repeated measures/paired t-tests Flashcards
what is a paired t test
used to compare means where we had two sets of measures that can be paired (the same person twice, or matched)
the two comparisons must be comparable
this could be:
- test retest
- testing twice for differing stimuli
- non independent (paired) individuals
what are the assumptions of the paired t test
the difference values have to be normally distributed
we can run this test by calculating a difference score for each participant/matched pair and running descriptive stats on all difference scores
for the independent samples t test, you also need homogeneity of variance for your two conditions. For a paired samples t test, you have the same PPs or matched so its not considered
in experiments, we assume random sampling of participants
what is the difference between standard error and standard deviation
standard error is the SD divided by √n
SE is estimated standard deviation within the population for samples of that size, not just the SD of our specific sample
what use are the t values
t value doesn’t tell us much on its own
we want to compare our t value with the frequency of all possible values that you could get for the population, if the null hypothesis is true
we want our t statistic not to be a typical result, as we aim to reject the null hypothesis
what does the shape of distribution depend on?
the degrees of freedom
what does the distribution tell us
how frequently you should observe each value of the t statistic for a sample if the mean difference is zero
values close to zero are high frequency and associated with a high probability
where does the p value come from
If we know the frequency an event occurs, we can describe the probability that it occurs
Looking at the t-distribution, you can see that for samples with greater degrees of freedom (larger sample sizes), the results are closer to the mean
We need to take into account the degrees of freedom in interpreting our t-value
For large sample sizes, more than two standard errors distance from the mean is very rare. Findings with t values this large are not representative of this distribution
If p < .05 for our t-value, we can decide to accept the alternative hypothesis that there is a difference between conditions.
what is the approach to deciding if we have a significant difference between our two conditions
1) use the data from our conditions to calculate a statistic (e.g., t statistic) based on differences between our two conditions
2) find out how unusual result is taking into account the degrees of freedom (value based on sample size)
3) Get our p-value based on the predicted distribution of values if there’s no effect (H0) (relies on knowing the spread of scores in our sample and estimating population sampling distribution)
4) Evaluate our p-value and decide if it is significant – less than .05?
what are the pros and cons of analysing difference scores
positive:
- less noise in the difference scores than the original scores, so t statistic will be larger when dividing by standard error
negative:
- but the degrees of freedom used for interpreting the t statistic and producing p-value is smaller, so less likely to get a significant result as sampling distribution is wider
