Understanding T-Tests: Repeated vs. Independent Analyses

1. T-testsPart 2PS1006 Lecture 3 Sam Cromie

2. From Repeated t to Unrelated t NOMENCLATURE within, repeated, paired vs. between, unrelated, independent

3. Generic form of a statistic Data – Hypothesis Error What you got – what you expected (null) The unreliability of your data

4. Repeated measures t test • PTSD symptoms measured before and after supportive counseling • Difference scores are used for the calculation • t calculates the likelihood of achieving these scores (using the concept of a sampling distribution), given there is there is no difference between before and after scores • Since there should be no difference we assume  (pop diff score) to be 0

5. SPSS repeated t output

6. Reporting the result • Supportive counselling resulted in a decrease (M= 8.22, SD=3.6) in the number of PTSD symptoms reported. A repeated measures t test showed these differences to be significant; t(8)=6.86, p<.001, two-tailed. • shorthand t(8)=6.86, p<.001, two-tailed • In exam - conclusion = supportive counselling reduced the number of PTSD symptoms • Reporting p Options are: > .05, <.05, <.01, <.001 Never state that p =.000 or that p is < .000

7. Independent groups t test • Used to analyse a between subjects design • Also referred to as a between subjects t test • Should realise our therapy trial could have been designed using two different groups rather than a repeated measures design • One group received therapy the other did not • There are no comparable scores within each group therefore groups as a whole have to be compared

8. Changing to between groups design • Same data presented as different groups • No comparable scores within each group - groups as a whole have to be compared • Test differences between sample means • Need a sampling distribution of differences between group means

9. = = = =

10. Equation elements • = mean of group 1 • = mean of group 2 • = the standard deviation of a sampling distribution based on the difference between the mean of two samples • = the variance of group 1 • = the variance of group 2 • n1= the number of participants in group 1 • n2= the number of participants in group 2

11. Allowing for Gs of different sizes • A sample variance should be weighted according to the number within the sample • Formula below calculates the pooled variance such that and are replaced by

12. Inputting data into SPSS • Basic rule - each participant occupies a single row • Repeated measures design: • each participant = 2 columns, 1 for before and 1 for after therapy • Between groups design: • all the scores go into 1 column since each participant only produces one score

13. With between groups each participant must also be identified in terms of the group they come from • A second column is designated the groupingvariable (sometimes referred to as dummy variable) - identifying which group the participant was in

14. SPSS output • Note SPSS uses the pooled variance formula

15. Degrees of freedom • Each group has 9 participants • df for each group = n - 1 = 9 - 1 = 8 • Since there are 2 groups • df = n1- 1 + n2 - 1 = n1 + n2 - 2 • = 9 + 9 - 2 = 16 df • New result t(16) = 4.133, p<.01, two-tailed • Value of t is smaller - independent groups design is less powerful and will always produce a smaller t result given the same data

16. Conditions of use For all parametric statistics, the data must fulfil three criteria with varying stringency • The data must be of interval quality • Both populations are sampled from populations with equal variances • Homogeneity of variance • Both groups are sampled from normal populations • Assumption of normality

17. Nonparametric equivalents • When the data produced do not conform to the requirements of parametric data, then there are nonparametric equivalents • Repeated measures t test - • Wilcoxon’s Matched-Pairs Signed-Ranks Test • Unrelated groups t test • Mann-Whitney (U) Test