differences between two groups (Will Begin Momentarily) Copyright 2009 BCG Institute for Workforce Development Visit BCGi Online

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1 /4/009 Itroductio ti to t-tests t t for measurig differeces betwee two groups (Will Begi Mometarily) Brought to you by: Copyright 009 BCG Istitute for Workforce Developmet Visit BCGi Olie While you are waitig for the webiar to begi, Do t forget to check out our other traiig opportuities through the BCGi website. Joi our olie learig commuity by sigig up (it s free) ad we will otify you of our upcomig free traiig evets as well as other iformatio of value to the HR commuity.

2 /4/009 HRCI Credit BCG is a HRCI Preferred Provider. CE Credits are available for attedig this webiar. Oly those who remai with us for at least 80% of the webiar will be eligible to receive the HRCI traiig completio form for CE submissio. i You will receive your certificate of completio via withi oe week. Copyright 009 BCG Istitute for Workforce Developmet COMPare v.0 will be available soo! A free versio of this powerful software package will be made available to members of BCGi! What is COMPare? Desiged specifically to help federal cotractors comply with compesatio aalysis requiremets from the OFCCP. Uses multiple regressio, t-tests ad specialized processes to evaluate data assumptios, idetify problem areas, create reports, ad eve calculate dollar amouts eeded to elimiate statistically sigificat disparities. Become a member of the BCGi olie learig commuity (membership is free) to make sure that you receive access to this great aalytical tool!

3 /4/009 About Our Sposor: BCG Assisted hudreds of cliets with cases ivolvig Equal Employmet Opportuity (EEO) / Affirmative Actio (AA) (both plaitiff ad defese) EEO Litigatio Support / OFCCP (federal cotractig) Audit Support Compesatio Aalyses / Test Developmet ad Validatio Published: Adverse Impact ad Test Validatio, d Ed., as a practical guide for HR professioals Editor & Publisher: EEO Isight a idustry e-joural Creator ad publisher of a variety of productivity Software/Web Tools: OPAC (Admiistrative Skills Testig) CritiCall (9-- Dispatcher Testig) AutoAAP (Affirmative Actio Software ad Services) C 4 (Cotact Ceter Employee Testig) Ecouter (Video Situatioal Judgmet Test) Adverse Impact Toolkit (free olie at AutoGOJA (Automated Guidelies Orieted Job Aalysis ) Idustry Leader 5 Copyright 009 BCG Istitute for Workforce Developmet Itroductio ti to t-tests t t for measurig differeces betwee two groups (Will Begi Mometarily) Brought to you by: 3

4 /4/009 Jim Higgis, Ed.D. Biddle Cosultig Group s Istitute for Workforce Developmet 93 Blue Ravie, Ste. 70 Folsom, CA Copyright 009 BCG Istitute for Workforce Developmet Overview of Presetatio Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 4

5 /4/009 What is a t-test A sigle summary umber that allows you to determie whether observed differeces betwee two groups are statistically sigificat or if the differeces are actually more likely due to chace. A very powerful statistical test that ca be used with small samples (this is importat!) Limitatio: It does ot, by itself tell you why the differeces occur (For that you eed a differet test OR a eperimetal research desig) Copyright 009 BCG Istitute for Workforce Developmet Whe to Use a t-test Two Mutually Eclusive Groups Two Related (or Correlated) Groups The is what a t-test test was desiged for! Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 5

6 /4/009 Applicatios Adverse Impact white/miority, 5 male/female, over/uder 4 40, etc. 3 Validatig Traiig Reduced ijuries, icreased retetio, improved customer service Program Evaluatio 6 Compare time to time, 4 compare multiple sites/compaies. 0 Customer Satisfactio Time Time Hired (%) Male Female Traied Not Traied Hired (%) Copyright 009 BCG Istitute for Workforce Developmet A quick review of Cetral Tedecy Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 6

7 /4/009 What is a Measure of Cetral Tedecy? A sigle summary umber that tells you about what is most commo. Gives you a idea about what is the most commo umber i a distributio of scores. Copyright 008. Jim Higgis, Ed.D. All Rights Reserved Copyright 009 BCG Istitute for Workforce Developmet Eamples of Cetral Tedecy Most scores fall i this cetral area Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 7

8 /4/009 Three Basic Measures of Cetral Tedecy Mode Mdi Media Mea Copyright 008. Jim Higgis, Ed.D. All Rights Reserved Copyright 009 BCG Istitute for Workforce Developmet The Mea The most importat measure of cetral tedecy. Also kow as The Average Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 8

9 /4/009 The Mea The formula! Copyright 008. Jim Higgis, Ed.D. All Rights Reserved Copyright 009 BCG Istitute for Workforce Developmet The Mea Break it dow This This is the symbol for the mea. symbol meas Sum of ad simply tells you to add thigs up refers to a variable. (A lower case N ) refers to the umber of s that you have. Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 9

10 /4/009 Readig the formula The mea equals The sum of the scores Divided by the umber of scores Copyright 008. Jim Higgis, Ed.D. All Rights Reserved Copyright 009 BCG Istitute for Workforce Developmet The Mea: Workig a eample: Suppose you asked 5 people their ages ad got the followig umbers: 9, 4, 3,, 0 What is the mea? = 07 = 5 Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 0

11 /4/009 Calculatig the Mea Copyright 008. Jim Higgis, Ed.D. All Rights Reserved Copyright 009 BCG Istitute for Workforce Developmet Quick Review: Measures of Cetral Tedecy There are 3 measures of cetral tedecy: Mode: Most Frequetly occurrig umber Media: Number where 50% are higher ad 50% are lower Mea: The arithmetic Average ad this is the most importat because it is used i most of the powerful statistical tests that we have available. Copyright 008. Jim Higgis, Ed.D. All Rights Reserved

12 /4/009 Measures of Variatio Copyright 008. Jim Higgis, Ed.D. All Rights Reserved Copyright 009 BCG Istitute for Workforce Developmet What is Variatio? Refers to how spread out scores are aroud the mea Tells you whether most scores are close to the mea or if they are really a lot differet Small variatio meas most scores are close to the mea Large variatio meas may of the scores are much higher or much lower tha the mea Copyright 008. Jim Higgis, Ed.D. All Rights Reserved

13 /4/009 Variatio: Eamples Little variatio: Most scores are close to the mea. Moderate variatio: While most scores ted to be close to the mea, some are farther away. Large variatio: A lot of the scores are far away from the mea. Copyright 008. Jim Higgis, Ed.D. All Rights Reserved Copyright 009 BCG Istitute for Workforce Developmet Importace of Measures of Variatio Alog with the mea, it helps you get a fuller picture of what is happeig with the data. Helps you put the mea i cotet. Whe you make predictios about scores, you are able to tell how accurate your predictios are likely to be. Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 3

14 /4/009 Four Importat Measures of Variatio Least Importat Most Importat Rage Sum of Squares Variace Stadard Deviatio Copyright 008. Jim Higgis, Ed.D. All Rights Reserved Copyright 009 BCG Istitute for Workforce Developmet The Stadard Deviatio The square root of the variace sd ( ) Whe you take the square root of the variace, you chage the variace from beig squared deviatio scores back ito raw scores. The stadard deviatio tells you, o average, how much scores deviate from the mea. Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 4

15 /4/009 Calculatig the Variace Salary $0 $ $3 $4 $5 Deviatio Scores Squared Deviatio Scores = 6.8 Σ = 0 Σ = 0.8 Variace = 0.8 / 4 = 50.7 Sum of Squares Stadard Dev. = SQRT(Variace) = SQRT(50.7) = 7. Copyright 008. Jim Higgis, Ed.D. All Rights Reserved Copyright 009 BCG Istitute for Workforce Developmet Eample 34% 34% % 4% 4% % Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 5

16 /4/009 This brigs us to t-tests Measurig Differeces betwee groups. A critical i statistical i test because of all of the ways it ca be used. They come i two flavors Idepedet Samples t-tests (used for thigs like Adverse Impact aalysis, Compesatio Aalysis) whe the two groups are Idepedet of each other. Depedet or Correlated Samples t-tests (Used whe the two groups are ot mutually eclusive). Copyright 008. Jim Higgis, Ed.D. All Rights Reserved t How Does A Idepedet Samples T-Test Work Copyright 009 BCG Istitute for Workforce Developmet Y ( ) ( Y ) Y y ( ) ( ) Poolig the variace betwee the two groups to measure the amout of oise Copyright 008. Jim Higgis, Ed.D. All Rights Reserved y Measures the total differece betwee groups y Adjustig for the sample size of the groups ot eeded if they are equal! 6

17 /4/009 How Does A T-Test Work? Noise Sigal Copyright 008. Jim Higgis, Ed.D. All Rights Reserved Copyright 009 BCG Istitute for Workforce Developmet How Does A T-Test Work? Sigal Noise Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 7

18 /4/009 8 How Does A T-Test Work Y? Y? Error Error Differeces al Error females males _ Re Real Differeces + Error = Real Differeces Error Copyright 008. Jim Higgis, Ed.D. All Rights Reserved How Does a Correlated Samples t- Test Work? ) ( ) ( ) ( ) ( ) )( ( ) ( ) ( pairs t As you ca clearly see, it is all really very simple! Copyright 009 BCG Istitute for Workforce Developmet

19 /4/009 How Does A Correlated Samples t- Test Work? t SD SD ( r SD SD ) This is the oly real differece. It subtracts the iheret correlatio betwee the two groups before determiig whether there is a differece. Copyright 009 BCG Istitute for Workforce Developmet The Reality Uless you are a little strage you are probably ot goig to be doig this stuff by had. Rather, you will let the computer do it all for you. 9

20 /4/009 Let s Take A Look At How To Do t- Tests i Microsoft Ecel Copyright 008. Jim Higgis, Ed.D. All Rights Reserved Copyright 009 BCG Istitute for Workforce Developmet For more iformatio If you eed statistical help Would like to lear more about statistics i If you ca t fid a book you like that makes it clear to you, I wrote a statistics guide I call the Radical Statisticia it s available through the BCGistitute.org website. I wrote it to help my college statistics studets rather tha with the itet to sell it so be forewared. Copyright 008. Jim Higgis, Ed.D. All Rights Reserved 0

21 /4/009 Questios/Commets? Jim Higgis, i Ed.D. Jhiggis@biddle.com BCG Istitute for Workforce Developmet 4 Copyright 009 BCG Istitute for Workforce Developmet