Question

A market researcher wants to determine how long the flavor last for a three different types of chewing gums made by a client. The researcher randomly selects participants and asks them to chew a different piece of gum in each of three days. The order of the gums was randomly determined for each participant. After two hours of chewing, participants recorded the intensity of the gum flavor. Below are the data. What can be concluded with α = 0.01?

gum 1	gum 2	gum 3
4 3 6 6 3 4 4 6 4	6 6 3 2 7 7 6 9 6	5 4 6 7 7 5 4 5 5

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

b) Compute the appropriate test statistic(s) to make a decision about H₀.
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

c) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
η² =  ;  ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

At least one of the gums differ on flavor intensity.None of the gums differs on flavor intensity.    

Answer 1

a) What is the appropriate test statistic?
Ans: One-way ANOVA.

b) Compute the appropriate test statistic(s) to make a decision about H₀.

Tests of Between-Subjects Effects
Dependent Variable: Intensity
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	8.296a	2	4.148	1.723	.200
Intercept	725.926	1	725.926	301.538	.000
Gum	8.296	2	4.148	1.723	.200
Error	57.778	24	2.407
Total	792.000	27
Corrected Total	66.074	26

p-value = 0.200 ; Decision: Fail to reject H0

c) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
η² = 8.296/66.074=0.1256 ; small effect

d) Make an interpretation based on the results.

Ans: None of the gums differs on flavor intensity.