## Thursday, May 29, 2014

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

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

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

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

The Games-Howell test is performed the same way as the Tukey-Kramer test except that standard error and degrees of freedom are calculated with different formulas as follows:

The Test Statistic q is calculated as follows:

(Click Image To See a Larger Version)

where SE (standard error) is calculated as follows:

(Click Image To See a Larger Version)

and

df = degrees of freedom =

(Click Image To See a Larger Version)

In Excel terms, the formula is expressed as the following:

df = ( ( (Var1/n1) + (Var2/n2) )^2 ) / ( ((Var1/n1)^2 / (n1 - 1) ) + ( (Var2/n2)^2 / (n2-1) ) )

The Excel ANOVA output for the sample data set is given once again as follows:

(Click Image To See a Larger Version)

The two groups having the largest difference in means are groups 2 and 3. This group pair will therefore be the first evaluated to determine if its difference is large enough to be significant.

Test Statistic q for this group pair will be calculated as follows:

q2,3 = ABS(x_bar2 – x_bar3) / SE2,3

ABS(x_bar2 – x_bar3) = 1.205

Var2 = 2.292

Var3 = 2.408

n2 = 23

n3 = 18

(Click Image To See a Larger Version)

SE2,3 = SQRT ( 1/2 * (Var2 /n2 + Var3 /n3) )

SE2,3 = =SQRT((0.5)*(2.292/23+2.408/18)) = 0.3416

q2,3 = 1.205/0.3416 = 3.527

(Click Image To See a Larger Version)

df2,3 = degrees of freedom =

= ( ( (Var2/n2) + (Var3/n3) )^2 ) / ( ((Var2/n2)^2 / (n2 - 1)) + ( (Var3/n3)^2 / (n3-1) ) )

df2,3 = 37

and number of groups equals 3

From the Studentized Range q table

qCritical = 3.453

(Click Image To See a Larger Version)

According to the Games-Howell test, the largest difference (pair 2,3) is significant because q(2,3) = 3.566 and is larger than q(2,3)Critical = 3.399. The differences between the other pairs are not significant because q(1,2) = 0.6809 is smaller than q(1,2)Critical = 3.433 and q(1,3) = 2.883 is smaller than q(1,3)Critical = 3.457.

The Tukey-Kramer test and the Games-Howell produced very similar results when applied to this data.

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
• Normality Testing in Excel
• Nonparametric Testing in Excel
• Post Hoc Testing 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