## Wednesday, May 28, 2014

### Variance Tests: Levene’s Test, Brown-Forsythe Test, and F-Test in Excel For 2-Sample Unpooled t-Test

This is one of the following six articles on 2-Independent-Sample Unpooled t-Tests in Excel

2-Independent-Sample Unpooled t-Test in 4 Steps in Excel 2010 and Excel 2013

Variance Tests: Levene’s Test, Brown-Forsythe Test, and F-Test in Excel For 2-Sample Unpooled t-Test

Excel Normality Tests Kolmogorov-Smirnov, Anderson-Darling, and Shapiro-Wilk For 2-Sample Unpooled t-Test

2-Sample Unpooled t-Test Excel Calculations, Formulas, and Tools

Effect Size for a 2-Independent-Sample Unpooled t-Test in Excel 2010 and Excel 2013

Test Power of a 2-Independent Sample Unpooled t-Test With G-Power Utility

# Variance Tests: Levene’s Test, Brown-Forsythe Test, and F Test for 2- Sample Unpooled t-Test in Excel

Pooled t-Tests are performed if the variances of both sample groups are similar. A rule-of-thumb is as follows: A Pooled t-Test should be performed if the standard deviation of one sample is no more than twice as large as the standard deviation in the other sample. That is definitely not the case here as the following are true:

s1 = sample1 standard deviation = 24.78

and

s2 = sample2 standard deviation = 11.80

## F Test For Sample Variance Comparison in Excel

An F Test is a hypothesis test commonly used to test for the equality of variances of two or more sample groups. An Excel F Test performed on the two sample groups produces the following output:

The Null Hypothesis of an F Test states that the variances of the two groups are the same. The p Value shown in the Excel F Test output equals 0.002. This is much smaller than the Alpha (0.05) that is typically used for an F Test so the Null Hypothesis can be rejected. The p value indicates that there is only a 0.2 percent of obtaining this result if the Null Hypothesis is true.

We therefore conclude as a result of the F Test that the variances are the not same. The F Test is sensitive to non-normality of data. The sample variances can also be compared using the nonparametric Levene’s Test and also the nonparametric Brown-Forsythe Test.

## Levene’s Test For Sample Variance Comparison in Excel

Levene’s Test is a hypothesis test commonly used to test for the equality of variances of two or more sample groups. Levene’s Test is more robust against non-normality of data than the F Test.

The Null Hypothesis of Levene’s Test is average distance to the sample mean is the same for each sample group. Acceptance of this Null Hypothesis implies that the variances of the sampled groups are the same. The distance to the mean for each data point of both samples is shown as follows:

Levene’s Test involves performing Single-Factor ANOVA on the groups of distances to the mean. This can be easily implemented in Excel by applying the Excel data analysis tool ANOVA: Single Factor. Applying this tool on the above data produces the following output:

The Null Hypothesis of Levene’s Test states that the average distance to the mean for the two groups are the same. Rejection of this Null Hypothesis would imply that the sample groups have the different variances. The p Value shown in the Excel ANOVA output equals 0.0025. This is much smaller than the Alpha (0.05) that is typically used for an ANOVA Test so the Null Hypothesis should be rejected.

We therefore conclude as a result of Levene’s Test that the variances are different. Levene’s Test is sensitive to outliers because relies on the sample mean, which can be unduly affected by outliers. A very similar nonparametric test called the Brown-Forsythe Test relies on sample medians and is therefore much less affected by outliers as Levene’s Test is or by non-normality as the F Test is.

## Brown-Forsythe Test For Sample Variance Comparison in Excel

The Brown-Forsythe Test is a hypothesis test commonly used to test for the equality of variances of two or more sample groups. The Null Hypothesis of the Brown-Forsythe Test is average distance to the sample median is the same for each sample group. Acceptance of this Null Hypothesis implies that the variances of the sampled groups are the same. The distance to the median for each data point of both samples is shown as follows:

The Brown-Forsythe Test involves performing Single-Factor ANOVA on the groups of distances to the median. This can be easily implemented in Excel by applying the Excel data analysis tool ANOVA: Single Factor. Applying this tool on the above data produces the following output:

The Null Hypothesis of the Brown-Forsythe Test states that the average distance to the median for the two groups are the same. Acceptance of this Null Hypothesis would imply that the sample groups have the same variances. The p Value shown in the Excel ANOVA output equals 0.0033. This is much smaller than the Alpha (0.05) that is typically used for an ANOVA Test so the Null Hypothesis should be rejected.

We therefore conclude as a result of the Brown-Forsythe Test that the variances are the not same.

Each of the above tests can be considered relatively equivalent to the others. We believe that the variances of both sample groups are dissimilar enough to force using an Unpooled test for this two-independent sample hypothesis test.

Excel Master Series Blog Directory

Statistical Topics and Articles In Each Topic

• Histograms in Excel
• Bar Chart in Excel
• Combinations & Permutations in Excel
• Normal Distribution in Excel
• t-Distribution in Excel
• Binomial Distribution in Excel
• z-Tests in Excel
• t-Tests in Excel
• Hypothesis Tests of Proportion in Excel
• Chi-Square Independence Tests in Excel
• Chi-Square Goodness-Of-Fit Tests in Excel
• F Tests in Excel
• Correlation in Excel
• Pearson Correlation in Excel
• Spearman Correlation in Excel
• Confidence Intervals in Excel
• Simple Linear Regression in Excel
• Multiple Linear Regression in Excel
• Logistic Regression in Excel
• Single-Factor ANOVA in Excel
• Two-Factor ANOVA With Replication in Excel
• Two-Factor ANOVA Without Replication in Excel
• Randomized Block Design ANOVA in Excel
• Repeated-Measures ANOVA in Excel
• ANCOVA in Excel
• Creating Interactive Graphs of Statistical Distributions in Excel
• Solving Problems With Other Distributions in Excel
• Optimization With Excel Solver
• Chi-Square Population Variance Test in Excel
• Analyzing Data With Pivot Tables
• SEO Functions in Excel
• Time Series Analysis in Excel
• VLOOKUP