paired samples t test

paired samples t-test

2 levels of IV

within subjects

paired samples eliminate some noise/disturbance variables

* reduces sampling error in denominator of t-obs, produces bigger t-obs

natural pairs: siblings, couples

* compared when looking for differences, not correlations

experimental matching: pairs formed based on matching variable

* participants are considered comparable and one is assigned to control and the other to experimental to compare data

N = number of pairs, smaller df

paired samples t-test is only better than independent samples t-test when we reduce enough error to offset reduced df (usually occurs

assumptions:

* difference scores are independently and randomly sampled from the population
* population of difference scores is normally distributed

paired samples sampling distribution

distribution of DIFFERENCE SCORES

distribution of all possible means of samples of difference scores of a given size

H0 = Mean difference = 0

H1 = mean difference =/= 0

t-obs = d-bar / standard error of the difference

paired samples effect size

Cohens D: d-bar/standard deviation (S(D)) not standard error

Eta squared: t^2 / t^2 + df

paired samples confidence intervals

CI = D-bar +/- (t-crit)(S(D-bar)) (standard error of the mean)

how to do paired samples by hand

* State null and alternative hypotheses
* compute difference scores and find sum and sum of squared difference scores
* compute standard deviation of difference scores: formula given
* compute standard error of difference scores: formula given
* compute observed t: D-bar / standard error
* draw conclusion + describe effect
* Report CI: D-bar +/- (t-crit)(standard error)
* Compute Cohen’s d and eta squared: formula given