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

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:

q_2,3 = ABS(x_bar₂ – x_bar₃) / SE_2,3

ABS(x_bar₂ – x_bar₃) = 1.205

Var₂ = 2.292

Var₃ = 2.408

n₂ = 23

n₃ = 18

(Click Image To See a Larger Version)

SE_2,3= SQRT ( 1/2 * (Var₂/n₂ + Var₃/n₃) )

SE_2,3= =SQRT((0.5)*(2.292/23+2.408/18)) = 0.3416

q_2,3 = 1.205/0.3416 = 3.527

(Click Image To See a Larger Version)

df_2,3 = degrees of freedom =

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

df_2,3 = 37

and number of groups equals 3

From the Studentized Range q table

q_Critical= 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

Technorati Tags: anova,post hoc,one-way anova,single-factor anova,excel,excel 2010,excel 2013,statistics,games-howell

Become an Excel Statistical Master

Excel Master Series - MBA-level statistics - Over 1,100+ Pages of Easy-To-Follow Instructions in Excel

It's a Full
Easy-To-Follow
MBA Course in Business Statistics

ALL IN EXCEL

&

MUCH Clearer

Than Your Text

Book

Download the
1,100+ Page Excel Statistical Master now

More Easy-To-

Follow eManuals

That You Will

Master Quickly

Step-By-Step Optimization With Excel Solver

What's In It?

For anyone who wants to be operating at a high level with the Excel Solver quickly, this is the book for you. Step-By-Step Optimization With Excel Solver is a 200+ page .pdf e-manual of simple yet thorough explanations on how to use the Excel Solver to solve today’s most widely known optimization problems. Loaded with screen shots that are coupled with easy-to-follow instructions, this book will simplify many difficult optimization problems and make you a master of the Excel Solver almost immediately.

Here are just some of the Solver optimization problems that are solved completely with simple-to-understand instructions and screen shots in this e-manual:

• The famous “Traveling Salesman” problem using Solver’s Alldifferent constraint and the Solver’s Evolutionary method to find the shortest path to reach all customers. This also provides an advanced use of the Excel INDEX function.

• The well-known “Knapsack Problem” which shows how optimize the use of limited space while satisfying numerous other criteria.

• How to perform nonlinear regression and curve-fitting on the Solver using the Solver’s GRG Nonlinear solving method.

• How to solve the “Cutting Stock Problem” faced by many manufacturing companies who are trying to determine the optimal way to cut sheets of material to minimize waste while satisfying customer orders.

• Portfolio optimization to maximize return or minimize risk.

• Venture capital investment selection using the Solver’s Binary constraint to maximize Net Present Value of selected cash flows at year 0. Clever use of the If-Then-Else statements makes this a simple problem.

• How use Solver to minimize the total cost of purchasing and shipping goods from multiple suppliers to multiple locations.

• How to optimize the selection of different production machine to minimize cost while fulfilling an order.

• How to optimally allocate a marketing budget to generate the greatest reach and frequency or number of inbound leads at the lowest cost.

Step-By-Step Optimization With Excel Solver has complete instructions and numerous tips on every aspect of operating the Excel Solver. You’ll fully understand the reports and know exactly how to tweek all of the Solver’s settings for total custom use. This e-manual also provides lots of inside advice and guidance on setting up the model in Excel so that it will be as simple and intuitive as possible to work with.

All of the optimization problems in this book are solved step-by-step using a 6-step process that works every time. In addition to detailed screen shots and easy-to-follow explanations on how to solve every optimization problem in the book, a link is provided to download an Excel workbook that has all problems completed exactly as they are in this e-manual.

Step-By-Step Optimization With Excel Solver is exactly the e-manual you need if you want to be optimizing at an advanced level with the Excel Solver quickly.

*******************

Become an Excel Statistical Master

It's a Full
Easy-To-Follow
MBA Course in Business Statistics

ALL IN EXCEL

&

MUCH Clearer

Than Your Text

Book

Download the
1,100+ Page Excel Statistical Master now

More Easy-To-

Follow eManuals

That You Will

Master Quickly

*******************

Become an Excel Statistical Master

It's a Full
Easy-To-Follow
MBA Course in Business Statistics

ALL IN EXCEL

&

MUCH Clearer

Than Your Text

Book

Download the
1,100+ Page Excel Statistical Master now

More Easy-To-

Follow eManuals

That You Will

Master Quickly

*******************

Become an Excel Statistical Master

It's a Full
Easy-To-Follow
MBA Course in Business Statistics

ALL IN EXCEL

&

MUCH Clearer

Than Your Text

Book

Download the
1,100+ Page Excel Statistical Master now

Immediate, Absolute, No-Questions-Asked, Money-Back Guarantee If Not TOTALLY, 100% Satisfied. In Other Words, If Any Excel Master Series eManual That You've Purchased Here Does Not Provide Instructions That Are CRYSTAL CLEAR and EASY TO UNDERSTAND, You Get All Of Your Money Back Immediately and Keep the eManual. Guaranteed!

Meet The Author