Logic of ANOVA: Testing Hypotheses about Means using Variance, Exams of Statistics

Download Logic of ANOVA: Testing Hypotheses about Means using Variance and more Exams Statistics in PDF only on Docsity! Logic of ANOVA Discuss the logic of the Analysis of Variance. How can a test of variances be used to test hypotheses about means? Assume you have 5 groups of subjects in your experiment. Each group gets a different treatment. You want to know if the treatments have any effect, that are the means of the groups d ifferent. Your experiment is layed out like this: If the null hypothesis is true, then these groups are nothing but 5 different random samples from the same population and any differences among the 5 means are just due to chance (ra ndom sa mpling erro r). The central limit theorem tells us how much variability there should be among means of samples from the same population. The c entral limit theorem says: The variance of the mean = the variance of the population divided by the sample size or Doing a little alg ebra, we see that the sample size times the variance of the mean is equal to the variance of the population or We can estima te the variance of the means ( ) by calculating the variance o f our five mean s. We then multiply the estimate times the sample size to estimate the left side of the above equation. In ANOVA this is called the Between Groups Variance or Between Groups Mean Squares or MSBG. We can estimate the variance of the population ( ) by computing the variance of any one of our groups (samples). This variance estimate is calculated only using the subject in the group. It is called a within group