# Two-way analysis of variance (ANOVA) with replication

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An experiment is conducted to study the effects of two sales approaches-high-pressure (H) and low-pressure (L)-and to study the effects of two sales pitches (1 and 2) on the weekly sales of a product. The data in Table (1) below are obtained by using a completely randomized design, and Figure (2) gives the Excel output of a two-way ANOVA of the sales experiment data.

a Perform graphical analysis to check for interaction between sales pressure and sales pitch.

b Test for interaction by setting a = .05.

c Test for differences in the effects of the levels of sales pressure by setting a _ .05. That is, test the significance of sales pressure effects with a = .05.

d Calculate and interpret a 95 percent individual confidence interval for

uH - uL

e Test for differences in the effects of the levels of sales pitch by setting a = .05. That is, test the significance of sales pitch effects with a = .05.

f Calculate and interpret a 95 percent individual confidence interval for

u1 - u2.

g Calculate a 95 percent (individual) confidence interval for mean sales when using high sales pressure and sales pitch 1. Interpret this interval.

(1) Results of the Sales Approach Experiment

Sales Pressure

1 2

H

32 32

29 30

30 28

L 28 25

25 24

23 23

(2) Excel Output of a Two-Way ANOVA of the

Sales Approach Data

Anova: Two-Factor with Replication

SUMMARY One Two Total

H

Count 3 3 6

Sum 91 90 181

Average 30.33333 30 30.16667p

Variance 2.333333 4 2.566667

L

Count 3 3 6

Sum 76 72 148

Average 25.33333 24 24.66667q

Variance 6.333333 1 3.466667

Total

Count 6 6

Sum 167 162

Average 27.83333r 27s

Variance 10.96667 12.8

ANOVA

Source of

Variation SS df MS F p-Value F Crit

Pressure 90.75 (a) 1 90.75 (f) 26.56098 (j) 0.00087 (k) 5.317645

Pitch 2.083333 (b) 1 2.083333 (g) 0.609756 (l) 0.457362 (m) 5.317645

Interaction 0.75 (c) 1 0.75 (h) 0.219512 (n) 0.651913 (o) 5.317645

Within 27.33333 (d) 8 3.416667(i)

Total 120.9167 (e) 11

(a) SS(1)

(b) SS(2)

(c) SS(int)

(d) SSE

(e) SSTO

(f) MS(1)

(g) MS(2)

(h) MS(int)

(i) MSE

(j) F(1)

(k) p-value for F(1)

(l) F(2)

(m) p-value for F(2)

(n) F(int)

(o) p-value for F(int)

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##### Solution Summary

In this solution we analyze and interpret a two-way analysis of variance (ANOVA). We show a graphical analysis to check for interaction along with a formal test for interaction. We calculate a confidence interval for the difference in means (main effects) and confidence interval for a cell mean.

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In this solution we analyze and interpret a two-way analysis of variance (ANOVA). We show a graphical ...

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