Chapter 10: ANOVA (Analysis of Variance)

Chapter 10: ANOVA (Analysis of Variance) New Vocabulary: Analysis of variance (ANOVA): the test used when comparing the means from a single dependent variable among two or more groups or categories Repeated-measures ANOVA: a test that examines a change over time in the sample population Homogeneity of variance: equal variances among the groups being compared Power: probability of detecting a difference that really exists ●​ You use ANOVA when comparing more than two groups or sample means Null and Alternative Hypothesis -​ Your null will be that all the groups will have similar means -​ Your alternative will be that the 3+ means are not equal -​ Not all of the 3 means have to be unequal. If even 2 are unequal you will reject the null hypothesis -​ The ANOVA test produces the F-ratio that relates the differences between the groups (the numerator) to the difference within the groups (the denominator) Degrees of Freedom -​ The numerator of the F-ratio has one number for degrees of freedom and the denominator has another number of degrees of freedom. -​ DF = (# of groups - 1) / (# of subjects - # of groups) -​ OR: DF = (between groups variation) / (within groups variation) Statistical Significance -​ When the null hypothesis is correct, and there is no difference in the means of the groups being studied,the F-ratio is close to 1 and will have an insignificant p-value -​ A larger F-ratio value indicates a greater difference when comparing the between-groups variation and the within-groups variation -​ You cannot conclude from the ANOVA test alone where the statistical significant difference is, only that there is one. You need to do further (post-HOC) tests to find where the difference lies Appropriate use of ANOVA -​ Assumptions must be met: 1.​ Samples must be independent (ideally random), and the outcome variable must be interval or ratio 2.​ The sample should have a normal distribution 3.​ Homogeneity of variance - equal variances among the groups being compared Repeated Measures ANOVA -​ -​ -​ -​ Used for dependent samples in order to see a change over time in the same sample population This can actually increase the power of the study because you are using the same subjects and can more easily see the differences due to your intervention It also decrease not only the individual variation error, but also the required sample size needed to find a significant result Issues with ANOVA: -​ Position or latency effects: occurs when a subject is exposed to more than one treatment over time, and the order of the treatment affected the outcome -​ Carryover effects: occurs when previous treatments continue to have an impact on following treatments Appropriate use of Repeated Measures ANOVA -​ Assumptions are required to be met: -​ Most of the assumptions are same as those for ANOVA but there's more -​ Compound symmetry: the measurements should be correlated and have equal variances -​ Homogeneity of variance Summary -​ ANOVA is used when comparing the sample means for 2 or more groups/samples -​ ANOVA produces an F-ratio with a corresponding p-value -​ The F-ratio compares the variation between the group means to the variation seen within the groups -​ Further testing is required to identify where the statistically significant difference is located -​ The repeated measures ANOVA is used to examine a change over time in the same sample population -​ You must consider latency effects and carryover effects