?Describe some of the reasons that group means might be different from each other in an

Why should you use ANOVA instead of several t tests to evaluate mean differences when an experiment consists of three or more treatment conditions?

Suppose that you conduct three different t-tests to analyze the results of an experiment with three independent samples. Each individual t-test uses \(\alpha=.05\). What is the probability of a Type 1 error occurring in any of the hypothesis tests? Is it greater than, equal to, or less than \(.05\)? Equation Transcription: Text Transcription: alpha =.05 .05

What value is expected for the F-ratio, on average, if the null hypothesis is true in an ANOVA? Explain why.

Describe some of the reasons that group means might be different from each other in an analysis of variance. Describe some of the reasons that individual scores might be different from each other.

Describe the similarities between an F-ratio and a t statistic.

Calculate \(S S_{\text {total }}\), \(S S_{\text {between }}\), and \(S S_{\text {within }}\) for the following set of data:

Calculate \(S S_{\text {total }}\), \(S S_{\text {between }}\), and \(S S_{\text {within }}\) for the following set of data:

A researcher uses an ANOVA to compare six treatment conditions with a sample of n = 12 in each treatment. For this analysis, find \(d f_{\text {total }}\), \(d f_{\text {between }}\), and \(d f_{\text {within }}\).

A researcher reports an F-ratio with \(d f_{\text {between }}=3\) and \(d f_{\text {within }}=40\) for an independent-measures ANOVA. a. How many treatment conditions were compared in the experiment? b. How many subjects participated in the experiment? c. Use Appendix B to find the critical value for F. Use \(\alpha=.05\). d. What is the critical region for \(\alpha=.01\)?

A researcher reports an F-ratio with df = 4, 62 from an independent-measures research study. a. How many treatment conditions were compared in the study? b. What was the total number of participants in the study? c. Use Appendix B to find the critical value for F. Use \(\alpha = .05\). d. What is the critical region for \(\alpha = .01\)?

The following values are from an independent-measures study comparing three treatment conditions. a. Compute the variance for each sample. b. Compute \(M S_{\text {within }}\), which would be the denominator of the F-ratio for an ANOVA. Because the samples are all the same size, you should find that \(M S_{\text {within }}\) is equal to the average of the three sample variances.

The following values are from an independent-measures study comparing three treatment conditions. a. Compute the variance for each sample. b. Compute \(M S_{\text {within }}\), which would be the denominator of the F-ratio for an ANOVA.

A researcher conducts an experiment comparing three treatment conditions with a separate sample of n = 6 in each treatment. An ANOVA is used to evaluate the data, and the results of the ANOVA are presented in the following table. Complete all missing values in the table. Hint: Begin with the values in the df column.

The following summary table presents the results from an ANOVA comparing five treatment conditions with n = 5 participants in each condition. Complete all missing values. (Hint: Start with the df column.)

A developmental psychologist is examining the development of language skills from age 2 to age 4. Three different groups of children are obtained, one for each age, with n = 16 children in each group. Each child is given a language-skills assessment test. The resulting data were analyzed with an ANOVA to test for mean differences between age groups. The results of the ANOVA are presented in the following table. Fill in all missing values.

The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with \(\alpha=.05\) to determine whether there are any significant mean differences among the treatments.

Many know the feeling of being too groggy to take an 8 a.m. exam—we need to be more alert and aroused to do our best. Some of us also know the feeling of being too aroused by the prospect of an exam to do our best. Thus, the best level of performance occurs when we are in the Goldilocks zone—not too aroused and not too groggy. Simon and Moghaddam (2016) recently replicated this observation in rats. Subjects were randomly assigned to one of three groups. Each group received a different dose (none, a medium dose, or a high dose) of Ritalin, which is a stimulant. Researchers measured the rats’ learning and cognitive performance and observed the highest level of performance in the group that received a medium dose of Ritalin. Suppose that the following data were obtained from a similar independent-measures research study comparing three treatment conditions. a. Use an \(A N O V A\) with \(\alpha=.05\) to determine whether there are any significant mean differences among the treatments. b. What test would a researcher use to compare the No Drug group to the High Dose group? c. Write the results of the \(A N O V A\) as they would appear in a research article. Equation Transcription: Text Transcription: ANOVA alpha =.05

Open positions in the highest-paying jobs, the best internships, and the most prestigious graduate programs can attract many applicants. Initial evaluations of applications are usually based on the applicant’s résumé or curriculum vitae. In a recent study, researchers demonstrated that two different kinds of fancy “graphical résumés,” which include graphic descriptions of things like the timeline of an applicant’s education, are no more effective than traditional text-based résumés (Popham, Lee, Sublette, Kent, & Carswell, 2017). In many ways, they actually might be worse. Suppose that a researcher is interested in studying the effect of résumé type on participants’ ratings of the competence of the job applicant. She randomly assigns participants to one of three groups. Group 1 receives a traditional text-based résumé. Group 2 receives a graphic résumé with photos of the college that was listed under the applicant’s education. Group 3 receives a graphic résumé with charts summarizing the amount of time the hypothetical applicant spent at each of their previous jobs. All participants rate the perceived competence of the job applicant. The hypothetical data are listed below. a. Use an ANOVA with \(\alpha=.05\) to determine whether there are any significant mean differences among the treatments. b. Suppose that a researcher wanted to compare text résumés to graphic type 1 résumés only. What test statistic would the researcher use? c. Write the results of the ANOVA as they would appear in a research article.

The following data were obtained from an independent-measures research study comparing three treatment conditions. Use an ANOVA with \(\alpha=.05\) to determine whether there are any significant mean differences among the treatments.

A research study comparing three treatment conditions produces T = 20 with n = 4 for the first treatment, T = 10 with n = 5 for the second treatment, and T = 30 with n = 6 for the third treatment. Calculate \(S S_{\text {between treatments }}\) for these data.

A research study comparing three treatment conditions produces T = 28 with n = 7 for the first treatment, T = 32 with n = 8 for the second treatment, and T = 108 with n = 9 for the third treatment. Calculate \(S S_{\text {between treatments }}\) for these data.

The following values are from an independent-measures study comparing three treatment conditions. a. Compute the variance for each sample. b. Compute \(M S_{\text {within }}\), which would be the denominator of the F-ratio for an ANOVA. Because the samples are all the same size, you should find that \(M S_{\text {within }}\) is equal to the average of the three sample variances.

A research report from an independent-measures study states that there are significant differences between treatments, F(4, 40) = 3.45, p < .05. a. How many treatment conditions were compared in the study? b. What was the total number of participants in the study? c. Would the result be significant if \(\alpha=.01\)?

Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or the denominator of the F-ratio, and indicate whether the size of the F-ratio would increase or decrease. a. Increase the differences between the sample means. b. Increase the size of the sample variances within each group.

A researcher used ANOVA and computed F = 4.25 for the following data. a. If the mean for Treatment III were changed to M = 25, what would happen to the size of the F-ratio (increase or decrease)? Explain your answer. b. If the SS for Treatment I were changed to SS = 1,400, what would happen to the size of the F-ratio (increase or decrease)? Explain your answer.

The following data were obtained from an independent-measures study comparing three treatment conditions. a. Calculate the sample variance for each of the three samples. b. Use an ANOVA with \(\alpha=.05\) to determine whether there are any significant differences among the three treatment means. (Note: In the ANOVA you should find that \(M S_{\text {within }}\) is equal to the average of the three sample variances.)

For the preceding problem you should find that there are significant differences among the three treatments. One reason for the significance is that the sample variances are relatively small. To create the following data, we kept the same sample means that appeared in problem 26 but doubled the SS values within each sample. a. Calculate the sample variance for each of the three samples. Describe how these sample variances compare with those from problem 26. b. Predict how the increase in sample variance should influence the outcome of the analysis. That is, how will the F-ratio for these data compare with the value obtained in problem 19? c. Use an ANOVA with \(\alpha=.05\) to determine whether there are any significant differences among the three treatment means. (Does your answer agree with your prediction in part b?)

The following data were observed in an independent-measures study comparing three treatment conditions. a. Use an ANOVA with \(\alpha=.05\) to determine whether there are any significant differences among the three treatment means. Note: Because the samples are all the same size, \(M S_{\text {within }}\) is the average of the three sample variances. b. Calculate \(\eta^{2}\) to measure the effect size for this study.

The following data summarize the results from an independent-measures study comparing three treatment conditions. a. Use an ANOVA with \(\alpha=.05\) to determine whether there are any significant differences among the three treatment means. Note: Because the samples are all the same size, \(M S_{\text {within }}\) is the average of the three sample variances. b. Calculate \(\eta^{2}\) to measure the effect size for this study.

An ANOVA produces an F-ratio with df = 1, 34. Could the data have been analyzed with a t test? What would be the degrees of freedom for the t statistic?

To create the following data we started with the same sample means and variances that appeared in problem 29, but doubled the sample size to \(n=10\). a. Predict how the increase in sample size should affect the F-ratio for these data compared to the values obtained in problem 29. b. Use an ANOVA with \(\alpha=.05\) to check your prediction. Note: Because the samples are all the same size, \(M S_{\text {within }}\) is the average of the three sample variances. c. Predict how the increase in sample size should affect the value of \(\eta^{2}\) for these data compared to the \(\eta^{2}\) in problem 29. Calculate \(\eta^{2}\) to check your prediction.

The following scores are from an independent-measures study comparing two treatment conditions. a. Use an independent-measures t test with \(\alpha =.05\) to determine whether there is a significant mean difference between the two treatments. b. Use an ANOVA with \(\alpha=.05\) to determine whether there is a significant mean difference between the two treatments. You should find that \(F=t^2\).