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

a)

Answer: two-way ANOVA

Explanation:

Since we want to see the effect of two factors Location and the Brand on the dependent variable (sales per day), the two-factor ANOVA with replication analysis is performed to test the hypothesis.

b)
Answer:

Location: critical value = 4.2597 ; test statistic = 20.8501
Decision: Reject H0

Brand: critical value = 4.2597; test statistic = 5.0247
Decision: Reject H0

Interaction: critical value = 4.2597 ; test statistic = 7.9678
Decision: Reject H0

Explanation:

The two factor ANOVA test three null hypothesis as shown below,

The Null and Alternative Hypotheses are,

H₀₁: There is no difference in the means of factor A

H_A1: There is a significant difference in the means of factor A

H₀₂: There is no difference in means of factor B

H_A2: There is a significant difference in means of factor B

H₀₃: There is no interaction between factors A and B

H_A3: There is a significant interaction between factors A and B

Where factor A is the Location, factor B is the Brand.

The test is performed in excel by using the following steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > ANOVA: Two Factor With Replication > OK.  The screenshot is shown below,

Step 3: Select Input Range: All the data values column, Rows per Sample: 7, Alpha = 0.05. The screenshot is shown below,

The result is obtained.  The screenshot is shown below,

Results of the study

Source of Variation	F		F crit	Decision
Location	20.8501	>	4.2597	Reject H0
Brand	5.0247	>	4.2597	Reject H1
Interaction	7.9678	>	4.2597	Reject H2

c)

Answer:

Location: η² = 0.3605; large effect
Brand: η² = 0.0869; medium effect
Interaction: η² = 0.1378 ; large effect

Explanation:

The effect size is obtained as follows,

For Location,

If the effect size is 0.14 or more, the effect is large

For Brand,

If the effect size is 0.06 to 0.14, the effect is medium

For interaction,

If the effect size is 0.14 or more, the effect is large