Paired samples t-tests Flashcards
What does a t-test tell us?
The t test tells us how likely it is that we will observe a difference - is this by chance?
why would we use a t test?
when one of our variables has more than one condition.
what kind of data design must we have to do a t-test?
repeated design
how many conditions must our IV have to do a t test?
2
How many participants do you need to do a t-test?
10
What scale should our data be on to use a t-test?
interval/ratio
The difference scores (change scores) for t tests must be…
Normally distributed :)
T tests are interested in the __________ between participant’s T1 and their T2 scores.
differences
When will the t value get bigger?
- when the difference scores are larger, assuming they are also consistently in the same direction.
- when there is less variation in difference scores.
___ variation is more likely to be significant as there is a much smaller distribution, this score is an extreme.
less
t (951) = -12.39, p< .001 (two tailed)
Anything missing?
Yes effect size!
If you use a 1 tailed hypothesis what do you have to do to the p value?
We have to half it!
what is a small effect size?
0.1
What is a medium effect size?
0.3
What is a large effect size?
> 0.5
What is the formula for r (effect size)?
√ t2/ (t2 + df)
t = -12.39 df= 951
Calculate the effect size.
√ t2/ (t2 + df)
√-12.39 squared/ (-12.39 squared + 951)
r = 0.37
Larger T value =…
larger difference and smaller variation
What do t-tests evaluate?
The difference in participants’ scores from one condition to the other.
What 2 non-parametric tests would you use?
2 conditions: Wilcoxon Signed ranks
3 or more conditions: Friedman Test
if you have 2 conditions what non-parametric test do you use?
Wilcoxon Signed Ranks
If you have 3 conditions or more, what non-parametric test do you use?
Friedman Test
What is the non-parametric equivalent to the t-test?
Wilcoxon signed Ranks
what conditions does non-parametric data reflect?
Less than 10 participants
Ordinal data
Data skewed
What does Wilcoxon Signed Ranks test?
whether data in 1 condition is consistently ranked more highly than in the other condition.
How does ranking work if people have the same score?
If we have 3 score 1’s.
1 + 2 + 3 = 6
6/3 = 2
The ___ value is always the smaller number of the 2 sums of ranks.
the T value :)
How is a Wilcoxon signed ranks reported?
T = 2, N= 8, p= .023 (two tailed).
What is the effect size in Wilcoxon Signed Ranks?
r = z / square-root-of-N
What are Cohen’s guidelines for effect sizes
r = .10 (small), .30 (medium), .50 (large
T = 2, N = 8, p = .023 (two-tailed), r = .80.
When would you not report effect size?
If p wasn’t significant.
What is an extension of the Wilcoxon?
Friedman- for 3 or more conditions :)
What is the standard form to report Friedmans?
χ2 (2) = 12.25, p = .002
After we get our Freidman’s what do we have to do?
We have to conduct follow up Wilcoxon’s to find out where the sig differences lie!
If we have 4 conditions, how many Wilcoxon follow up tests do we have to do?
A v B A v C A v D B v C B v D C v D
6 tests!!!
What do Wilcoxon follow up tests inflate?
They inflate the chances of making a type I errors.
How do we resolve the increased chance of makimg a type I error in a follow up Wilcoxon test?
We do a bonferromi Correction!
What is a Bonferroni Correction?
Divide the level of significance (0.05) by the number of tests you are conducting.
I you have 3 Wilcoxon follow up tests- what is the significance value?
0.05/3 = 0.017
What is the appropriate effect size to use for paired sample t-tests?
Cohen’s d
