{"id":115,"date":"2024-08-21T12:05:21","date_gmt":"2024-08-21T12:05:21","guid":{"rendered":"http:\/\/localhost\/researchmethods\/?post_type=content&p=115"},"modified":"2024-09-13T11:13:02","modified_gmt":"2024-09-13T11:13:02","slug":"chapter-23-multi-factorial-anova-designs","status":"publish","type":"content","link":"https:\/\/staging.routledgelearning.com\/researchmethods\/student-resources\/chapter-23-multi-factorial-anova-designs\/","title":{"rendered":"Chapter 23 – Multi-factorial ANOVA designs"},"content":{"rendered":"\n
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\n\tHome<\/a>\n<\/span>\u203a<\/span>\n\tStudent Resources<\/a>\n<\/span>\u203a<\/span>\n\tChapter 23 \u2013 Multi-factorial ANOVA designs\n<\/span><\/div>\n\n

Chapter 23 – Multi-factorial ANOVA designs<\/h1>\n\n\n

This chapter deals with between groups multi-factorial ANOVA, where more than one independent variable is manipulated or observed. <\/p>\n<\/div>\n<\/div>\n\n\n\n

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Exercises<\/h2>\n\n\n\n

Exercise 23.1<\/h3>\n\n\n\n

Calculating two way unrelated ANOVA on a new data set<\/strong><\/p>\n\n\n\n

The data set used to calculate the example of a two-way unrelated ANOVA in this chapter is provided below and is named two way unrelated (book).sav. An Excel file with the same name is also provided.<\/p>\n\n\n\n

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Download – Two way unrelated (book) Data Sets<\/a><\/div>\n<\/div>\n\n\n\n

The data set provided below (two-way unrelated ex) is one of fictitious data from a research project on leadership styles. Each participant has an LPC score, which stands for \u2018least preferred co-worker\u2019. People with high scores on this variable are able to get along with and accept relatively uncritically even those workers whom they least prefer to interact with. Such people make good leaders when situations at work are difficult (they are \u2018people oriented\u2019). By contrast low LPC people make good task leaders and are particularly effective when working conditions are good but tend to do poorly as leaders when conditions are a little difficult.<\/p>\n\n\n\n

The variables in the file are sitfav with levels of highly favourable and moderately favourable (work conditions) and lpclead with levels of high and low being the categories of high and low LPC scorers. Hence in these results we would expect to find an interaction between situation favourability and LPC leadership category. High LPC people should do well in moderately favourable conditions whereas low LPC people should do well in highly favourable conditions. How well the leaders do is the dependent variable and is measured on a scale of 1-10 as assessed by a panel of independent raters. Let\u2019s see what the spoof data says. Conduct a two-way unrelated ANOVA analysis, including relevant means and standard deviations, and checking for homogeneity of variance and for effect sizes and power for each test.<\/p>\n\n\n\n

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Download – 2 way unrelated EX Data Sets<\/a><\/div>\n<\/div>\n\n\n\n

The answers I got are revealed when you select the button below.<\/p>\n\n\n\n

Show answer<\/summary>\n

The main effect for LPC leadership is not significant (overall one type of leader did no better than the other), F<\/em>(1,20) = 0.220, p<\/em> = .644. The main effect for situation was also not significant (leadership performances overall were similar for highly and moderately favourable conditions), F<\/em>(1,20) = 0.220, p<\/em> = .644). However, there was a significant interaction between situation and leadership type. In highly favourable conditions, High LPC leaders (M = 5.33, SD = 1.03) scored lower than low LPC leaders (M = 6.5, SD = 1.64), whereas in moderately favourable conditions they scored higher (M = 7.0, SD = 1.41) than low LPC leaders (M = 5.33, SD = 1.03), F<\/em>(1,20) = 7.049, p<\/em> = .015. Levene\u2019s test for homogeneity of variance was not significant so homogeneity was assumed. Partial eta-squared for the interaction was .261 with power estimated at .714.<\/p>\n<\/details>\n\n\n\n

Exercise 23.2<\/h3>\n\n\n\n

Interpreting an SPSS output for a two-way unrelated analysis.<\/strong><\/p>\n\n\n\n

Here is part of the SPSS output data for a quasi-experiment in which participants were grouped according to their attitude towards students. This is the \u2018attitude group\u2019 variable in the display below. Each group was exposed to just one of several sets of information about a fictitious person including their position on reintroducing government grants to students. Participants were later asked to rate the person on several characteristics including \u2018liking\u2019. It can be assumed for instance that participants who were pro students would show a higher liking for someone who wanted to introduce grants than someone who didn\u2019t. Study the print out and try to answer the questions below.<\/p>\n\n\n\n

Levene’s test of equality of error variancesa<\/strong><\/p>\n\n\n\n

Dependent Variable: liking<\/p>\n\n\n\n

F<\/td>df1<\/td>df2<\/td>Sig.<\/td><\/tr>
2.757<\/td>5<\/td>41<\/td>.031<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Tests of between-subjects effects<\/strong><\/p>\n\n\n\n

Dependent Variable: liking<\/p>\n\n\n\n

Source<\/td>Type III sum of squares<\/td>df<\/td>Mean square<\/td>F<\/td>Sig.<\/td><\/tr>
Corrected Model<\/td>114.601a<\/td>5<\/td>22.920<\/td>7.947<\/td>.000<\/td><\/tr>
Intercept<\/td>1880.558<\/td>1<\/td>1880.558<\/td>652.033<\/td>.000<\/td><\/tr>
Information<\/td>3.670<\/td>2<\/td>1.835<\/td>.636<\/td>.534<\/td><\/tr>
Attitudegroup<\/td>15.953<\/td>1<\/td>15.953<\/td>5.531<\/td>.024<\/td><\/tr>
Information * attitudegroup<\/td>93.557<\/td>2<\/td>46.778<\/td>16.219<\/td>.000<\/td><\/tr>
Error<\/td>118.250<\/td>41<\/td>2.884<\/td> <\/td> <\/td><\/tr>
Total<\/td>2135.000<\/td>47<\/td> <\/td> <\/td> <\/td><\/tr>
Corrected total<\/td>232.851<\/td>46<\/td> <\/td> <\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
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  1. R Squared = .492 (Adjusted R Squared = .430)<\/li>\n<\/ol>\n\n\n\n
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