BS704_HypothesisTesting-Anova_print.html.pdf - Hypothesis Testing Analysis of Variance(ANOVA Introduction This module will continue the discussion of

BS704_HypothesisTesting-Anova_print.html.pdf - Hypothesis...

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Hypothesis Testing - Analysis of Variance (ANOVA) Introduction This module will continue the discussion of hypothesis testing, where a specific statement or hypothesis is generated about a population parameter, and sample statistics are used to assess the likelihood that the hypothesis is true. The hypothesis is based on available information and the investigator's belief about the population parameters. The specific test considered here is called analysis of variance (ANOVA) and is a test of hypothesis that is appropriate to compare means of a continuous variable in two or more independent comparison groups. For example, in some clinical trials there are more than two comparison groups. In a clinical trial to evaluate a new medication for asthma, investigators might compare an experimental medication to a placebo and to a standard treatment (i.e., a medication currently being used). In an observational study such as the Framingham Heart Study, it might be of interest to compare mean blood pressure 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 an extension of the two independent samples procedure discussed previously which applies when there are exactly two independent comparison groups. The ANOVA technique applies when there are two or more than two independent groups. The ANOVA procedure is used to compare the means of the comparison groups and is conducted using the same five step approach used in the scenarios discussed in previous sections. Because there are more than two groups, however, the computation of the test statistic is more involved. The test statistic must take into account the sample sizes, 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 hand 1. Appropriately interpret results of analysis of variance tests 2. Distinguish between one and two factor analysis of variance tests 3. Identify the appropriate hypothesis testing procedure based on type of outcome variable and number of samples 4. The ANOVA Approach
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Consider an example with four independent groups and a continuous outcome measure. The independent groups might be defined by a particular characteristic of the participants such as BMI (e.g., underweight, normal weight, overweight, obese) or by the investigator (e.g., randomizing participants to one of four competing treatments, call them A, B, C and D). Suppose that the outcome is systolic blood pressure, and we wish to test whether there is a statistically significant difference in mean systolic blood pressures among the four groups. The sample data are organized as follows: Group 1 Group 2 Group 3 Group 4 Sample Size n 1 n 2 n 3 n 4 Sample Mean Sample Standard Deviation s 1 s 2 s 3 s 4 The hypotheses of interest in an ANOVA are as follows: H 0 : μ 1 = μ 2 = μ 3 ... = μ k H 1 : Means are not all equal.
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