Amy Sperback Final Essay
Allen G. Bluman, author of Elementary Statistics: A Step by Step Approach, describes the F- Test in detail. However, I had found other scholarly sources to explain the way the Levene’s Test can be used. While using Minitab both of the tests results are displayed when testing for significance. They both compute the same basic information but you will use the F-test when data is normally distributed and the Levene’s test when you do not have normal data.
The F-test is used to determine if variances of two different samples are the same or not. Otherwise you can use the Bartlett’s test for more than one set if the data are normally distributed. The variance or standard deviation can be used when dealing with discrete or continuous nominal data. The F-test takes all the means and tells if they are all equal or not. If they are then one can infer that the data can be from the same origin. In order for this to work it must be used with data that are normally distributed and independent of one another. The F-test can be used in determining any mean comparisons as long as these needs are met.
To perform the F-test you start by stating the null and the alternative hypothesis. Then you decide what the alpha is going to be and if you are using a Right-tailed, Left-tailed, or Two-tailed test. Then one will determine the degrees of freedom using a chart. After that you plug the variances into the formula. The formula is not difficult and can be stated as such: F equals S superscript 2, subscript 1, over, S superscript 2, subscript 2. The larger variance goes on the top. If standard deviations are given instead of variances then make sure that each one is squared. Finally you need to make a decision if the null hypothesis was rejected or accepted, and explain the answer. (Bluman)
The Levene’s Test is not much different from the F-test in terms of what purpose we use it for. Its basically a “one-way analysis of variance on the absolute values of the differences between each observation and the of its group” (Glass). Usually it is paired with ANOVA since it does not need to have normally distributed data (Keyes). And because we can use it with ANOVA we can say that it works with quantitative data as well as nominal. There is still the process of creating a hypothesis and determining the alpha that one will base the p-value given against.
Here you can compare more than one group together at one time it is sometimes more often compared to Bartlett’s test since a F-test usually deals with only two groups. Alan Heckert describes the different groups of Levene’s Test into 3 levels. He says, “The three choices for defining Zij determine the robustness and power of Levene’s test. By robustness, we mean the ability of the test to not falsely detect non-homogeneous groups when the underlying data is not normally distributed and the groups are in fact homogeneous.” There are the hand calculations to do a Levene’s test would be extremely difficult so we use programs like Minitab to take care of that. Even though are four different syntax computations, they are really grouped into three different ones that are done under the Levene’s test. The Levene test and Median Levene Test both use the median as the base. There is a Mean Levene Test that uses the mean and a Trimmed Mean Levene Test which actually computes the trimmed mean based Levene Test. It trims the Lowest 10% and Highest 10 % of the data. This helps with outliers that may occur randomly (Heckert).
These tests of significance are really good to use when deciding if something has the same variance or not. It can define which statistical test will be the best one to use. These are used in ANOVA’s, and T-test’s. If I was studying the populations in a few of the African tribes I could take certain samples and decide if they has the same variance or not. If the means turn out to be the same with alpha .05 then I can scientifically make assertions about these tribes.
Works Cited
Bartlett’s test (or the F test) versus Levene’s test for equal variances. Dec. 14 2006. 27 April 2008. <http://www.minitab.com/support/answers/answer.aspx?log=0&id=1183>.
Bluman, Allan G. Elementary Statistics: A Brief Version. 3rd ed. New York: McGraw-Hill, 2006.
Glass, Gene V. “Testing Homogeneity of Variances.” American Educational Research Journal, Vol. 3, No. 3 (May, 1966): 187-190 <http://www.jstor.org/stable/view/1161802?seq=4>.
Heckert, Alan. Dataplot. 4 April 2003. National Institute of Standards and Technology. 27 April 2008. <http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/levetest.htm>.
Keyes, Tim K. Martin S. Levy. “Analysis of Levene’s Test Under Design Imbalance” Journal of Educational and Behavioral Statistics, Vol.22, No.2 (summer, 1997): 227-236. JSTOR. 27 April 2008. <http://www.jstor.org/stable/view/1165379?seq=9>.
