ANOVA

Independent ANOVA Scores vary – why? Total variability can be divided up into 2 parts 1) Between treatments 2) Within treatments

Between design Total variability Between treatments Treatment effect Individual differences Experimental error Within treatments Individual differences Experimental error

F = variance between treatments variance within F = treatment + indiv diffs + error indiv diffs + error

INDEPENDENT ANOVA assumptions 1)the observations within each sample must be independent 2) the populations from which the samples were selected must be normal 3) the populations from which the samples are selected must have equal variances (homogeneity of variance) Same assumptions for t test

F measures variance which is standard deviation squared F = (differences between sample) 2 (differences expected by chance) 2 F = t 2

Figure 1 Mean calories in hotdogs

Post hoc test

Information about the purpose of the experiment. The number of participants. Descriptive Statistics (effect size –more later) Analysis result Post hoc differences

The difference in calories between beef, (n=20), meat (n=17) and poultry (n=17) hotdogs was tested. Mean calorie level was determined for each hotdog type, beef (22.64), meat (25.24) and poultry (22.55). Confidence intervals for the means in each group are shown in figure 1.The calorie level varied between the hotdog types F(2,51) = 16.07, p<.05. MS = Post hoc test show poultry had fewer calories than both meat (LSD =-38 p<.05) and beef (LSD= p<.05).

APA To examine the effects of memory training on retention of words, 20 college students were randomly assigned to four training conditions (n=5) defined by the instructions to participants: story method, imagery method thyme method, and control (no specific instructions). Mean recall out of a possible 20 words (and the sample standard deviation) were for each of the conditions: story 13.2(1.3), imagery 14.4 (1.8), rhyme 13.4 (1.3) and control 10.0 (1.6). Confidence intervals for the means in each group are shown in figure 1. Mean recall differed significantly among the four instruction conditions, F(3,16) = 7.8, p<.05. MS = … Post hoc test show….

Repeated Measures ANOVA

Total variability Between treatment variability Treatment effect Experimental error Within treatment variability Individual differences Experimental error Between subject variability Individual differences Error variability Experimental error

F= treatment effect + experimental error experimental error

Figure 1 Mean Anxiety by Trial Number

F(3,33) =

assumptions