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Chapter 11: The t Test for Two Related Samples - Coggle Diagram
Chapter 11: The t Test for Two Related Samples
Repeated-Measures Design
One group of participants is measured in two different treatment conditions.
Difference score = Post-treatment score minus pre-treatment score
*The sign of each D score tells you the direction of the change.
Null hypothesis
*There will always be some error between a sample mean & the pop mean so we do not expect the pop. mean diff to be exactly 0.
Alternate hypothesis: there is a treatment effect that causes the scores in one treatment condition to be systematically higher/lower than the scores in the other condition
Key Characteristics
Requires fewer subjects
Can observe behaviors that change or develop over time
Reduces or eliminates problems caused by individual differences
SS and variance are computed for the difference scores
More sensitive to difference between sample means (greater power)
It is possible that participation in the first treatment influences the score in the second treatment (order effects) and can be remedied through counterbalancing
The t statistic
All calculations are done using the difference scores and there is only one D score for each subject.
With a sample of n participants, the number of D scores is n, and the t statistic has df = n-1.
(actual difference between the sample & the hypothesis) / (expected difference between sample & hypothesis with no treatment effect)
Assumptions of the related-samples t test:
1) Inside each treatment the scores are obtained from different individuals & should be independent of each other.
2) The population distribution of D values must be normal.
Matched-Subjects Design
Each individual in a sample is matched with an individual in the other sample. The matching is done so that the two individuals are equivalent/nearly equivalent with respect to a specific variable(s) that the researcher would like to control.
Uses separate sample of participants in each of the two treatment conditions (independent-measures design)
A difference score is computed for each matched pair (repeated-measures design)
The data used to compute diff scores & the hyp test for the matched-subjects design is the same as the t test used for the repeated-measures design.
A matched-subjects design is not the same as a repeated-measures design
as the matched pairs of participants are not really the same people.
Effect Size, Confidence Intervals, Sample Size & Variance
The confidence interval estimates the size of the treatment effect by estimating the pop mean diff between the two treatment conditions.
A larger percentage produces a wider interval
A larger sample size produces a narrower interval
Relationships
Larger sample size --> smaller standard error
Larger variance --> larger standard error
Larger sample size --> larger t-value -->increased likelihood to reject null hyp
Larger variance --> smaller t-value --> less likelihood to reject null hyp
Larger variance --> smaller measures of effect size
High variability --> no consistent treatment effect
