Question

What is a research question i can use two-way ANOVA to figure out? And what is the solution to it.

Answer 1

Research question for two-way ANOVA:

If three sales men, each sold products in three different market areas, determine:

1. if the mean difference of number of products sold between sales men is significant,

2. if the mean difference of number of products sold between market areas is significant and

3. if there is any interaction effect between Sales men and market areas.

Solution:

Hypotheses:

Null Hypothesis(H0):

1. The mean difference of number of products sold between sales men is not significant.

2. The mean difference of number of products sold between market areas is not significant.

3. There is no interaction effect between Sales men and market areas.

Alternative Hypothesis(H1):

1. The mean difference of number of products sold between sales men is significant.

2. The mean difference of number of products sold between market areas is significant.

3. There is an interaction effect between Sales men and market areas.

Number of products sold by each sales man in 3 different market areas:

[Rows 1,2,3 are Sales men 1,2,3 respectively

Columns 1,2,3 are Market areas 1,2,3 respectively].

ANOVA results:

Let the significance level =0.05

Conclusion:

1.

P-value for rows(sales men): 0.8278 > 0.05 (failed to reject H0). There is no sufficient evidence to claim that the difference of mean number of products sold between sales men is significant.

2.

P-value for columns (market areas): 0.5384 > 0.05 (failed to H0). There is no sufficient evidence to claim that the difference of mean number of products sold between market areas is significant.

3.

P-value for interaction (rows x columns): 0.9571 > 0.05 (failed to reject H0). There is no sufficient evidence to claim that there is an interaction effect between Sales men and Market areas.