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The t Test for Two Related Samples - Coggle Diagram
The t Test for Two Related Samples
Study Designs
Repeated-Measures Design – The same participants are tested in multiple conditions
Within-Subjects Design – Another name for repeated measures
Related Samples – Measurements connected because they come from the same people or matched pairs
Matched-Subjects Design – Different participants paired based on similar characteristics
Pretest-Posttest Design – Measures participants before and after a treatment
Difference Scores
Difference Score (D) – The difference between two related measurements
Mean Difference (\(M_D\)) – The average of all difference scores
Sum of Difference Scores (\(\sum D\)) – All the difference scores added together
Variance of Difference Scores (\(s_D^2\)) – How spread out the difference scores are
Standard Deviation of Differences (\(s_D\)) – The typical variation in difference scores
Hypothesis Testing
Repeated-Measures t Statistic – Tests whether the average difference is statistically significant
Null Hypothesis (\(H_0\)) – Assumes no average difference between conditions
Alternative Hypothesis (\(H_1\)) – Predicts a difference or change between conditions
Estimated Standard Error – Estimates how much the sample mean difference varies
Degrees of Freedom (df) – Number of difference scores minus one
Strengths and Limitations
Individual Differences – Natural differences between people that can affect results
Order Effects – When the order of conditions influences performance
Practice Effects – Participants improve because they've done the task before
Fatigue Effects – Participants perform worse because they're tired or bored
Counterbalancing – Changing the order of conditions across participants to reduce order effects
Effect Size and Confidence
Cohen's d – Measures the size of the average difference in standard deviation units
r² (Coefficient of Determination) – Proportion of variance accounted for by the treatment effect
Confidence Interval – A range of plausible values for the population mean difference
Population Mean Difference (\(\mu_D\)) – The true average difference in the population
Critical Value – The cutoff used to determine statistical significance