Question

Research Scenario: The following scenario is based loosely on an actual study conducted in 2013 by Ahn, Kim, and Aggarwal– please note that methods and data have been modified for educational purposes.

Do you turn off the light when you leave the room? South Korean researchers wondered how they could increase the number of people who do by use of posters (Ahn, Kim, & Aggarwal, 2013). In one, an image of a light bulb was anthropomorphized by giving it eyes, nose, and a mouth, as well as adding the words, “I’m burning hot, turn me off when you leave!”. In a second, there were no human features on the light bulb and the text simply said, “Our bulbs are burning hot, turn the lights off when you leave!”.

They compared how people would respond to the two posters by having each displayed in separate coffee rooms for two weeks. Although the coffee rooms were different, they were matched as closely as possible on as many parameters as possible (similar business, # of employees, et cet) such that this is a correlated groups design. Percent likelihood of someone turning off the light upon exiting was calculated every day and is presented below. Select and conduct the most appropriate statistical test based on the premise that all assumptions are met for a parametric test and this is a correlated groups design. Determine whether there is a difference in likelihood of turning off the light based on the poster campaign.

Anthropomorphism	Nonanthropomorphism
87.2	76.3
78.1	86.2
77.5	76.5
91.9	87.0
86.6	77.6
87.4	86.8
76.5	76.2
65.7	65.2
88.3	55.4
57.5	51.7
68.6	61.8
67.9	53.7
73.5	62.9
77.7	57.6

If the assumptions had been violated, what would the most appropriate statistical test be?

Answer 1

Introduction:

Denote μ₁ as the mean percent likelihood of turning off the light upon exiting, in case of anthropomorphism, and μ₂ as the mean percent likelihood of turning off the light upon exiting, in case of no anthropomorphism.

Denote the difference between the two means above as, μ_d = μ₁ – μ₂.

In order to test whether there is a difference in likelihood of turning off the light based on the poster campaign, the null and alternative hypotheses can be defined as follows:

.

Parametric test:

At first, it is assumed that all the assumptions for a parametric test are satisfied.

Since the study design is a correlated groups design, it is implied that the two groups- Anthropomorphism and Nonanthropomorphism are not independent, but correlated. In this situation, assuming that the data are approximately normally distributed, the Paired t-test can be used to test the given hypotheses.

We have performed the analyses using Excel.

Open the data in an Excel sheet.

Go to Data > Data Analysis > t-Test: Paired Two Sample for Means > OK.

In Variable 1 Range, enter $A$1:$A$15. In Variable 2 Range, enter $B$1:$B$15.

Enter the Hypothesized Mean Difference as 0, tick on Labels, enter Alpha as 0.05 and click OK.

(We have taken the level of significance as 0.05; you can take any other suitable value according to your wish, if no information is given.)

The output is given below:

Since the alternative hypothesis is “not equal to” type, the conducted test is both-tailed.

In the output, the p-value for a two-tailed test is given by “P(T<=t) two-tail” the value of which is 0.0122 (correct to two decimal places).

The rejection rule is: “Reject H₀ if p-value ≤ α”.

Here, p-value (0.0122) is less than α (0.05). Hence, reject the null hypothesis.

Thus, the parametric test (paired t-test) provides enough evidence to suggest that there is a difference in likelihood of turning off the light based on the poster campaign.

Non-parametric situation:

Wilcoxon signed-rank test is the non-parametric counterpart of the paired t-test. Hence, if the assumptions for a parametric test had been violated, the most appropriate statistical test would be Wilcoxon signed-rank test.