Profile Analysis Equations Psy 524 Andrew Ainsworth Example Data Group Belly dancers Mean BD Politicians Mean P Administrators Mean A Grand Mean Read Dance TV Ski 7 8 5 6 7 6 6 4 6 5 6 4 5 3 5 4 7 6 5 5 53 10 9 10 10 8 9 4 4 4 5 6 5 4 8 1 3 2 1 3 2 5 4 6 5 5 6 7 5 8 4 5 5 6 6 5 2 1 1 2 2 3 1 8 4 27 5 7 8 8 9 7 4 4 3 6 7 5 5 2 5 5 4 3 3 8 5 4 Average across activities 7 7 25 7 7 5 7 75 7 3 4 4 5 5 25 6 25 5 5 1 75 3 5 3 25 3 5 3 75 3 15 5 15 Profile of Example data Profiles for Leisure time Ratings for Three Occupations 10 9 8 Mean Rating 7 6 Belly dancers 5 Politicians 4 Administrators 3 2 1 0 Read Dance TV Leisure Activity Ski Steps to Profile Analysis Profile analysis is similar to MANOVA with one exception and some rearranging of the data Steps to Profile Analysis Equal Levels is a univariate test each persons score is the average across all of the DVs and the group average is found by averaging the groups mean score on each DV Steps to Profile Analysis 2 Y GM np Y GM p Y Y ij j ij j y 2 2 i j j i j SSTotal SSbg SS wg N is the number of subjects in each group equal n case P is the number of DVs Steps to Profile Analysis SSbg 5 4 7 3 5 15 2 5 5 15 2 3 15 5 15 2 SS wg 4 7 7 3 2 7 25 7 3 2 3 75 3 15 2 Steps to Profile Analysis A normal univariate ANOVA summary table is created Sourceof Variance Between Groups Within Groups SS 172 9 23 5 DF 2 12 MS 86 45 1 958 F 44 145 Sig 000 Steps to Profile Analysis Preparing the data for the Multivariate tests Creating segments DVs can be combined in any number of ways but one of the easiest is taking the difference between parallel sections of the DVs It has been shown that what linear combination you use is irrelevant Steps to Profile Analysis Segmented data Group Read Dance Dance TV 3 4 1 4 5 5 4 4 Belly dancers 1 1 Mean BD 2 8 3 6 0 0 2 1 0 0 0 0 Politicians 1 1 Mean P 0 2 0 4 2 0 2 2 2 0 6 1 Administrators 3 0 Mean A 3 0 2 Grand Mean 0 13 1 13 TV Ski 1 2 3 2 2 1 6 0 2 1 1 1 0 2 1 4 3 2 0 2 1 13 Steps to Profile Analysis Parallelism Really asks the question is there a difference between groups on difference scores made by subtracting parallel scores on the DVs Steps to Profile Analysis Parallelism In the example Is the difference between reading and dancing the same for dancers politicians and administrators and simultaneously asks Is the difference in ratings of dancing and skiing the same for each group etc Steps to Profile Analysis Parallelism In the example a one way MANOVA would be used to tests the parallelism hypothesis Each segment represents a slope between two original DVs if a multivariate effect is found than there is a difference in slope between at least two of the groups Steps to Profile Analysis Flatness This is a test that the average slope segment is different than zero for at least one pair of DVs Performs the multivariate equivalent to a one sample t test called a one sample Tau squared Hotelling s T2 Steps to Profile Analysis Flatness Basically the average of each segment across groups is used to compute this and each score has zero subtracted from is is squared and divided by the pooled error SSCP matrix Swg Matrix Equations Parallelism For the first belly dancer 3 2 8 0 2 Y111 M 1 4 3 6 0 4 1 1 6 2 6 0 2 Y111 M 1 Y111 M 1 0 4 0 2 0 4 2 6 2 6 Matrix Equations This is done for every case and added together to create the Swg matrix S wg 29 6 13 2 6 4 13 2 15 2 6 8 6 4 6 8 26 Matrix Equations Now for the between groups S matrix you need to get the difference between each group mean and the grand mean for each segment for the first group Matrix Equations 2 8 0 13 2 93 M 1 GM 3 6 1 13 2 47 1 6 1 13 47 2 93 M 1 GM M 1 GM 2 47 2 93 2 47 47 47 Matrix Equations This is done for each group and added together then each entry in the matrix is multiplied by the number of people in each group This results in the Sbg matrix 84 133 50 067 5 133 Sbg 50 067 46 533 11 933 5 133 11 933 13 733 Matrix Equations Lambda is calculated the same way etc Matrix Equations Flatness is tested by subtracted a hypothesized grand mean 0 from the actual grand mean 0 13 0 0 13 GM 0 1 13 0 1 13 1 13 0 1 13 Matrix Equations 1 wg Hotelling s N GM S GM 2 05517 04738 00119 13 2 15 13 1 13 1 13 04738 11520 01847 1 13 00119 01847 04358 1 13 2 5825 Matrix Equations N k p 2 2 F p 1 15 3 4 2 2 5825 8 608 F 4 1 1 1 27913 2 1 1 2 5825