T-test+and+ANOVA

+ Analysis of variance. Measures variation by using variance instead of standard deviation

+ Similar to t-test (”two-sample t-test”), but with ANOVA we can use many categories instead of only two

+ Both t-test and ANOVA base investigation on difference between means


 * Hypothesis testing with ANOVA**

+ The H0 is that the population means are the same:

+ H0: μ1= μ2= μ3 = … = μk

+ ANOVA asks “are the differences between the sample means so large that we can conclude that the populations represented by the samples are different?”

+ If the H0 is true, the sample means should be about the same value

+ If the H0 is false, there should be substantial differences between categories, combined with relatively little difference within categories


 * Between and within**

+ The larger the differences between the (category) sample means, the more likely the H0 is false - especially when there is little difference within categories

+ When we reject the H0, we are saying there are differences between the populations represented by the sample