Question

It might be predicted that consumer buying behavior would vary with the location of products in a store. Therefore, a team of market researchers looked at the sales per day for a known and unknown brand of candy bars. Additionally, the researchers placed the candy bars in the usual location and next to the cash register in different stores. What can the market researchers conclude with an α of 0.05?

known brand		unknown brand
usual	register	usual	register
16 24 29 17 26 30 18	25 15 16 20 31 27 19	11 6 9 13 14 7 11	19 18 16 21 22 17 19

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Obtain/compute the appropriate values to make a decision about H₀.
Location: critical value = _______________ ; test statistic = _______________
Decision:  ---Select---  Reject H0 or Fail to reject H0


Brand: critical value = _______________ ; test statistic = _______________
Decision:  ---Select---  Reject H0 or Fail to reject H0


Interaction: critical value = _______________ ; test statistic = _______________
Decision:  ---Select--- Reject H0 or Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Location: η² =  _______________ ;  ---Select--- na trivial effect small effect medium effect large effect
Brand: η² = _______________ ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  _______________ ;  ---Select--- na trivial effect small effect medium effect large effect

Answer 1

Using Excel, input data in the following manner:

	Usual	Register
Known	16	25
	24	15
	29	16
	17	20
	26	31
	30	27
	18	19
Unknown	11	19
	6	18
	9	16
	13	21
	14	22
	7	17
	11	19

Go to Data, select Data Analysis, choose Anova: Two-Factor With Replication. Select all cells along with headings and put rows per sample = 7.

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Brand	432.143	1	432.143	20.850	0.000	4.260
Location	104.143	1	104.143	5.025	0.035	4.260
Interaction	165.143	1	165.143	7.968	0.009	4.260
Within	497.429	24	20.726
Total	1198.857	27

a) two-way ANOVA

b) Location: critical value = 4.260; test statistic = 104.143

Decision: Reject H0

Brand: critical value = 4.26 ; test statistic = 20.85
Decision: Reject H0
Interaction: critical value = 4.26 ; test statistic = 7.968
Decision: Reject H0

c) Location: η² =  SS Location/SS Total = 104.143/1198.857 = 0.087 (Small)
Brand: η² = SS Brand/SS Total = 432.143/1198.857 = 0.36 (Small)
Interaction: η² =  SS Interaction/SS Total = 165.143/1198.857 = 0.138 (Small)