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The t Test for Two Related Samples, image, image, image, image - Coggle…
The
t
Test for Two Related Samples
11-1 Introduction to Repeated-Measures Designs
A research design that uses the same group of individuals in all of the different treatment conditions is called a
repeated-measures design
or a
within-subjects design.
The main advantage of a repeated-measures study is that it uses exactly the same individuals in all treatment conditions.
11-2 The
t
Statistic for a Repeated-Measures Research Design
The
difference scores
, or D values, are shown in the last column of the table. Typically, the difference scores are obtained by subtracting the first score (before treatment) from the second score (after treatment) for each person.
difference score = D = X2 - X1
It should be noted that the repeated-measures t statistic is conceptually similar to the t statistics we have previously examined:
t = sample statistic - population parameter/estimated standard error
11-3 Hypothesis Tests for the Repeated-Measures Design
In some repeated-measures studies, the researcher has a specific prediction concerning the direction of the treatment effect. This kind of directional prediction can be incorporated into the statement of the hypotheses, resulting in a directional, one-tailed, hypothesis test.
Step 1 -
State the Hypotheses and Select the Alpha Level
Step 2 -
Locate the Critical Region
Step 3 -
Compute the
t
Statistic
Step 4 -
Make a Decision
The repeated-measures
t
statistic requires two basic assumptions:
The observations within each treatment condition must be independent. Notice that the assumption of independence refers to the scores within each treatment. Inside each treatment, the scores are obtained from different individuals and should be independent of one another.
The population distribution of difference scores (D values) must be normal.
11-4 Effect Size, Confidence Intervals, and the Role of Sample Size and Sample Variance for the Repeated-Measures
t
The confidence interval provides an alternative way to measure and describe the treatment effect size. In the case of the repeated-measures
t
-test, the sample mean difference is used to estimate the population mean difference (
μ
). This interval helps quantify the treatment effect by estimating the true difference between the two treatment conditions.
A close look at the sample data from a research study makes it easier to see the size of the treatment effect and to understand the outcome of the hypothesis test.
11-5 Comparing Repeated- and Independent-Measures Design
Changes in scores that are caused by participation in an earlier treatment are called
order effects
and can distort the mean differences found in repeated-measures research studies.
The primary advantage of a repeated-measures design is that it reduces or eliminates problems caused by individual differences.
Individual differences
are characteristics such as age, IQ, gender, and personality that vary from one individual to another. These individual differences can influence the scores obtained in a research study, and they can affect the outcome of a hypothesis test.
In a
matched-subjects design
, each individual in one sample is matched with an individual in the other sample. The matching is done so that the two individuals are equivalent (or nearly equivalent) with respect to a specific variable (or variables) that the researcher would like to control.
