Exam 12: GlM 1: Comparing Several Independent Means

A business analyst was interested in the variation of sales income across four shops in a retail chain. He ran an ANOVA with the predictor variable 'shop location', which had four categories, 'High street', 'Outlet', 'Online' and 'Suburb'; the outcome variable was 'monthly sales income'. His ANOVA had an F-statistic of 98.12 (p 0.02). How would you interpret his findings?

A psychologist was looking at the effects of an intervention on depression levels. Three groups were used: waiting list control, treatment and post-treatment (a group who had had the treatment 6 months before). -The SPSS output is below. Based on this output, what should the researcher report? $\quad$$\quad$ Test of Homogeneity of Variances BDIDIF Levene Statistic df1 df2 Sig. 4.246 2 45 .020 $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$ ANOVA BDIDIF Sum of Squares df Mean Square Sig. Between Groups 529.437 2 264.719 5.110 .010 Within Groups 2331.135 45 51.803 Total 2860.572 47 $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$ Robust Tests of Equality of Means BDIDIF df1 df2 Sig. Welch 4.345 2 26.436 .023 Brown-Forsythe 5.110 2 35.104 .011 a. Asymptotically $\mathrm { F }$ distributed.

A teacher in a school was interested in examining the differences in children's maths scores across a year group, which consisted of three classes. She was particularly interested in whether the class the child was in had a possible influence on the child's maths score. She ran an ANOVA with the predictor variable 'class', which had three categories, 'Yellow Class', 'Green Class' and 'Purple class'; the outcome variable was 'maths score'. Her ANOVA had an F-statistic of 4.23 (p 0.68). How would you interpret her findings?

The student welfare office was interested in trying to enhance students' exam performance by investigating the effects of various interventions. They took five groups of students before their statistics exams and gave them one of five interventions: (1) a control group just sat in a room contemplating the task ahead (Control); (2) the second group had a yoga class to relax them (Yoga); (3) the third group were told they would get monetary rewards contingent upon the grade they received in the exam (Bribes); (4) the fourth group were given beta-blockers to calm their nerves (Beta-Blockers); and (5) the fifth group were encouraged to sit around winding each other up about how much revision they had/hadn't done (You're all going to fail). The student welfare office made four predictions: (1) all interventions should be different from the control; (2) yoga, bribery and beta-blockers should lead to higher exam scores than panic; (3) yoga and bribery should have different effects than the beta-blocker drugs; and (4) yoga and bribery should also differ. Which of the following planned contrasts (with the appropriate group codings) are correct to test these hypotheses?

Robust ANOVA tests are able to work with which two data 'violations'?

What two assumptions must not be violated when running an ANOVA?a. By reviewing the standard error.

What is the F-statistic?

The table below contains the length of time (minutes) for which different groups of students were able to stay awake to revise statistics after consuming 500 ml of one of three different types of stimulants. What is the variation in scores from groups A to B to C known as? A B C 20 15 40 15 12 33 120 7 50 57 18 135