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h groups (or columns) ijXX Copyright 169。 2022 by Harcourt, Inc. All rights reserved. ????njjjn12b e t w e e n)( SS XXAnalysis of Variance Sum of squares Copyright 169。 2022 by Harcourt, Inc. All rights reserved. Analysis of Variance Sum of squares = individual scores, ., the ith observation or test unit in the jth group = grand mean nj = number of all observations or test units in a group jXX Copyright 169。 2022 by Harcourt, Inc. All rights reserved. 1??cSSMSb e tw e enb e tw e enAnalysis of Variance Mean Squares Between Copyright 169。 2022 by Harcourt, Inc. All rights reserved. cSSMSw it hi nw it hi n??Analysis of Variance Mean Square Within Copyright 169。 2022 by Harcourt, Inc. All rights reserved. w it hinbe tw e e nMSMSF ?Analysis of Variance Calculation of FRatio Copyright 169。 2022 by Harcourt, Inc. All rights reserved. A Test Market Experiment on Pricing Sales in Units (thousands) Regular Price $.99 130 118 87 84 X1= X= Reduced Price $.89 145 143 120 131 X2= CentsOff Coupon Regular Price 153 129 96 99 X1= Test Market A, B, or C Test Market D, E, or F Test Market G, H, or I Test Market J, K, or L Mean Grand Mean Copyright 169。 2022 by Harcourt, Inc. All rights reserved. ANOVA Summary Table Source of Variation ? Between Groups ? Sum of Squares – SSBETWEEN ? Degrees of Freedom – c1 where c=number of groups ? Mean SquaredMSBETWEEN – SSBETWEEN/c1 Copyright 169。 2022 by Harcourt, Inc. All rights reserved. ? Within Groups ? Sum of Squares – SSWITHIN ? Degrees of Freedom – c where c=number of groups, n= number of observations in a group ? Mean SquaredMSWITHIN – SSWITHIN/c ANOVA Summary Table Source of Variation Copyright 169。 2022 by Harcourt, Inc. All rights reserved. ? Total ? Sum of Squares – SSTOTAL ? Degrees of Freedom – 1 where c=number of groups, n= number of observations in a group W I T H I NBET W EENMSMSF ?ANOVA Summary Table Source of Variation Copyright 169。 2022 by Harcourt, Inc. All rights reserved. Type of Measurement Differences between two independent groups Ordinal MannWhitney Utest Wilcocon test