One Way ANOVAs One Way ANOVAs Used to compare the means of more than 2 conditions. Comparisons and Alpha level. In a study with 3 conditions ABC we need to make 3 comparisons A to B A to C B to C

Alpha Levels For each comparison we add an additional 5% chance of making a type I error. So overall, if we used 3 t-tests to do this analysis, we would have an alpha level of .15 not .05. In other words, if we found a significant difference, we would only be 85% sure it was not simply due to chance.

ONE OF THESE THINGS IS NOT LIKE THE OTHER? Is that true or false? Which things are different from which other things?

If Scientific Hypothesis is True, the Means of the distributions should shift but they should have very similar variances. Singles Married Divorced Happiness Scores

If Null Hypothesis is True, the Means of the distributions should not shift and they should still have very similar variances. Singles Married Divorced Happiness Scores

WE USE THE AVERAGE VARIANCE OF THE THREE GROUPS AS AN ESTIMATE OF WHAT THE OVERALL VARIANCE SHOULD BE IF THE NULL HYPOTHESIS IS TRUE. Happiness Scores

Singles Married Divorced Happiness Scores

. Happiness Scores

. F=

F= . Between Group Variance This includes Error Variance and Variance Due to Treatment F= Within Group Variance Error variance only

F= = ? . Between Group Variance This is the Variance we actually obtained F= = ? Within Group Variance This is the variance we would expect IF The null hypothesis is true

The p value given is the probability of getting an F value as large as the one you actually obtained IF THE NULL HYPOTHESIS IS CORRECT. In other words, it is the probability of making a TYPE I Error. If it is less than .05 we reject the null hypothesis and conclude that the difference AMONG the conditions are significant. We can then continue on and interpret the multiple comparisons.