DOC PREVIEW
WCU ECO 252 - Tests for Equality of Variances

This preview shows page 1 out of 3 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 3 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 3 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

252mvar 3/31/046. Tests for Equality of Variancesa. IntroductionEquality of Multiple Means (ANOVA)Equality of Multiple Medians (Kruskal-Wallis and Friedman)Equality of Multiple Proportions (Chi-squared)So for completeness we need Tests for Equality of Multiple Variances.b. The Bartlett Testc. The Levene Test(i) Find the median of each column. (This is the middle number or the average of the two middle numbers.)(ii) Subtract the median of each column from the column from which it comes and take the absolute value of the result.(iii) Do a 1-way ANOVA on the result. If the results would lead you to reject the null hypothesis (because the computed F is above the table F or the p-value is below your significance level), reject the null hypothesis of equal variances.Levene Test Example: Test the following data for equality of variances.252mvar 3/31/046. Tests for Equality of Variancesa. IntroductionWe have now covered tests for Equality of Multiple Means (ANOVA)Equality of Multiple Medians (Kruskal-Wallis and Friedman)Equality of Multiple Proportions (Chi-squared)So for completeness we need Tests for Equality of Multiple Variances.b. The Bartlett TestThis test seems to require that the underlying distribution be Normal. It should not be used to compare two columns, since a simple F test described earlier is more appropriate. Recall that in the test for comparing 2 means with equal variances we used a pooled variance    211ˆ212222112nnsnsnsp. Assume that we have c columns representing c independent samples. Then the pooled variance would be        cnnnnsnsnsnsnscccp321223322221121111. The test statistic used when there are 6 or more rows is       2212log1ˆlog130259.2jjpjcsnsnd where cnncdjj1111311For smaller examples (less than 6 rows) a special table is required and the instructions that I have found are very confusing. Use the computer.Bartlett Test Example (Kanji – heavily edited): Test the following data for equal variances.4220153129.1147.1164.447.5432124232221nnnnssss       cnnnnsnsnsnsnscccp321223322221121111       44220153129.114147.111964.41447.530 10489.46293.21796.641.164 7488.810488.909 Note that the denominator can be written as    cnnjj1. The test statistic used is       2212log1ˆlog130259.2jjpjcsnsnd where cnncdjj1111311  104141119114130153111          0096153.024902.0052632.0071429.0033333.01511  0115.11726807.1511       2212log1ˆlog130259.2jjpjcsnsnd          29.11log4147.11log1964.4log1447.5log307488.8log1040115.130259.2          052694.141059563.119666518.014737987.030941948.01040115.130259.2 160454.4313164.20331252.9139610.22962592.970115.130259.2 2837.7199636.30115.130259.2 This has 3141 c degrees of freedom and the chi-squared table says that  305.27.8147 Since our computed chi-squared is less than the table chi-square, do not reject the null hypothesis.c. The Levene TestThis test is quite simple. It can be used for non-Normal data and can be used to compare two columns as well as more than two columns.(i) Find the median of each column. (This is the middle number or the average of the two middle numbers.)(ii) Subtract the median of each column from the column from which it comes and take the absolute value of the result.(iii) Do a 1-way ANOVA on the result. If the results would lead you to reject the null hypothesis (because the computed F is above the table F or the p-value is below your significance level), reject the null hypothesis of equal variances. Levene Test Example: Test the following data for equality of variances.Method 1 Method 2 Method 3 Method 4 1.31 1.08 0.85 1.31 1.27 1.10 1.02 1.27 1.28 1.05 0.78 1.28 1.22 1.02 0.87 1.22 1.19 0.99 0.80 1.19 1.30 0.95 0.96 1.30If we write out the numbers in Method 1 in order, we get (1.19, 1.22, 1.27, 1.28, 1.30, 1.31)The median for Method 2 is the halfway point between 1.27 and 1.28, or 1.275. The other medians are 1.035, 0.86 and 1.275. If we subtract the medians we get the following. Method 1 Method 2 Method 3 Method 4 0.035 0.045 -0.01 0.035 -0.005 0.065 0.16 -0.005 0.005 0.015 -0.08 0.005 -0.055 -0.015 0.01 -0.055 -0.085 -0.045 -0.06 -0.085 0.025 -0.085 0.10 0.0252If we take absolute values we get the following. Method 1 Method 2 Method 3 Method 4 0.035 0.045 0.01 0.035 0.005 0.065 0.16 0.005 0.005 0.015 0.08 0.005 0.055 0.015 0.01 0.055 0.085 0.045 0.06 0.085 0.025 0.085 0.10 0.025If we subject these results to a one-way ANOVA, we get the table below and conclude that we cannot rejectthe hypothesis of equal variances.Source SS DF MS F 05.F 0HBetween 0.00491 3 0.00164 1.10ns 10.320,3FVariances equalWithin 0.02980 20 0.00149 Total 0.03471 23 For computer examples see


View Full Document

WCU ECO 252 - Tests for Equality of Variances

Documents in this Course
Load more
Download Tests for Equality of Variances
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Tests for Equality of Variances and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Tests for Equality of Variances 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?