Paired and independent t-tests

Dependent (paired t-test)

2 samples are related, typically that the 2 samples come from the same person measured twice

What question does a paired t-test answer?

are the differences in the scores on average significantly different from zero

Conditions for paired t-test

both groups will have the same number of responses since the scores for each response are matched
-can't have missing data

sample size for paired t-test

the number of paired values (half the number of total responses)

null hypothesis for paired t test

mean of the difference is equal to zero

assumptions for paired t-test

-random sampling
-independent observations
-normal population distribution or large sample (25+)

alpha level

.05

standard deviation

sqrt(sum of differences between observed and average difference of scores)/n-1

independent t-test

comparing 2 groups of unrelated responses to see if the group means are significantly different

how are independent t-tests different from paired t-tests?

independent t-test involves 2 entirely separate groups

assumptions of independent t-test

-random samples
-independent observations
-normal population distribution or large sample
-independent samples

paired t-test alternate hypothesis

mean of differences does not equal zero

null hypothesis for independent t test

(mean of group one)-(mean of group 2)=0

alternate hypothesis for independent t-test

(mean of group one)-(mean of group 2) does not equal zero

degrees of freedom of independent t test

smaller sample size minus one

bar chart of means

error bars are based on standard error
-if bars overlap there is no significant difference
-if they do not overlap there is a significant difference

when writing hypothesis notation for independent t test

the order which you subtract the two group means does not matter as long as it's the same way calculated during t test

When to reject the null hypothesis

When the t-stat is more extreme than the t-critical

When to fail to reject the null hypothesis

when the t-stat falls between the t-critical values

degrees of freedom of paired t-test

population size minus 1