Question

Overview

The SPSS output tables below are all based on a larger study of product assessments for an ecologically friendly engine oil. Participants saw the packaging of an ecologically friendly engine oil on their computer screen and were asked several questions regarding how they perceived this product. The tables below focus on only a few of the variables used in the study.

Coding

Gender was coded as 1=female and 2=male

PWOP_M_S refers to perceived warmth of product. Participants were asked to which extent they perceived the product as “warm.” The assumption is that the perception of the color of the product’s packaging influences this assessment. For this Chapter 11 exercise, I performed a median split on the variable. Thus, the variable is now dichotomous with 1=low perceived warmth and 2=high perceived warmth.

FLUEN_M_S refers to processing fluency. Participants were asked to which extent they perceived the product and its packaging as easy to process, well organized, logical, etc. For this Chapter 11 exercise, I performed a median split on the variable. Thus, the variable is now dichotomous with 1=low fluency and 2=high fluency.

A_PI refers to purchase intentions. This variable is continuous on a scale from 1 to 7. Higher values represent higher purchase intentions.

Note 1: It may be true that you are not fully familiar with the constructs and do not know much about the study context, but you can nevertheless interpret the results provided in a table from a statistical point of view.

Note 2: When responding to the questions, please provide your answers in a way which will encourage the reader to believe that you understood the logic of these statistical tests. For example, it is helpful to point out which numbers in the tables are important, and what the meaning of these numbers is.

Question 11.1

The following two tables are equivalent to Exhibit 11.10 in your textbook (Crosstab Chi-Square example).

Please provide an interpretation of the two tables. What are the insights we can obtain from the SPSS output shown below? What is the meaning of the “count” vs. the “expected count” information in the table? (explain the logic with an example from the table). What is the logic of the Chi Square tests (and specifically, what is the meaning of the numbers shown in the “Asymp. Sig” column?

PWOP_M_S * GENDER Crosstabulation
			GENDER		Total
			female	male
PWOP_M_S	1.00	Count	115	95	210
		Expected Count	104.7	105.3	210.0
		% within PWOP_M_S	54.8%	45.2%	100.0%
		% within GENDER	55.3%	45.5%	50.4%
		% of Total	27.6%	22.8%	50.4%
	2.00	Count	93	114	207
		Expected Count	103.3	103.7	207.0
		% within PWOP_M_S	44.9%	55.1%	100.0%
		% within GENDER	44.7%	54.5%	49.6%
		% of Total	22.3%	27.3%	49.6%
Total		Count	208	209	417
		Expected Count	208.0	209.0	417.0
		% within PWOP_M_S	49.9%	50.1%	100.0%
		% within GENDER	100.0%	100.0%	100.0%
		% of Total	49.9%	50.1%	100.0%

Chi-Square Tests
	Value	df	Asymptotic Significance (2-sided)
Pearson Chi-Square	4.033a	1	.045
Likelihood Ratio	4.039	1	.044
Linear-by-Linear Association	4.023	1	.045
N of Valid Cases	417
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 103.25.
b. Computed only for a 2x2 table

Answer 1

The first table gives the data regarding how the participants perceived the warmth of the product. The participants are further divided between females and males. The perception of warmth is further divided into low perceived warmth that is indicated by 1 and high perceived warmth that is indicated by 2. For the purpose of the analysis the candidates are subject to product and asked whether the product is warm or not. The controlling aspect becomes the color of the product packaging which is tested to understand whether the product is perceived warm by the participants by just the look of its color.

The first table is the data table that consists the information of the number of participants that are both male and female that perceive the product as both low warm and high warm. Consequently we have a 2x2 table with actual data and the given table also notifies the expected data. Further statistics such as expected count and actual count and the percentage of male and female participants with perceived warmth are given.

The second table denotes the chi square test statistics which gives the pearsons chi square statistic, likelihood ratio statistic and the linear by linear association statistic.

One can observe from the test statistic table that at 5% level of significance one can reject the null hypothesis that the color of the product packaging does not affect the perception of the participants whether the products are warm or not.

Count is the actual number of participants who responded to about the low and high warmth of the product. This actual count is also bifurcated into males and females. The expected count information in the table denotes the expected number of participants who should have responded to the warmth of the products given their exact bifurcation in the population. For example, out of 210 who responded low warmth 49.9% of 210 i.e. 104.7 females should have responded low warmth as opposed to 115 actual count.

The chi squared test works under the null hypothesis that there is no association between the gender of the participants and the color of the product packaging. The test is asymptotic two-sided since it takes into account both the positive as well as the negative association of the variables under consideration.

From the test results one can conclude that there is certainly some association between the gender as well as the colour of the product that makes the participant perceive it as warm.