Paired t test Flashcards
What is the alpha level?
Corresponds to the size of the rejection region
e.g. if an alpha level is .05 then the rejection region is 5%
The largest probability that the researcher is willing to accept in order to reject the null hypothesis
What is the critical value?
T value exceeds the critical value, the value will fall into the rejection region
End of a tail on a graph
In these conditions, we reject the null hypothesis
What is a paired t test?
Compare means where we have 2 sets of measures that can be paired (same person twice or matched)
This could be:
- test retest (one group of ps, measure performance twice, same measures, same ps)
- testing twice to test for differences based on type of stimulus (one group of ps, same measures, different stimuli, same ps)
- non independent (paired) individuals (different ps, same measure, same time)
What are t values? What are the t distributions?
Compare our t value with all the possible values that you could get in a population
We need the distribution of all sample means which we use a t distribution for. The shape of the distribution depends on the degrees of freedom
The distribution tells us how often you should observe each t statistic if the sample mean difference is zero
Closer to 0= high frequency and high probability
How does the p value affect the t distribution and degrees of freedom?
In t distributions, the greater the sample size with greater df, the results are closer to the mean
For larger sample sizes, more than 2 standard errors from the mean is rare, t values at this point aren’t representative of the distribution
More degrees of freedom, larger p value
What are paired t test assumptions?
- The different values have to be normally distributed
- Tested by calculating a difference score for each ps/matched pair and running descriptive statistics on all the different scores
- Same ps or matched ps
- Assume random sampling of each ps
What is null hypothesis significance testing?
Deciding if we have a significant difference between 2 conditions
- use the data to calculate a statistic
- find out how unusual the result is by taking into account degrees of freedom
- p value based on the predicted distribution values if there’s no effect
- evaluate the p value and decide if it’s significant if >.05
How do researchers calculate paired t tests in 2 samples?
Each ps has a score in both conditions
Better to look at the differences in scores for each ps
Then work out the mean difference across ps
If the null hypothesis is true, then there’s no effect and the mean difference should be 0
What are degrees of freedom?
df is n - 1 for paired t tests
n - 2 for independent t tests
n is the sample size
What is the standard error?
Standard deviation from the mean in the sample
divided by the sample size
Predicts the spread of sample means around the population means
What are the pros of difference scores?
The higher the correlation, the more statistical power by reducing the variance through matching pairs
What are the cons of difference scores?
If correlation between scores is zero or negative, statical power is lost by matching pairs e.g. t distribution has lower degrees of freedom, so less likely to have significant p values
Sampling distribution can be wider because there’s smaller degrees of freedom and p values so there’s less likely to be a significant result
