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An analysis of variance, also known as ANOVA, is used in research situations where the researcher wants to compare means on a quantitative Y outcome variable across two or more groups (Warner, 2012). A one-way ANOVA would be the most appropriate analysis because one is able to compare variances between two or more groups. An example of a research question in which an ANOVA test would be the most appropriate would be a pharmaceutical company seeking to test the effectiveness of a newly developed anxiety medication. One variable would be the control group, the group in which no medication is given, the second variable would be the group that is given a known and standardized anxiety medication; example Xanax, etc. The last variable would be the group that is given the newly developed medication. The test statistics in this scenario show that the differences amongst the sample means are no more then what would be expected. Thus, one would fail to reject the null hypothesis. The newly developed anxiety medication while effective was no more effective than existing anxiety medication.
Warner, R. M. (20120410). Applied Statistics: From Bivariate Through Multivariate Techniques, 2nd Edition [VitalSource Bookshelf version]. Retrieved from https://bookshelf.vitalsource.com/books/9781483305974
The outcome variables should be quantitative, the distribution should be approximately normal, there should be equal variance among scores, and samples shouldn’t correlate in a one-way between-S anova (Warner, 2013). Warner (2013) says “between-S” means samples are only part of one group. To meet these requirements, this study will see how different caffeine levels effect test scores on an exam. There will be four predictor variables ranging from no caffeine, 60 mg. of caffeine, 120 mg. of caffeine, and 180 mg. of caffeine. The outcome variable will be interval. The pool of students will be out of 24 in the same grade whom have a GPA of 3.5 or higher. There will be 6 students in each group. Warner (2013) states similar participants, standardized testing, and control of extraneous variables will give accurate results and lead to higher f ratios.
A histogram will show the distribution and a Levene test can show the assumption of variance. Although, the distribution for an F test is typically positively skewed because zero is the minimum score for an F test (Warner, 2013). According to Warner (2013), the degrees of freedom will be 20 and 3 because the number of participants minus the number of groups equals 20, and the number of groups minus one equals 3. Higher scores are expected with higher amounts of caffeine. There should be the biggest difference between the group with no caffeine and the group with 180 mg. of caffeine. Since there should be high variance among groups, Warner (2013) claims F ratios and SS between will be high. Variance within groups will likely be small, so SS within will probably be low.
Warner, M. (2013). Applied statistics: from bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications, Inc.