This homework covers Chapter 11, Related Sample t-tests. Each question is worth 1 point unless noted. Feel free to add in as much space as necessary to respond to problems. Show your work. Round your answers to 2 decimal places as needed. There are a total of 39 points in this assignment; it is worth 3% of your final grade, just like the other homework assignments.
1.For each study design below, choose whether it is a one-sample t-test, an independent t-test, or a related-samples t-test.
a.The average GPA for incoming first year students at UML is computed and compared to the national average GPA for first year students throughout the country.
b.A gym class takes a fitness test and then after 10 weeks of training takes another fitness test and the before and after scores are compared.
c.The average test scores for a class of students taking Research I with one professor are compared with scores from a different class of students taking research one with another professor.
2.What is the denominator for the repeated-measures t-test?
3.What is the alternate hypothesis for the repeated-measures t-test?
4.The following data were obtained from a repeated-measures research study. What is the value of MD for these data?
Subject |
1^{st} |
2^{nd} |
1 |
3 |
4 |
2 |
2 |
6 |
3 |
5 |
8 |
4 |
5 |
7 |
6.What is the null hypothesis, generally, for the repeated-measures t-test?
7.A repeatedmeasures study uses a sample of n = 37 participants. What are the degrees of freedom for a t-test?
8.A researcher uses a repeated-measures study to compare two treatment conditions with a set of 98 scores in each treatment. What would be the value of df for the repeated-measures t statistic? Think about this carefully. (Hint: Be sure you understand what n is in a repeated measures study, and how you get the df.)
9.A repeated-measures study and an independent-measures study both produced a t statistic with df = 47.
a.How many individuals participated in each study? (Hint: It’s not the same number for both!)
b.Explain your answer to 10a.
10.A sample of difference scores has a MD = 23 with a variance of s² = 64. If effect size is measured using Cohen’s d, what is the value of d? (Hint: Use the formula for Cohen’s d, and remember that the standard deviation is the square root of the variance!)
11.A researcher obtains t(27) = 3.00 for a repeated-measures study. What is r2?
12.A researcher conducts a repeated-measures study to evaluate a treatment with a sample of n = 35 participants and obtains a t statistic of t = 4.29 and a sig (or p) value for that specific t value of .055. The treatment is expected to increase scores, and the sample mean does show an increase. Do we accept or reject the null for a one tailed test using α = .05?
13.A report describing the results from a repeated-measures study states: “The data show no significant difference between the two treatments, t(18) = 1.65, p > .05.” Based on this statement, what is the total number of individuals in the research study? (Hint: If you are confused, review the slide on “APA in focus” on presenting a repeated-measures t-test.)
14.A sample of college students get a Study Skills Workshop. Each student’s grade point average (GPA) is recorded before the workshop and after the workshop. The average GPA improved by MD = 0.50. The 95% confidence interval is .50 plus or minus .05. What does that mean, in terms of the actual numerical improvement in GPA?
15.Briefly describe one advantage and one disadvantage of using a repeated-measures design as opposed to an independent-measures design. Don’t just say whatever comes into your head, have a look at the slides or text.
16.A researcher wants to examine how the chemical tryptophan, contained in foods such as turkey, can affect mental alertness, at an alpha of .05, two tailed. A sample of n = 35 college students is obtained and each student’s performance on a familiar video game is measured before and after eating a traditional Thanksgiving dinner including roast turkey.
After the meal, the average decrease in scores was M = 8 points, with s² = 322 for the difference scores.
a.What are the df?
b.What is the standard error? Make sure you calculate the standard error for a related-samples t-test.
c.What is the calculated value of t?
d.Assume the critical cutoff for a two-tailed t is plus or minus 2.35. Is your finding significant or not? Say something about why you can or cannot reject the null
e.Compute r2 to measure the size of the effect.
f.Write a sentence demonstrating how the outcome of the test and the measure of effect size would appear in a research report.
SPSS Portion
Independent Sample t-test
There is research being conducted on chow for small dogs. Below are the comparison between weights (wt) of a group of dogs with normal food and with the special food. Group 1 is the group that had the Normal Diet, and Group 2 is the group that had the Special Diet.
Wt Group
4 1
6 1
5 1
5 1
6 1
5 1
4 1
6 1
5 1
4 1
9 2
8 2
6 2
8 2
5 2
6 2
8 2
7 2
4 2
5 2
Once you have entered the data in SPSS (you can copy and paste the table from above into SPSS, instead of entering it by hand),
Go to Analyze → Compare Means → Independent Samples.
You will see a dialogue box that has boxes for “Test Variables” and “Grouping Variables.”
Click on the weight variable to go in the “Test Variable” box, and the group variable to go in the “Grouping Variable” box.
Under the “Grouping Variable” box you will see where it says “Define Groups…” Click on that.
Another dialogue box will open which says “Define Groups.”
Put a 1 in the “Group 1” box and a 2 in the “Group 2” box (you have just told the program that your data is divided into two groups, and that the groups are identified with the number 1 and the number 2.) Then hit OK. An output box will open. Copy and paste that output into your homework document.
Use the output to respond to the following questions:
17. Looking at the “Group Statistics” output box, what is the mean and standard deviation for weight in group one, and in group two?
18.Look at the next output box that says “Independent Samples Test.” Ignore the first two columns about Levene’s equality of variances—this is not the outcome of the t-test, you don’t need to focus on that right now. Go right to the columns with t and df.
a.What are the t and the df in the first row of data in this box (in the “equal variances assumed” row)?
b.What is the significance level? Make sure it is for the t-test, not the Levene’s test. What does this mean about whether we are “in” the null distribution? (2 points)
c.Are the weights for the Normal and Special diets different or not different, according to this test?
d.What is the 95% confidence interval for the difference (it is in the output!), and what do these numbers mean in words? (2 points)
Repeated Measures t-test
Enter the below data, being sure to keep it aligned. There is research being conducted on chow for small dogs. Below are the comparison between weights of a group of the same dogs before and after the special diet.
Before After
9.00 4.00
8.00 6.00
6.00 5.00
8.00 5.00
5.00 6.00
6.00 5.00
8.00 4.00
7.00 6.00
4.00 5.00
5.00 4.00
Once you have entered the data (again, you can copy and paste it),
Go to Analyze → Compare Means → Paired-Samples t-test.
A dialogue box will open, with a spot for “paired variables.”
Put one variable into the box for “Variable1,” and the other into the box for “Variable2” (not below it).
Then click “OK.” You will get more output. Copy and paste the output into your homework document.
19. Looking at the group statistics box,
a.What are the mean and standard deviation for their weight at time one, and at time two?
b.Where have you seen these numbers before?
20. Now look below at the paired samples test.
a.What is the t value?
b.Is it significant?
c.Is it the same or different from the t value from the test above?
d.The data are the same in both cases. If the t value is different, why do you think that is? (2 points)