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Assignment Instructions: The t-test for two measures (paired samples)
To-Do Date
Assignment Instructions: The t-test for two measures (paired samples)
To-Do Date: Apr 2 at 11:59pm
INSTRUCTIONS:
Start the assignment below immediately, but only after reading the illustration that shows you how to do the assignment. Ask further questions about the assignment in the discussion as you work on it.
Enumerate your answers to the questions, as below. When you have completed the assignment, you will use the Assignment tab at the end of the Canvas module to submit your work for grading and comment.
Unlike the other assignments in this class, you will not use the NCS data file. Instead, enter the hypothetical data below in SPSS to use for the assignment. The SPSS commands: ′file′, ′new′, ′data′ will create a spreadsheet in which to enter the data below (manually).
Case Before After
1 5 6
2 4 7
3 5 5
4 4 6
5 5 5
6 6 6
7 5 5
8 4 6
9 5 5
10 5 10
The hypothetical data above are from a hypothetical experiment in which 10 participants were assessed for depression before and after treatment with psilocybin (high numbers indicate high depression).
In conceptual terms, the hypothesis is that depression will differ after treatment (hopefully, lower, but possibly higher). State this hypothesis in statistical terms and include the correct notation.
Explain why the t-test for dependent (paired) samples is the appropriate test for the hypothesis in terms of the formula for t (see page 218).
Compute the means, standard deviations, and t-test (see pages 221-223). Upload the SPSS output file.
Compute and interpret the effect size (ES) for the differences between means (see page 225).
Are the differences between the measures meaningful? why or why not?
Summarize the results of the t-test, including the correct notation (see page 224). Is t statistically significant? What is the probability of a type 1 error? Should you reject or retain the null hypothesis?
Are the differences between the measures likely in the population? why or why not?
What is a possible biased conclusion that might be drawn from the results you reported above?
Assignment Illustration: The t test for two measures (paired samples)
To-Do Date: Apr 2 at 11:59pm
In conceptual terms, the hypothesis is that depression will differ after treatment (hopefully, lower, but possibly higher). State this hypothesis in statistical terms and include the correct notation.
For illustration, assume a researcher tests the hypothesis that weight will differ after dieting (presumably, weight will be lower, but research shows that people gain weight after dieting)
The statistical hypotheses are:
Null hypothesis: The mean weight before dieting equals the mean weight after dieting.
H0: u pre ＝ u post
Research Hypothesis: The mean weight before dieting does not equal the mean weight after dieting
H0: M pre
≠
M post.
2. Explain why the t-test for dependent (paired) samples is the appropriate test for the hypothesis in terms of the formula for t (see page 218).
The t-test for paired samples is appropriate because it computes the mean of the differences between pairs of scores for two measures, and accounts for the variability and sample size for the differences between the two measures.
3. Compute the means, standard deviations, and t-test (see pages 221-223). Upload the SPSS output file.
Assume you computed the following: M pre ＝ 120, SD pre ＝ 5, M post ＝ 150, SD post ＝ 4, t (999) ＝ 7.5, p ˂ .01.
4. Compute and interpret the effect size (ES) for the differences between means (see page 225)
Assume you computed an ES ＝ 5. This is a large effect size.
5. Are the differences between the measures meaningful? why or why not?
Large effect sizes are likely to be meaningful (moderate effect sizes are somewhat meaningful, and small effect sizes are less likely to be meaningful)
6. Summarize the results of the t-test, including the correct notation (see page 224). Is t statistically significant? What is the probability of a type 1 error? Should you reject or retain the null hypothesis?
Weight is significantly higher after dieting, t (999) ＝ 7.5, p ˂ .01. Reject the null hypothesis because the probability of error is less than 1%.
7. Are the differences between the measures likely in the population? why or why not?
The difference is likely in the population given that t is significant, not due to sampling error.
9. What is a possible biased conclusion that might be drawn from the results you reported above?
Biased conclusions would include…
– the difference would be found in populations other than the one sampled
– dieting causes weight gain (you need a control group to determine cause and effect; the pre-post differences may have occurred without dieting)
– the difference is meaningful because t is statistically significant (meaningfulness is based on the effect size, or other information, not t)
– the difference is statistically significant because the effect size is large (significance is based on t, not the effect size)
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