{"id":530,"date":"2015-07-17T09:22:50","date_gmt":"2015-07-17T13:22:50","guid":{"rendered":"http:\/\/sites.berry.edu\/vbissonnette\/?page_id=530"},"modified":"2016-06-23T10:00:14","modified_gmt":"2016-06-23T14:00:14","slug":"two-factor-anova-cr-design","status":"publish","type":"page","link":"https:\/\/sites.berry.edu\/vbissonnette\/index\/stats-homework\/documentation\/two-factor-anova-cr-design\/","title":{"rendered":"Two-Factor ANOVA (CR Design)"},"content":{"rendered":"

Your homework problem:<\/h3>\n

Aronson, Willerman, & Floyd (1966) investigated the impact of perceived\u00a0 competence on interpersonal liking. Participants were randomly\u00a0 assigned to one of four treatment conditions. In each, they listened to an\u00a0 audio recording of another student playing the part of a contestant on the\u00a0 ‘College Quiz Bowl’ game, where he would have to answer a number of\u00a0 interesting factual questions (similar to ‘Trivial Pursuit’).\u00a0 For half of the participants, the contestant was described as above average\u00a0 in every respect – he was an honor student, the editor of the campus yearbook,\u00a0 and a member of the school track team. For the other half of the participants,\u00a0 the contestant was described as average – he got average grades, he was a\u00a0 proofreader for the yearbook, and he tried out for the track team but did not compete.\u00a0 All the participants listened as the contestant played the Quiz Bowl game and\u00a0 answered many of the questions correctly (same male voice for all). For half of\u00a0 the participants, in the middle of one of his responses, the contestant spilled his\u00a0 coffee all over himself and sounded embarrassed about this accident. For the other\u00a0 half of the participants, the contestant did not spill his coffee.\u00a0 After the completion of the Quiz Bowl, the participants were asked to rate how much\u00a0 they liked the contestant – higher scores indicate greater interpersonal liking.<\/p>\n

Here are some data similar to those collected by Aronson et al.:<\/p>\n\n\n\n\n\n
Ability
\nLevel<\/td>\n		Spilled Coffee<\/td>\nDid Not Spill Coffee<\/td>\n<\/tr>\n
Average Ability<\/td>\n2, 4, 5, 4, 3, 5<\/td>\n6, 4, 4, 5, 6, 3<\/td>\n<\/tr>\n
High Ability<\/td>\n8, 6, 9, 7, 9, 8<\/td>\n6, 4, 5, 7, 3, 6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Did the manipulation of the contestant’s ability and whether or not he\u00a0\u00a0had an accident significantly affect the participants liking for him\u00a0 (alpha = .05)? Conduct a two-factor ANOVA to test the main effect for\u00a0 perceived competence of the contestant, the main effect for whether or\u00a0 not the contestant had an accident, and the interaction between the
\ntwo factors.<\/p>\n

If you would like some help with your hand-written work,\u00a0 click here<\/a>.<\/p>\n

\n

Separate Variable Approach<\/h4>\n

Enter these data into Stats Homework’s\u00a0<\/i> data manager as four separate variables, and rename the variables. It’s important that you name your variables carefully — each\u00a0 variable name indicates the level of perceived ability (‘Avg’ and ‘High,’\u00a0 and the level of accident (‘Yes’ or ‘No’). Your screen should\u00a0 look like this:<\/p>\n

\"anova_cr2_12\"<\/a><\/p>\n

To conduct your analysis,\u00a0 pull down the Analyze<\/b> menu, choose Analysis of Variance<\/b>,\u00a0 and then choose Two-Factor ANOVA for Completely-Randomized Design<\/b>. You\u00a0 will be presented with a dialog that asks you to specify the data-management approach that you are using:<\/p>\n

\"anova_cr2_13\"<\/a><\/p>\n

In this case, you should click the first button — you have entered your data as four separate variables. \u00a0This will take you to the next dialog:<\/p>\n

\"anova_cr2_14\"<\/a>You should enter the names of your two factors — ‘Ability’ and ‘Accident.’ \u00a0Then, enter the number of levels of each factor — 2 and 2. \u00a0Finally, check all the output options and click\u00a0Next Step<\/strong>. \u00a0This brings up the next dialog:<\/p>\n

\"anova_cr2_15\"<\/a><\/p>\n

Here, you will label the levels of each factor. \u00a0Enter ‘Yes’ and ‘No’ for your levels of Accident, and ‘Average’ and ‘High’ for your levels of Ability. \u00a0Now, click\u00a0Next Step<\/strong>. \u00a0This brings up the last dialog:<\/p>\n

\"anova_cr2_16\"<\/a><\/p>\n

Here, you will specify how the variables that you entered into the data manager will be associated with the cells of your experimental design. \u00a0You will click on a variable on the left, and then use the ‘===>’ button to move this variable to your design. \u00a0So, you need to start with the variable that contains the data for the Ability = Average + Accident = Yes cell. \u00a0When you are finished, this dialog should look like this:<\/p>\n

\"anova_cr2_17\"<\/a><\/p>\n

Now you can see why we entered our data into four variables in exactly this order — this makes it quite easy to specify our design for our analysis. In addition, you can now see why it is so important to name your variables in such a way that you indicate the levels of each of your independent variables. Pause here and study this design dialog to make sure that you have set up your analysis correctly.<\/p>\n

Indicator Variable Approach<\/h4>\n

You will enter three variables — two indicator (independent) variables, and one dependent variable. \u00a0You can use numeric or non-numeric indicator variables. \u00a0Your data manager will look something like this:<\/p>\n

\"anova_cr2_25\"<\/a><\/p>\n

Note that I prefer to use non-numeric indicator variables. \u00a0This makes it clear which cell is which. \u00a0You will see this clarity when you see the results for this analysis. \u00a0When you call on the two-factor ANOVA procedure, you will start with this dialog:<\/p>\n

\"anova_cr2_23\"<\/a><\/p>\n

Choose the second option — you have entered two indicator variables and one data variable. \u00a0Now you will specify the design:<\/p>\n

\"anova_cr2_24\"<\/a><\/p>\n

Move the indicator variable for Ability to the first blank, the indicator variable for Accident to the second blank, and the data variable to the third blank. \u00a0Check all the options and click\u00a0Compute<\/strong>. \u00a0Did you notice that setting up the analysis this way was much easier? \u00a0That’s because you did a lot of the work when you created your data — i.e., you specified the names of your factors and the labels for the factor levels. \u00a0The program will figure out that you have a 2 X 2 Design by itself.<\/p>\n

Basic Output<\/h4>\n

\"anova_cr2_18\"<\/a><\/p>\n

Descriptive Statistics<\/b>. This table includes descriptive statistics for each treatment group \/ cell in your design.<\/p>\n

ANOVA Source Table<\/b>. This table details the result of the two-factor analysis of variance (ANOVA). This analysis partitions your variance into four sources: 1) the main effect for the first factor, 2) the main effect for the second factor, 3) the interaction between the factors, and 4) error (i.e., within-groups). Each variance component is associated with its own sum of squares (SS), degrees of freedom (df), and mean square (MS).<\/p>\n

Each F<\/i> statistic is equal to MS(effect) \/ MS(Within). Next to each F<\/i> statistic is the corresponding value of p<\/i> — the chance probability \/ significance level of the value of F<\/i>.<\/p>\n

Levene’s Test<\/b>. One of the assumptions of your F<\/i> test is that the treatment groups have equal variance. Levene’s W<\/i> provides a formal test of this assumption. If the p<\/i> value of W<\/i> is less than .05, you would be concerned that your groups have unequal variance.<\/p>\n

Optional Output<\/h4>\n

\"anova_cr2_19\"<\/a>Effect Size<\/b>. Eta Squared and Omega Squared describe the proportion of variance in your scores that can be attributed to your treatment effect. Omega Squared is an unbiased<\/u> estimate of variance accounted for — i.e., it compensates for sample size. This table displays the values of overall<\/u> Eta and Omega Squared, and partial<\/u> Eta and Omega Squared. Discuss these effect size statistics with your instructor and decide which might be most appropriate for your analysis.<\/p>\n

\"anova_cr2_20\"<\/a><\/p>\n

Critical Values<\/b>. These are the values from a\u00a0statistical table of critical values for the F<\/i> test.<\/p>\n

\"anova_cr2_21\"<\/a><\/p>\n

Supplemental Statistics<\/strong>. \u00a0These are the preliminary statistics that you need to conduct this analysis by hand.<\/p>\n

\"anova_cr2_22\"<\/a><\/p>\n

Line Chart<\/strong>. \u00a0<\/i>This graph\u00a0can help you interpret a significant interaction, like in the case of this analysis. Note, for example, how there is not much of a difference in perceived liking when the contestant does not have an accident (i.e., the cell means above ‘No Acc’). However, there is a considerable difference in perceived liking when the contestant has an accident (i.e., the cell means above ‘Accident’). We especially like above-average people more than average people when they prove to be human by committing a blunder.<\/p>\n

You can modify this chart in several ways — you can reverse the factors, resize the chart, and rescale the Y axis. \u00a0Then, you can save the chart to disk or copy it to your clipboard.<\/p>\n

 <\/p>\n

\n

See Hand-Written Solution<\/a><\/p>\n

Return to Table of Contents<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Your homework problem: Aronson, Willerman, & Floyd (1966) investigated the impact of perceived\u00a0 competence on interpersonal liking. Participants were randomly\u00a0 assigned to one of four treatment conditions. In each, they […]<\/p>\n","protected":false},"author":34,"featured_media":0,"parent":282,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"site-container-style":"default","site-container-layout":"default","site-sidebar-layout":"default","site-transparent-header":"default","disable-article-header":"default","disable-site-header":"default","disable-site-footer":"default","disable-content-area-spacing":"default","footnotes":""},"class_list":["post-530","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/530","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/users\/34"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/comments?post=530"}],"version-history":[{"count":12,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/530\/revisions"}],"predecessor-version":[{"id":948,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/530\/revisions\/948"}],"up":[{"embeddable":true,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/282"}],"wp:attachment":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/media?parent=530"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}