies.

Standardized mean effect sizes are not available in SPSS – hand calculate or use a spreadsheet calculator.

title: Effect size


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