This is one of the following sixteen articles on Single-Factor ANOVA in Excel

Overview of Single-Factor ANOVA

Single-Factor ANOVA in 5 Steps in Excel 2010 and Excel 2013

Shapiro-Wilk Normality Test in Excel For Each Single-Factor ANOVA Sample Group

Kruskal-Wallis Test Alternative For Single Factor ANOVA in 7 Steps in Excel 2010 and Excel 2013

Levene’s and Brown-Forsythe Tests in Excel For Single-Factor ANOVA Sample Group Variance Comparison

Single-Factor ANOVA - All Excel Calculations

Overview of Post-Hoc Testing For Single-Factor ANOVA

Tukey-Kramer Post-Hoc Test in Excel For Single-Factor ANOVA

Games-Howell Post-Hoc Test in Excel For Single-Factor ANOVA

Overview of Effect Size For Single-Factor ANOVA

ANOVA Effect Size Calculation Eta Squared in Excel 2010 and Excel 2013

ANOVA Effect Size Calculation Psi – RMSSE – in Excel 2010 and Excel 2013

ANOVA Effect Size Calculation Omega Squared in Excel 2010 and Excel 2013

Power of Single-Factor ANOVA Test Using Free Utility G*Power

# Levene’s and Brown-

Forsythe Tests in Excel

For Single-Factor ANOVA

Sample Group Variance

Comparison

Single-Factor ANOVA requires that the variances of all sample groups be similar. Sample groups that have similar variances are said to be **homoscedastistic**. Sample groups that have significantly different variances are said to be **heteroscedastistic .**

A rule-of-thumb is as follows:** Variances are considered similar if the standard deviation of any one group is no more than twice as large as the standard deviation of any other group.** That is the case here as the following are true:

s_{1} = Group1 standard deviation = 1.495

s_{2} = Group2 standard deviation = 1.514

s_{3} = Group3 standard deviation = 1.552

The variances of all three groups are very similar. A quick look at the box plot of the data would have confirmed that as well.

Two statistical tests are commonly performed when it is necessary to evaluate the equality of variances in sample groups. These tests are Levene’s Test and the Brown-Forsythe Test. The Brown-Forsythe Test is more robust against outliers but Levene’s Test is the more popular test.

## Levene’s Test in Excel For Sample

Group Variance Comparison

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 much more robust against non-normality of data than the F Test. That is why Levene’s Test is nearly always preferred over the F Test as a test for variance equality.

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:

*(Click 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**. Here is the completed dialogue box for this test:

*(Click Image To See a Larger Version)*

Applying this tool on the above data produces the following output:

*(Click Image To See a Larger Version)*

The Null Hypothesis of Levene’s Test states that the average distances to the mean for the two groups are the same. Acceptance of this Null Hypothesis would imply that the sample groups have the similar variances. The p Value shown in the Excel ANOVA output equals 0.9566. 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 in Excel For

Sample Group Variance Comparison

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 similar. The distance to the median for each data point of the three sample groups is shown as follows:

*(Click 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**. Here is the completed dialogue box for this test:

*(Click Image To See a Larger Version)*

Applying this tool on the above data produces the following output:

*(Click Image To See a Larger Version)*

The Null Hypothesis of the Brown-Forsythe Test states that the average distances to the median for the three groups are the same. Acceptance of this Null Hypothesis would imply that the sample groups have similar variances. The p Value shown in the Excel ANOVA output equals 0.9582. 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 these two variance tests can be considered relatively equivalent to the others.

### Alternative Tests To Single-Factor ANOVA When Sample Group Variances Are Not Similarity

When groups cannot be shown to have homogeneous (similar) variances, either Welch’s ANOVA or the Brown-Forsythe F test should be used in place of Single-Factor ANOVA. Both of these tests will be performed on this example’s data in blog articles that follow this one.

**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
- Overview of the Normal Distribution
- Normal Distribution’s PDF (Probability Density Function) in Excel 2010 and Excel 2013
- Normal Distribution’s CDF (Cumulative Distribution Function) in Excel 2010 and Excel 2013
- Solving Normal Distribution Problems in Excel 2010 and Excel 2013
- Overview of the Standard Normal Distribution in Excel 2010 and Excel 2013
- An Important Difference Between the t and Normal Distribution Graphs
- The Empirical Rule and Chebyshev’s Theorem in Excel – Calculating How Much Data Is a Certain Distance From the Mean
- Demonstrating the Central Limit Theorem In Excel 2010 and Excel 2013 In An Easy-To-Understand Way

- t-Distribution in Excel
- Binomial Distribution in Excel
- z-Tests in Excel
- Overview of Hypothesis Tests Using the Normal Distribution in Excel 2010 and Excel 2013
- One-Sample z-Test in 4 Steps in Excel 2010 and Excel 2013
- 2-Sample Unpooled z-Test in 4 Steps in Excel 2010 and Excel 2013
- Overview of the Paired (Two-Dependent-Sample) z-Test in 4 Steps in Excel 2010 and Excel 2013

- t-Tests in Excel
- Overview of t-Tests: Hypothesis Tests that Use the t-Distribution
- 1-Sample t-Tests in Excel
- 1-Sample t-Test in 4 Steps in Excel 2010 and Excel 2013
- Excel Normality Testing For the 1-Sample t-Test in Excel 2010 and Excel 2013
- 1-Sample t-Test – Effect Size in Excel 2010 and Excel 2013
- 1-Sample t-Test Power With G*Power Utility
- Wilcoxon Signed-Rank Test in 8 Steps As a 1-Sample t-Test Alternative in Excel 2010 and Excel 2013
- Sign Test As a 1-Sample t-Test Alternative in Excel 2010 and Excel 2013

- 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

- 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

- Paired (2-Sample Dependent) t-Tests in Excel
- Paired t-Test in 4 Steps in Excel 2010 and Excel 2013
- Excel Normality Testing of Paired t-Test Data
- Paired t-Test Excel Calculations, Formulas, and Tools
- Paired t-Test – Effect Size in Excel 2010, and Excel 2013
- Paired t-Test – Test Power With G-Power Utility
- Wilcoxon Signed-Rank Test in 8 Steps As a Paired t-Test Alternative
- Sign Test in Excel As A Paired t-Test Alternative

- Hypothesis Tests of Proportion in Excel
- Hypothesis Tests of Proportion Overview (Hypothesis Testing On Binomial Data)
- 1-Sample Hypothesis Test of Proportion in 4 Steps in Excel 2010 and Excel 2013
- 2-Sample Pooled Hypothesis Test of Proportion in 4 Steps in Excel 2010 and Excel 2013
- How To Build a Much More Useful Split-Tester in Excel Than Google's Website Optimizer

- 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
- z-Based Confidence Intervals of a Population Mean in 2 Steps in Excel 2010 and Excel 2013
- t-Based Confidence Intervals of a Population Mean in 2 Steps in Excel 2010 and Excel 2013
- Minimum Sample Size to Limit the Size of a Confidence interval of a Population Mean
- Confidence Interval of Population Proportion in 2 Steps in Excel 2010 and Excel 2013
- Min Sample Size of Confidence Interval of Proportion in Excel 2010 and Excel 2013

- Simple Linear Regression in Excel
- Overview of Simple Linear Regression in Excel 2010 and Excel 2013
- Complete Simple Linear Regression Example in 7 Steps in Excel 2010 and Excel 2013
- Residual Evaluation For Simple Regression in 8 Steps in Excel 2010 and Excel 2013
- Residual Normality Tests in Excel – Kolmogorov-Smirnov Test, Anderson-Darling Test, and Shapiro-Wilk Test For Simple Linear Regression
- Evaluation of Simple Regression Output For Excel 2010 and Excel 2013
- All Calculations Performed By the Simple Regression Data Analysis Tool in Excel 2010 and Excel 2013
- Prediction Interval of Simple Regression in Excel 2010 and Excel 2013

- Multiple Linear Regression in Excel
- Basics of Multiple Regression in Excel 2010 and Excel 2013
- Complete Multiple Linear Regression Example in 6 Steps in Excel 2010 and Excel 2013
- Multiple Linear Regression’s Required Residual Assumptions
- Normality Testing of Residuals in Excel 2010 and Excel 2013
- Evaluating the Excel Output of Multiple Regression
- Estimating the Prediction Interval of Multiple Regression in Excel
- Regression - How To Do Conjoint Analysis Using Dummy Variable Regression in Excel

- Logistic Regression in Excel
- Logistic Regression Overview
- Logistic Regression in 6 Steps in Excel 2010 and Excel 2013
- R Square For Logistic Regression Overview
- Excel R Square Tests: Nagelkerke, Cox and Snell, and Log-Linear Ratio in Excel 2010 and Excel 2013
- Likelihood Ratio Is Better Than Wald Statistic To Determine if the Variable Coefficients Are Significant For Excel 2010 and Excel 2013
- Excel Classification Table: Logistic Regression’s Percentage Correct of Predicted Results in Excel 2010 and Excel 2013
- Hosmer- Lemeshow Test in Excel – Logistic Regression Goodness-of-Fit Test in Excel 2010 and Excel 2013

- Single-Factor ANOVA in Excel
- Overview of Single-Factor ANOVA
- Single-Factor ANOVA in 5 Steps in Excel 2010 and Excel 2013
- Shapiro-Wilk Normality Test in Excel For Each Single-Factor ANOVA Sample Group
- Kruskal-Wallis Test Alternative For Single Factor ANOVA in 7 Steps in Excel 2010 and Excel 2013
- Levene’s and Brown-Forsythe Tests in Excel For Single-Factor ANOVA Sample Group Variance Comparison
- Single-Factor ANOVA - All Excel Calculations
- Overview of Post-Hoc Testing For Single-Factor ANOVA
- Tukey-Kramer Post-Hoc Test in Excel For Single-Factor ANOVA
- Games-Howell Post-Hoc Test in Excel For Single-Factor ANOVA
- Overview of Effect Size For Single-Factor ANOVA
- ANOVA Effect Size Calculation Eta Squared in Excel 2010 and Excel 2013
- ANOVA Effect Size Calculation Psi – RMSSE – in Excel 2010 and Excel 2013
- ANOVA Effect Size Calculation Omega Squared in Excel 2010 and Excel 2013
- Power of Single-Factor ANOVA Test Using Free Utility G*Power
- Welch’s ANOVA Test in 8 Steps in Excel Substitute For Single-Factor ANOVA When Sample Variances Are Not Similar
- Brown-Forsythe F-Test in 4 Steps in Excel Substitute For Single-Factor ANOVA When Sample Variances Are Not Similar

- Two-Factor ANOVA With Replication in Excel
- Two-Factor ANOVA With Replication in 5 Steps in Excel 2010 and Excel 2013
- Variance Tests: Levene’s and Brown-Forsythe For 2-Factor ANOVA in Excel 2010 and Excel 2013
- Shapiro-Wilk Normality Test in Excel For 2-Factor ANOVA With Replication
- 2-Factor ANOVA With Replication Effect Size in Excel 2010 and Excel 2013
- Excel Post Hoc Tukey’s HSD Test For 2-Factor ANOVA With Replication
- 2-Factor ANOVA With Replication – Test Power With G-Power Utility
- Scheirer-Ray-Hare Test Alternative For 2-Factor ANOVA With Replication

- Two-Factor ANOVA Without Replication in Excel
- Randomized Block Design ANOVA in Excel
- Repeated-Measures ANOVA in Excel
- Single-Factor Repeated-Measures ANOVA in 4 Steps in Excel 2010 and Excel 2013
- Sphericity Testing in 9 Steps For Repeated Measures ANOVA in Excel 2010 and Excel 2013
- Effect Size For Repeated-Measures ANOVA in Excel 2010 and Excel 2013
- Friedman Test in 3 Steps For Repeated-Measures ANOVA in Excel 2010 and Excel 2013

- ANCOVA in Excel
- Normality Testing in Excel
- Creating a Box Plot in 8 Steps in Excel
- Creating a Normal Probability Plot With Adjustable Confidence Interval Bands in 9 Steps in Excel With Formulas and a Bar Chart
- Chi-Square Goodness-of-Fit Test For Normality in 9 Steps in Excel
- Kolmogorov-Smirnov, Anderson-Darling, and Shapiro-Wilk Normality Tests in Excel

- Nonparametric Testing in Excel
- Mann-Whitney U Test in 12 Steps in Excel
- Wilcoxon Signed-Rank Test in 8 Steps in Excel
- Sign Test in Excel
- Friedman Test in 3 Steps in Excel
- Scheirer-Ray-Hope Test in Excel
- Welch's ANOVA Test in 8 Steps Test in Excel
- Brown-Forsythe F Test in 4 Steps Test in Excel
- Levene's Test and Brown-Forsythe Variance Tests in Excel
- Chi-Square Independence Test in 7 Steps in Excel
- Chi-Square Goodness-of-Fit Tests in Excel
- Chi-Square Population Variance Test in Excel

- Post Hoc Testing in Excel
- Creating Interactive Graphs of Statistical Distributions in Excel
- Interactive Statistical Distribution Graph in Excel 2010 and Excel 2013
- Interactive Graph of the Normal Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the Chi-Square Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the t-Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the t-Distribution’s PDF in Excel 2010 and Excel 2013
- Interactive Graph of the t-Distribution’s CDF in Excel 2010 and Excel 2013
- Interactive Graph of the Binomial Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the Exponential Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the Beta Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the Gamma Distribution in Excel 2010 and Excel 2013
- Interactive Graph of the Poisson Distribution in Excel 2010 and Excel 2013

- Solving Problems With Other Distributions in Excel
- Solving Uniform Distribution Problems in Excel 2010 and Excel 2013
- Solving Multinomial Distribution Problems in Excel 2010 and Excel 2013
- Solving Exponential Distribution Problems in Excel 2010 and Excel 2013
- Solving Beta Distribution Problems in Excel 2010 and Excel 2013
- Solving Gamma Distribution Problems in Excel 2010 and Excel 2013
- Solving Poisson Distribution Problems in Excel 2010 and Excel 2013

- Optimization With Excel Solver
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- Minimizing Cutting Stock Waste With Excel Solver
- Optimal Investment Selection With Excel Solver
- Minimizing the Total Cost of Shipping From Multiple Points To Multiple Points With Excel Solver
- Knapsack Loading Problem in Excel Solver – Optimizing the Loading of a Limited Compartment
- Optimizing a Bond Portfolio With Excel Solver
- Travelling Salesman Problem in Excel Solver – Finding the Shortest Path To Reach All Customers

- Chi-Square Population Variance Test in Excel
- Analyzing Data With Pivot Tables
- SEO Functions in Excel
- Time Series Analysis in Excel
- VLOOKUP

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