Exam 11: The T Test for Two Related Samples

A sample of n = 9 college students is used to evaluate the effectiveness of a new Study Skills Workshop.Each student's grade point average (GPA)is recorded for the semester before the workshop and for the semester after the workshop.The average GPA improved by M_D = 0.60 points with s² = 0.09.The researcher would like to use the sample to estimate how much effect the workshop would have for the entire college population.What is the 80% confidence interval for these data?​

A researcher uses a repeated-measures study to compare two treatment conditions with a set of 20 scores in each treatment.What would be the value of df for the repeated-measures t statistic?​

A repeated-measures test usually is more likely to detect a real treatment effect than an independent-measures test because the repeated-measures design typically has a smaller variance and a smaller estimated standard error.

The estimated standard error in the denominator of the repeated-measures t statistic measures the average mean difference that is expected for a sample when there is a zero mean difference for the population.

What is indicated by a large variance for a sample of difference scores?​

A sample of difference scores has a mean of M_D = 5 with a variance of s² = 100.If effect size is measured using Cohen's d,what is the value of d?​

A researcher obtains t = 2.35 for a repeated-measures study using a sample of n = 8 participants.Based on this t value,what is the correct decision for a two-tailed test?​

For a repeated-measures design,the sample mean difference is always located exactly in the center of the confidence interval estimate for the population mean difference.

Although the original data for a repeated-measures study consist of two scores for each participant,the calculation of the mean and variance are done with only one score for each participant.

A repeated-measures research study comparing two treatments with a set of 10 scores in each treatment will produce a t statistic with df = 19.

One of the major advantages of a repeated-measures design is that it removes individual differences from the variance and,therefore,reduces the standard error.The following two sets of data demonstrate this fact.The first set of data represents the original results from a repeated-measures study.To create the second set of data we started with the original scores but increased the individual differences by adding 10 points to each score for subject B,adding 20 points to each score for subject C,and adding 30 points to each score for subject D.Note that this change produces a huge increase in the differences from one subject to another and a huge increase in the variability of the scores within each treatment condition.​​ ​ a. Find the difference scores for each set of data and compute the mean and variance for each sample of difference scores. b. You should find that both sets of data produce the same mean difference and the same variance for the difference scores. Explain what happened to the huge individual differences that were added to the second set of data.

What is the value of the estimated standard error for the following set of D-scores?Scores: 2,2,10,2​

A repeated-measures study and an independent-measures study both produce a t statistic with df = 20.The repeated-measures study used more subjects than the independent-measures study.

A related-sample design consists of scores in one set that are directly related,one-to-one,with the scores in the second set.

One advantage of a repeated-measures design is that it typically requires fewer participants than an independent-measures design.

A researcher would like to determine if relaxation training will affect the number of headaches for chronic headache sufferers.For a week prior to training,each participant records the number of headaches suffered.Participants then receive relaxation training and for the week following training the number of headaches is again measured.The data are as follows: Before After 6 4 5 1 3 3 3 1 6 2 2 1 4 3 4 2 a. Compute the mean and variance for the sample of difference scores. b. Do the results indicate a significant difference? Use a two-tailed test with α = .05. c. Compute Cohen's d to measure the size of the effect.

If the null hypothesis is true,what value is expected,on average,for the repeated-measures t statistic?​

For a repeated-measures study,a small variance for the difference scores indicates that the treatment effect is consistent across participants.

If other factors are held constant,which set of data is most likely to produce a significant value for the repeated-measures t statistic?​

A repeated-measures design has the maximum advantage over an independent-measures design when ____.​