This is one of the following seven articles on 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

# Variance Tests Levene’s

Test and Brown-Forsythe

Test In Excel For Two-

Factor ANOVA With

Replication

Each of the three F Tests of Two-Factor ANOVA With Replication requires that the variances of all sample groups in the same F Test 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.** This is equivalent to stating that no data group’s variance can be more than four times the variance of another data group in the same F Test. That is the case here as the following are true for the levels of Factor 1 and Factor 2:

If the sample variance, VAR() in Excel, of the data groups at each factor level are calculated, the results are as follows:

*(Click Image To See a Larger Version)*

__Variances of Factor 1 Levels__

Var (Factor 1 Level 1) = 1,597

Var (Factor 1 Level 2) = 1,064

Var (Factor 1 Level 3) = 532

None of the Factor 1 Level data groups have a sample variance that is more than four times as large as the sample variance of another Factor 1 level group. The variance rule-of-thumb indicates that the variances of all data groups that are part of the Factor 1 Main Effects F Test should be considered similar. All of the Factor 1 level data groups are therefore **homoscedastistic** (have similar variances).

__Variances of Factor 2 Levels__

Var (Factor 2 Level 1) = 852

Var (Factor 2 Level 2) = 1,368

None of the Factor 2 Level data groups have a sample variance that is more than four times as large as the sample variance of another Factor 2 level group. The variance rule-of-thumb indicates that the variances of all data groups that are part of the Factor 2 Main Effects F Test should be considered similar. All of the Factor 2 level data groups are therefore homoscedastistic (have similar variances).

In addition to the variance comparison rule-of-thumb, 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 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.

Separate Levene’s Test will now be performed on the data groups for Factor 1 Main Effects F Test and for the Factor 2 Main Effects F Test. The absolute value of the distance from each sample point to the sample mean must be calculated. Single-Factor ANOVA in Excel is then run on these data sets.

Levene’s Test is performed on the Factor 1 level groups as follows:

*(Click Image To See a Larger Version)*

*(Click Image To See a Larger Version)*

α was set at 0.05 for this ANOVA test. The p Value of 0.2526 is larger than 0.05. This indicates that the average distances to the sample mean for each Factor 1 level data group are not significantly different. This result of Levene’s test is interpreted to mean that the Factor 1 level data groups have similar variances and are therefore homoscedstistic.

Levene’s Test is performed on the Factor 2 level groups as follows:

*(Click Image To See a Larger Version)*

α was set at 0.05 for this ANOVA test. The p Value of 0.2519 is larger than 0.05. This indicates that the average distances to the sample mean for each Factor 2 level data group are not significantly different. This result of Levene’s test is interpreted to mean that the Factor 2 level data groups have similar variances and are therefore homoscedastistic.

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

Separate Brown-Forsythe Test will now be performed on the data groups for Factor 1 Main Effects F Test and for the Factor 2 Main Effects F Test. The absolute value of the distance from each sample point to the sample median must be calculated. Single-Factor ANOVA in Excel is then run on these data sets.

The Brown-Forsythe Test is performed on the Factor 1 level groups as follows:

*(Click Image To See a Larger Version)*

*(Click Image To See a Larger Version)*

α was set at 0.05 for this ANOVA test. The p Value of 0.2530 is larger than 0.05. This indicates that the average distances to the sample mean for each Factor 1 level data group are not significantly different. This result of this Brown-Forsythe test is interpreted to mean that the Factor 1 level data groups have similar variances and are therefore homoscedastistic.

The Brown-Forsythe Test is performed on the Factor 2 level groups as follows:

*(Click Image To See a Larger Version)*

*(Click Image To See a Larger Version)*

α was set at 0.05 for this ANOVA test. The p Value of 0.3065 is larger than 0.05. This indicates that the average distances to the sample mean for each Factor 2 level data group are not significantly different. This result of this Brown-Forsythe test is interpreted to mean that the Factor 2 level data groups have similar variances and are therefore homoscedastistic.

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

Each of these two variance tests, Levene’s Test and the Brown-Forsythe Test, can be considered relatively equivalent to the other.

**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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- 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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