{"id":517,"date":"2015-07-17T08:20:22","date_gmt":"2015-07-17T12:20:22","guid":{"rendered":"http:\/\/sites.berry.edu\/vbissonnette\/?page_id=517"},"modified":"2024-06-01T10:33:44","modified_gmt":"2024-06-01T14:33:44","slug":"one-factor-anova-rm-design","status":"publish","type":"page","link":"https:\/\/sites.berry.edu\/vbissonnette\/index\/stats-homework\/documentation\/one-factor-anova-rm-design\/","title":{"rendered":"One-Factor ANOVA (RM Design)"},"content":{"rendered":"

Your homework problem:<\/h3>\n

You are interested in the effects of arousal on motor performance.\u00a0 A random sample of\u00a0\u00a0 subjects perform a complex motor task under\u00a0 3 conditions: no caffeine (low arousal), a small dose of caffeine\u00a0 (moderate arousal), and a large dose of caffeine (high arousal).\u00a0The dependent variable represents performance level: higher\u00a0 scores represent better performance.<\/p>\n

This study resulted in the following data:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n
Subject<\/td>\nLow
\nDifficulty<\/td>\n		Moderate
\nDifficulty<\/td>\n		High
\nDifficulty<\/td>\n<\/tr>\n
1<\/td>\n15<\/td>\n17<\/td>\n19<\/td>\n<\/tr>\n
2<\/td>\n2<\/td>\n7<\/td>\n4<\/td>\n<\/tr>\n
3<\/td>\n11<\/td>\n12<\/td>\n6<\/td>\n<\/tr>\n
4<\/td>\n13<\/td>\n15<\/td>\n5<\/td>\n<\/tr>\n
5<\/td>\n12<\/td>\n12<\/td>\n7<\/td>\n<\/tr>\n
6<\/td>\n2<\/td>\n18<\/td>\n11<\/td>\n<\/tr>\n
7<\/td>\n8<\/td>\n12<\/td>\n5<\/td>\n<\/tr>\n
8<\/td>\n9<\/td>\n14<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Did the perceived level of caffeine significantly affect the\u00a0 participants’ performance (alpha = .05)? If your analysis reveals a\u00a0 significant overall effect, then make sure to explore all possible\u00a0 mean differences with a post-hoc analysis (same alpha).<\/p>\n

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

\n

Enter these data into Stats Homework’s\u00a0<\/i> data manager and rename the variables. Your screen should\u00a0 look like this:<\/p>\n

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

Make sure to double-check and save your data. To conduct your analysis,\u00a0 pull down the Analyze<\/b> menu, choose Analysis of Variance<\/b>,\u00a0 and then choose One-Factor ANOVA for Repeated-Measures Designs<\/b>. You \u00a0will be presented with this user dialog:<\/p>\n

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

Move your three variables under “Dependent Variables,” select all the output options, and press the Compute<\/strong> button.<\/p>\n

Basic Output<\/h4>\n

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

Descriptive Statistics<\/b>. This table includes\u00a0 descriptive statistics for each treatment condition.<\/p>\n

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

Mauchly’s Test for Sphericity.<\/strong>\u00a0 If you request it, this table presents the results of Mauchly’s test – whether your data depart from the assumption of sphericity.\u00a0 If the Chi-Squared test is significant here, you should be cautious about interpreting the p-value associated with the F test in the ANOVA.\u00a0 If this test is significant, you might be interested in adjusting the df in your analysis with one of the adjustments provided.<\/p>\n

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

ANOVA Source Table<\/b>. This table details the result of your analysis\u00a0 of variance (ANOVA). You have three sources of variance: treatment condition\u00a0 variance, subject variance, and error variance. Each variance component is\u00a0 associated with its own sum of squares (SS), degrees of freedom (df),\u00a0 and mean square (MS).\u00a0 When you select the option for sphericity statistics, you will also be provided with all of the adjusted results in this table.<\/p>\n

The F<\/i> statistic is equal to MS(Treatment) \/\u00a0 MS(Error) (5.80). Next to the F<\/i> statistic is p<\/i> — the chance\u00a0 probability \/ significance level of your result (.015).\u00a0 Again, this would be the\u00a0F<\/em> statistic and\u00a0p<\/em> value that we would interpret if your data demonstrate sphericity.\u00a0 If you do not request the sphericity statistics, you will be presented with a simplified ANOVA Source Table:<\/p>\n

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

Optional Outputs<\/h4>\n

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

Effect Size<\/b>. Eta Squared and Omega Squared describe the proportion\u00a0 of variance in your scores that can be attributed to your treatment effect.\u00a0 Omega Squared is an unbiased<\/u> estimate of variance accounted for —\u00a0 i.e., it compensates for sample size.<\/p>\n

This table displays the overall<\/u> effect sizes — these\u00a0 give you the proportion of the total variance accounted for. In addition, it\u00a0 displays the partial<\/u> effect sizes — these give you the proportion of\u00a0 variance accounted for after you have removed the subject variance.<\/p>\n

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

Post-Hoc Testing<\/strong>. \u00a0If you request it, Stats Homework will also produce this output\u00a0if<\/span> your overall F statistic is significant and you have more than two groups. \u00a0You are presented with the results of all pair-wise comparisons, where each test has been adjusted with the Bonferroni correction (basically, you multiply the p<\/em> value for each test by the number of tests).<\/p>\n

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

Critical Values<\/b>. These are the values from a\u00a0 statistical\u00a0 table of critical values<\/a> for the F<\/i> test.\u00a0 In our case, we are conducting a test with alpha = .05.\u00a0 So, we would compare the value of our obtained F\u00a0<\/i> (7.82) to 3.74. Again, using this\u00a0F<\/em> value as your critical value assumes sphericity.<\/p>\n

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

Supplemental Statistics Used in Hand Calculations<\/b>. These are statistics\u00a0 that can be helpful if you would\u00a0 like to double check your hand-written computations.<\/p>\n

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

Box Plots<\/strong>. \u00a0Finally, you will be presented with graphical box plots of your data. \u00a0You can modify these plots in a variety of ways, save them to disk, or copy them to your clipboard.<\/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: You are interested in the effects of arousal on motor performance.\u00a0 A random sample of\u00a0\u00a0 subjects perform a complex motor task under\u00a0 3 conditions: no caffeine (low […]<\/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-517","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/517","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=517"}],"version-history":[{"count":15,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/517\/revisions"}],"predecessor-version":[{"id":2280,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/517\/revisions\/2280"}],"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=517"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}