Repeated anova measures ppt


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Repeated measure ANOVA; how it works, F statistic, assumptions and its pros and cons

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Repeated anova measures ppt

  1. 1. Presented toMs Maryium GulPresented byAamna HaneefRoll no: 05MS (2012-2014)Lahore College for WomenUniversity
  2. 2. Repeated Measures ANOVA
  3. 3. Repeated measures ANOVA isalso referred to as a• “within-subjects ANOVA”,• “Dependent groups” or• “ANOVA for correlatedsamples”Other Names
  4. 4. Why the repeated factor iscalled a “within” subjects factor?Because comparisons aremade multiple times("repeated") “within” thesame subject rather thanacross ("between") differentsubjects
  5. 5. In within subject design• Each participant is measured morethan once• Same subjects across the levels of theIV• Levels can be ordered like time ortreatment• Or levels can be un-ordered (e.g. casestake three different types ofdepression inventories)
  6. 6. What RM ANOVA does?Like T-Tests, repeated measuresANOVA gives the statistic toolsto determine whether or notchange has occurred over timeT-Tests compareaverage scores attwo different timeperiodsRM ANOVAcompared theaverage score atmultiple timeperiods
  7. 7. The logic of RM ANOVAAny differences that are foundbetween treatments can beexplained by only two factors:1. Treatment effect2. Error or Chance
  8. 8. Cont…A particular subject’s scores will bemore alike than scores collected frommultiple subjectsLess variability decrease insampling error
  9. 9. Cont…Subject A B CEach rowrepresentsonesubjectmeasuredundereach of kconditions.1subj1 undercondition Asubj1 undercondition Bsubj1 undercondition C2subj2 undercondition Asubj2 undercondition Bsubj2 undercondition C3subj3 undercondition Asubj3 undercondition Bsubj3 undercondition CAnd so on…
  10. 10. AssumptionsDependent variableIt should be measured at theinterval or ratio level (continuous),such as• revision time• Intelligence• exam performance• weight
  11. 11. Assumptions Cont…Independent variableIt should consist of at least twocategorical, "related groups" or"matched pairs“• 10 individuals performance in aspelling test before and after new formof computerized teaching method• measuring changes in blood pressuredue to an exercise-training program
  12. 12. Assumptions Cont…No significant outliers differencesData values that are "far away" fromthe main group of data• Distorting the differencesbetween the related groups• Reduces the accuracy ofresults
  13. 13. Assumptions Cont…Normally distributed Dependentvariable• The dependent variable between thetwo or more related groups should beapproximately normally distributed• It is quite "robust" to violations ofnormality• The Shapiro-Wilk test of normalitycan test for normality
  14. 14. Assumptions Cont…Sphericity• Refers to differences betweenvariances in levels of the repeated-measures factor (Time)• Violation of the assumption ofsphericity, causes the test to becometoo liberal (leads to an increase in theType I error)• Mauchlys Test of Sphericity can helpto test for its violation
  15. 15. Hypothesis for RM ANOVAThe repeated measures ANOVA tests forwhether there are any differencesbetween related population meansH0: µ1 = µ2 = µ3 = … = µkH0: There are no differences betweenpopulation means.HA: At least one treatment orobservation mean is significantlydifferent
  16. 16. Sources of Variability• In repeated measure ANOVA, there arethree potential sources of variability:1. Treatment variability: between columns,2. Within subjects variability: betweenrows, and3. Random variability: residual(chancefactor or experimental error beyond thecontrol of a researcher) .• A repeated measure design is powerful, asit controls for all potential sources ofvariability.
  17. 17. FORMULAvariance between treatmentsF = ------------------------------------------Error variance• A large F value indicates that thedifferences betweentreatments/observations aregreater than would be expected bychance or error alone.
  18. 18. Approaches to RM ANOVASPSS conducts 3 types of tests if thewithin-subject factor has more than 2levels• The standard univariate ANOVA test• The alternative univariate tests• The multivariate test
  19. 19. Advantages• Using the same participants indifferent experimental manipulations• Exclude the effects of individualdifferences• This design is also very economical• Removing variance due to differencesbetween subjects from the errorvariance greatly increases the power(probability of correctly rejecting afalse null hypothesis)
  20. 20. Disadvantages• Practice effects causing participants’results to improve• Carry-over effects (bias)• Demand characteristics (moreexposure, more time to think aboutmeaning of the experiment).• Boredom and lack of concentration
  21. 21. TidbitsWhy it is always called F statistic?The F statistic was named afterRonald A. Fisher, who mainlydeveloped ANOVA