The test statistic for testing H 0: μ 1 = μ 2 =. The alternative hypothesis, as shown above, capture all possible situations other than equality of all means specified in the null hypothesis. The research hypothesis captures any difference in means and includes, for example, the situation where all four means are unequal, where one is different from the other three, where two are different, and so on. The research or alternative hypothesis is always that the means are not all equal and is usually written in words rather than in mathematical symbols. The null hypothesis in ANOVA is always that there is no difference in means. Where k = the number of independent comparison groups. The hypotheses of interest in an ANOVA are as follows: The sample data are organized as follows: 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. Identify the appropriate hypothesis testing procedure based on type of outcome variable and number of samplesĬonsider 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).Distinguish between one and two factor analysis of variance tests.Appropriately interpret results of analysis of variance tests.Learning ObjectivesĪfter completing this module, the student will be able to: The fundamental strategy of ANOVA is to systematically examine variability within groups being compared and also examine variability among the groups being compared. Analysis of variance avoids these problemss by asking a more global question, i.e., whether there are significant differences among the groups, without addressing differences between any two groups in particular (although there are additional tests that can do this if the analysis of variance indicates that there are differences among the groups). If one is examining the means observed among, say three groups, it might be tempting to perform three separate group to group comparisons, but this approach is incorrect because each of these comparisons fails to take into account the total data, and it increases the likelihood of incorrectly concluding that there are statistically significate differences, since each comparison adds to the probability of a type I error. The test statistic must take into account the sample sizes, sample means and sample standard deviations in each of the comparison groups. Because there are more than two groups, however, the computation of the test statistic is more involved. 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. The ANOVA technique applies when there are two or more than two independent groups. 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. 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.
CRITICAL VALUE Z SCORE CALCULATOR TRIAL
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). For example, in some clinical trials there are more than two comparison groups. 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. The hypothesis is based on available information and the investigator's belief about the population parameters. 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. Hypothesis Testing - Analysis of Variance (ANOVA)īoston University School of Public Health
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