?For the data in the following matrix: (a) Which two means are compared to describe the

Define each of the following terms: (a) Factor (b) Level (c) Two-factor study

The structure of a two-factor study can be presented as a matrix with the levels of one factor determining the rows and the levels of the second factor determining the columns. With this structure in mind, describe the mean differences that are evaluated by each of the three hypothesis tests that make up a two-factor ANOVA.

Briefly explain what happens during the second stage of the two-factor ANOVA.

For the data in the following matrix: (a) Which two means are compared to describe the treatment main effect? (b) Which two means are compared to describe the gender main effect? (c) Is there an interaction between gender and treatment? Explain your answer.

The following matrix presents the results from an independent-measures, two-factor study with a sample of n = 10 participants in each treatment condition. Note that one treatment mean is missing. (a) What value for the missing mean would result in no main effect for factor A? (b) What value for the missing mean would result in no main effect for factor B? (c) What value for the missing mean would result in no interaction?

The following matrix presents the results of a two-factor study with n = 10 scores in each of the six treatment conditions. Note that one of the treatment means is missing. (a) What value for the missing mean would result in no main effect for factor A? (b) What value for the missing mean would result in no interaction?

For the data in the following graph: (a) Is there a main effect for the treatment factor? (b) Is there a main effect for the age factor? (c) Is there an interaction between age and treatment?

A researcher conducts an independent-measures, two-factor study with two levels of factor A and two levels of factor B, using a sample of n = 8 participants in each treatment condition. (a) What are the df values for the F-ratio evaluating the main effect of factor A? (b) What are the df values for the F-ratio evaluating the main effect of factor B? (c) What are the df values for the F-ratio evaluating the interaction?

A researcher conducts an independent-measures, two-factor study with two levels of factor A and three levels of factor B, using a sample of n = 10 participants in each treatment condition. (a) What are the df values for the F-ratio evaluating the main effect of factor A? (b) What are the df values for the F-ratio evaluating the main effect of factor B? (c) What are the df values for the F-ratio evaluating the interaction?

A researcher conducts an independent-measures, two-factor study using a separate sample of n = 5 participants in each treatment condition. The results are evaluated using an ANOVA and the researcher reports an F-ratio with df = 1, 24 for factor A, and an F-ratio with df = 2, 24 for factor B. (a) How many levels of factor A were used in the study? (b) How many levels of factor B were used in the study? (c) What are the df values for the F-ratio evaluating the interaction?

A researcher conducts an independent-measures, two-factor study using a separate sample of n = 10 participants in each treatment condition. The results are evaluated using an ANOVA and the researcher reports an F-ratio with df = 2, 108 for factor A, and an F-ratio with df = 3, 108 for factor B. (a) How many levels of factor A were used in the study? (b) How many levels of factor B were used in the study? (c) What are the df values for the F-ratio evaluating the interaction?

The following results are from an independent-measures, two-factor study with n = 10 participants in each treatment condition. (a) Use a two-factor ANOVA with \(\alpha = .05\) to evaluate the main effects and the interaction. (b) Compute \(\eta^{2}\) to measure the effect size for each of the main effects and the interaction. Text Transcription: alpha=.05 eta^2

The following results are from an independent-measures, two-factor study with n = 5 participants in each treatment condition. (a) Use a two-factor ANOVA with \(\alpha = .05\) to evaluate the main effects and the interaction. (b) Test the simple main effects using \(\alpha = .05\) to evaluate the mean difference between treatment \(A_{1 }\) and \(A_{2}\) for each level of factor B. Text Transcription: alpha=.05 A_1 A_2

Most sports injuries are immediate and obvious, like a broken leg. However, some can be more subtle, like the neurological damage that may occur when soccer players repeatedly head a soccer ball. To examine effects of repeated heading, McAllister et al. (2012) examined a group of football and ice hockey players and a group of athletes in noncontact sports before and shortly after the season. The dependent variable was performance on a conceptual thinking task. Following are hypothetical data from an independent-measures study similar to the one by McAllister et al. The researchers measured conceptual thinking for contact and noncontact athletes at the beginning of their first season and for separate groups of athletes at the end of their second season. (a) Use a two-factor ANOVA with \(\alpha = .05\) to evaluate the main effects and interaction. (b) Calculate the effects size (\(\eta^{2}\)) for the main effects and the interaction. (c) Briefly describe the outcome of the study. Text Transcription: alpha=.05 (eta^2)

Research results indicate that 5-year-old children who watched a lot of educational programming such as Sesame Street and Mr. Rogers had higher high-school grades than their peers (Anderson, Huston, Wright, & Collins, 1998). The same study reported that 5-year old children who watched a lot of non-educational TV programs had relatively low high-school grades compared to their peers. A researcher attempting to replicate this result using an independent-measures study with four separate groups of high school students obtained the following data. The dependent variable is a rating of high school academic performance, with higher scores indicating higher levels of performance. (a) Use a two-factor ANOVA with \(\alpha = .01\) to evaluate the main effects and interaction. (b) Calculate the effect size (\(\eta^{2}\)) for the main effects and the interaction. (c) Briefly describe the outcome of the study. Text Transcription: alpha=.01 eta^2

Some people like to pour beer gently down the side of the glass to preserve bubbles. Others, splash it down the center to release the bubbles into a foamy head and free the aromas. Champagne, however, is best when the bubbles remain concentrated in the wine. A group of French scientists recently verified the difference between the two pouring methods by measuring the amount of bubbles in each glass of champagne poured two different ways and at three different temperatures (Liger-Belair et al., 2010). The following data present the pattern of results obtained in the study. (a) Use a two-factor ANOVA with \(\alpha = .05\) to evaluate the mean differences. (b) Briefly explain how temperature and pouring influence the bubbles in champagne according to this pattern of results. Text Transcription: alpha=.05 eta^2

The following table summarizes the results from a two-factor study with 2 levels of factor A and 4 levels of factor B using a separate sample of n = 5 participants in each treatment condition. Fill in the missing values. (Hint: Start with the df values.)

The following table summarizes the results from a two-factor study with 2 levels of factor A and 3 levels of factor B using a separate sample of n = 8 participants in each treatment condition. Fill in the missing values. (Hint: Start with the df values.)

The following table summarizes the results from a two-factor study with 2 levels of factor A and 2 levels of factor B using a separate sample of n = 15 participants in each treatment condition. Fill in the missing values. (Hint: Start with the df values.)

The following data are from a two-factor study examining the effects of two treatment conditions on males and females. (a) Use an ANOVA with \(\alpha = .05\) for all tests to evaluate the significance of the main effects and the interaction. (b) Compute \(\eta^{2}\)to measure the size of the effect for each main effect and the interaction. Text Transcription: alpha=.05 eta^2

The following data are from a two-factor study examining the effects of three treatment conditions on males and females. (a) Use an ANOVA with \(\alpha = .05\) for all tests to evaluate the significance of the main effects and the interaction. (b) Test the simple main effects using \(\alpha = .05\) to evaluate the mean difference between males and females for each of the three treatments. Text Transcription: alpha=.05

The following data are representative of many studies examining the relationship between arousal and performance. The general result of these studies is that increasing the level of arousal (or motivation) tends to improve the level of performance. (You probably have tried to “psych yourself up” to do well on a task.) For very difficult tasks, however, increasing arousal beyond a certain point tends to lower the level of performance. (Your friends have probably advised you to “calm down and stay focused” when you get overanxious about doing well.) This relationship between arousal and performance is known as the Yerkes-Dodson law. (a) Use a two-factor ANOVA with \(\alpha = .05\) to evaluate the significance of the main effects and the interaction. (b) Calculate the \(\eta^{2}\) values to measure the effect size for the two main effects. (c) Describe the pattern of results. How does the level of arousal (motivation) affect performance? Text Transcription: alpha=.05 eta^2

Kirschner and Karpinski (2010) report that college students who are on Facebook (or have it running in the background) while studying had lower grades than students who did not use the social network. A researcher would like to know if the same result extends to students in lower grade levels. The researcher planned a two-factor study comparing Facebook users with non-users for middle school students, high school students, and college students. For consistency across groups, grades were converted into six categories, numbered 0–5 from low to high. The results are presented in the following matrix. (a) Use a two-factor ANOVA with \(\alpha = .05\) to evaluate the mean differences. (b) Describe the pattern of results. Text Transcription: alpha=.05

In Chapter 11 we described a research study in which the color red appeared to increase men’s attraction to women (Elliot & Niesta, 2008). The same researchers have published other results showing that red also increases women’s attraction to men but does not appear to affect judgments of same sex individuals (Elliot et al., 2010). Combining these results into one study produces a two-factor design in which men judge photographs of both women and men, which are shown on both red and white backgrounds. The dependent variable is a rating of attractiveness for the person shown in the photograph. The study uses a separate group of participants for each condition. The following table presents data similar to the results from previous research. (a) Use a two-factor ANOVA with \(\alpha = .05\) to evaluate the main effects and the interaction. (b) Describe the effect of background color on judgments of males and females. Text Transcription: alpha=.05

In a classic research study, Shrauger (1972) examined the effect of an audience on the performance of two different personality types. Data from this experiment are as follows. The dependent variable is the number of errors made by each participant. (a) Use an ANOVA with \(\alpha = .05\) to evaluate the data. Describe the effect of the audience and the effect of self-esteem on performance. (b) Calculate the effect size (\(\eta^{2}\)) for each main effect and for the interaction. Text Transcription: alpha=.05 (eta^2)