Week 2 Lecture 2 - t-tests Flashcards
How many IVs and levels should there be to use a t test?
1 IV, 2 levels
What do t-tests estimate?
Whether pop. means under 2 levels of IV are different
What are the 2 types of variance?
variance between IV levels (ppts in different group getting different scores)
variance within IV levels (ppts in same group getting different scores)
What contributes to variance between IV levels for an independent t-test?
- manipulation of IV
- individual differences
- experimental error (random error and constant error)
What contributes to variance within IV levels for an independent t-test?
- individual differences
- experimental error (random error)
What is the main point of interest for contributing factors to variance?
manipulation of the IV
How would you find the mean difference between 2 sample means from 2 pops.
Mean A - Mean B = Mean D (difference)
What are standard error units?
can express the extent to which an individual sampled mean difference deviates from 0
How to calculate ESE for differences in an independent t-test?
ESE D = sqrt((s^2A / nA) +(s^2B/ nB))
Is t a ratio?
yes - reflects the difference between the sample means, expressed in SE units
How to calculate a t-stat for an independent t-test for difference?
t = mean D / ESE D
A small variance between IV levels relative to within IV levels leads to a t value that is
close to 0
A large variance between IV levels relative to within IV levels leads to a t value that is
further from 0
What are degrees of freedom?
the difference between no. of measurements made and the number of parameters estimated
i.e., sample size - no. of parameters (n-1)
True or false
the larger the DOF, the more reliable
true
What is the dof for an independent t test?
n total - 2
When dof = infinity, what is the critical t value?
1.96
what are the 4 assumptions for an independent t test?
- normality
- homogeneity of variance
- equivalent sample size
- independence of observations
What is normality for an independent t test?
DV is normally distributed, under each level of the IV
What is homogeneity of variance for an independent t test?
the variance in the DV, under each level of the IV, should be reasonably equivalent
What does Levene’s test check?
checking the assumptions of homogeneity of variance
testing to see if there’s a difference in variances
no difference = homogeneity
difference = heterogeneity
What is equivalent sample size for an independent t test?
sample size under each IV level should be roughly equal
particularly important fir small samples
What is independence of observations for an independent t test?
scores under each IV level should be independent
particularly important for quasi-experimental
If the assumptions for an independent t test are violated, what should you do?
use the none parametric alternative - Mann-Whitney U test
What is a paired t test for?
for within subjects designs
How do you calculate mean D for a paired t test?/
= sum (xiA - xiB) / n
How do you calculate ESE D for a paired t test?
s D / sqrt n
What contributes to variance between IV levels in paired t tests?
- manipulation of IV
- experimental error
What contributes to variance within IV levels in paired t tests?
- experimental error
What are the assumptions of a paired t test?
- normality
- sample size
What is normality in a paired t test
distribution of difference scores between IV levels should be approx normal
assume to be normal if n>30
If the assumptions for an paired t test are violated, what should you do?
use non-parametric alternative –> Wilcoxon t test
Can you determine if a result is likely to be significant using 95% confidence interval plots?
yes for independent groups
no for repeated measures
What is the dof for a paired t test?
n-1
What is Cohen’s D?
the magnitude of difference between 2 IV level means, expressed in SD units
i.e., a standardised value expressing the difference between the IV level means
How do you calculate Cohen’s D?
(mean A - Mean B) / ((s A + s B) /2)
how do you quantify effect sizes in Cohen’s D?
small = 0.2
medium = 0.5
large = 0.8
What kind of overlap is there for a small and large effect size in Cohen’s D?
small = large overlap
large = small overlap
