Friday, May 30, 2014

Excel Variance Tests: Levene’s, Brown-Forsythe, and F Test For 2-Sample Pooled t-Test in Excel 2010 and Excel 2013

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

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

Excel Variance Tests: Levene’s, Brown-Forsythe, and F Test For 2-Sample Pooled t-Test in Excel 2010 and Excel 2013

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

Two-Independent-Sample Pooled t-Test - All Excel Calculations

2-Sample Pooled t-Test – Effect Size in Excel 2010 and Excel 2013

2-Sample Pooled t-Test Power With G*Power Utility

Mann-Whitney U Test in 12 Steps in Excel as 2-Sample Pooled t-Test Nonparametric Alternative in Excel 2010 and Excel 2013

2- Sample Pooled t-Test = Single-Factor ANOVA With 2 Sample Groups

 

Excel Variance Tests:

Levene’s, Brown-

Forsythe, and F Test For

2-Sample Pooled t-Test

Two-independent-sample t-Test are performed as either as a Pooled test or Unpooled tests. 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 the case here as the following are true:

s1 = sample1 standard deviation = 16.92

and

s2 = sample2 standard deviation = 15.28

 

F Test For Sample Group Variance

Comparison in Excel

An Excel F Test performed on the two sample groups produces the following output:

levenes test,levene,levene's brown-forsythe,variance, pooled t-test, t test,excel,excel 2010,excel 2013,statistcs (Click On Image To See a Larger Version)

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 0.345. This is much larger than the Alpha (0.05) that is typically used for an F Test so the Null Hypothesis cannot be rejected.

We therefore conclude as a result of the F Test that the variances are the 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 Group

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:

levenes test,levene,levene's brown-forsythe,variance, pooled t-test, t test,excel,excel 2010,excel 2013,statistcs (Click On Image To See a Larger Version)

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:

levenes test,levene,levene's brown-forsythe,variance, pooled t-test, t test,excel,excel 2010,excel 2013,statistcs (Click On Image To See a Larger Version)

The Null Hypothesis of Levene’s Test states that the average distance to the mean 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 0.6472. This is much larger than the Alpha (0.05) that is typically used for an ANOVA Test so the Null Hypothesis cannot be rejected.

We therefore conclude as a result of Levene’s Test that the variances are the same or, at least, that we don’t have enough evidence to state 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

Group 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:

levenes test,levene,levene's brown-forsythe,variance, pooled t-test, t test,excel,excel 2010,excel 2013,statistcs (Click On Image To See a Larger Version)

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:

levenes test,levene,levene's brown-forsythe,variance, pooled t-test, t test,excel,excel 2010,excel 2013,statistcs (Click On Image To See a Larger Version)

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 0.6627. This is much larger than the Alpha (0.05) that is typically used for an ANOVA Test so the Null Hypothesis cannot be rejected.

We therefore conclude as a result of the Brown-Forsythe Test that the variances are the same or, at least, that we don’t have enough evidence to state that the variances are different.

Each of the above tests can be considered relatively equivalent to the others. The variances of both sample groups are verified to be similar enough to permit using a Pooled test for this two-independent sample hypothesis test.

 

Excel Master Series Blog Directory

Statistical Topics and Articles In Each Topic

 

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