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Hypothesis Testing - Analysis of Variance (ANOVA)IntroductionThis module will continue thediscussion of hypothesistesting, where a specificstatement or hypothesis isgenerated about apopulation parameter, andsample statistics are used toassess the likelihood that thehypothesis is true. Thehypothesis is based onavailable information and theinvestigator's belief aboutthe population parameters.The specific test considered here is called analysis of variance (ANOVA) and is a test ofhypothesis that is appropriate to compare means of a continuous variable in two ormore independent comparison groups. For example, in some clinical trials there aremore than two comparison groups. In a clinical trial to evaluate a new medication forasthma, investigators might compare an experimental medication to a placebo and to astandard treatment (i.e., a medication currently being used). In an observational studysuch as the Framingham Heart Study, it might be of interest to compare mean bloodpressure or mean cholesterol levels in persons who are underweight, normal weight,overweight and obese. The technique to test for a difference in more than two independent means is anextension of the two independent samples procedure discussed previously whichapplies when there are exactly two independent comparison groups. The ANOVAtechnique applies when there are two or more than two independent groups. TheANOVA procedure is used to compare the means of the comparison groups and isconducted using the same five step approach used in the scenarios discussed inprevious sections. Because there are more than two groups, however, the computationof the test statistic is more involved. The test statistic must take into account the samplesizes, sample means and sample standard deviations in each of the comparison groups.Learning Objectives After completing this module, the student will be able to:Perform analysis of variance by hand1.Appropriately interpret results of analysis of variance tests2.Distinguish between one and two factor analysis of variance tests3.Identify the appropriate hypothesis testing procedure based on type of outcomevariable and number of samples4.The ANOVA Approach
Consider an example with four independent groups and a continuous outcomemeasure. The independent groups might be defined by a particular characteristic of theparticipants such as BMI (e.g., underweight, normal weight, overweight, obese) or by theinvestigator (e.g., randomizing participants to one of four competing treatments, callthem A, B, C and D). Suppose that the outcome is systolic blood pressure, and we wishto test whether there is a statistically significant difference in mean systolic bloodpressures among the four groups. The sample data are organized as follows:Group 1Group 2Group 3Group 4Sample Sizen1n2n3n4Sample MeanSampleStandardDeviations1s2s3s4The hypotheses of interest in an ANOVA are as follows:H0: μ1= μ2= μ3... = μkH1: Means are not all equal.