1. T-tests Part 2 PS1006 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 grouping variable (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 New result
df for each group = n - 1 = = 8
Since there are 2 groups
df = n n2 - 1 = n1 + n2 - 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

18. Conditions of use Formula Value interested in Population value
Denominator
Pop mean and SD known - interested in score of ind
Score of individual
Population mean
Population standard deviation
Pop mean and SD known - interested in mean of sample
Mean of sample
Standard error of sampling distribution of mean
Pop mean but SD unknown - interested in mean of sample
SE of sampling distribution of mean
Interested in difference between 2 repeated measures
Mean difference between two repeated measures
zero
SE of sampling distribution of mean difference scores
Interested in difference between 2 independent Gs
Difference between means of 2 independent Gs
SE of differences between means