Use SPSS To Conduct Non-Parametric Tests - SPSS Help

Our main purpose is to examine the effects of Gender and Income on the frequency of visits to the popular North American hamburger chain, McDonald’s for its Bloomingdale location. We recorded the following variables in our database:

• Frequency (Number of visits to McDonalds)

• Income: It is recorded in its raw form, and then it's codified into categories:

1: 0 – 24K
2: 25 – 49K
3: 50 – 74K

4: 75K and above

• Gender: Female = 1, Male = 2

The raw dataset is shown below:

INFLUENCE OF GENDER OVER FREQUENCY:

We need to test the following hypotheses:

\[\begin{align} & {{H}_{0}}:\text{ Gender and Frequency are independent} \\ & {{H}_{A}}:\text{ Gender and Frequency are NOT}\text{ independent} \\ \end{align}\]

We'll use a crosstab and the Chi-Square test. The analysis makes sense since both variables are categorical.

We have the following summary of the analysis.

• The crosstab between Frequency and Gender is shown below:

• The results of the Chi-Square Test are shown below:

The significance of the test is

\[p=0.813\]

Since the p-value is not less than 0.05, we fail to reject the null hypothesis of independence. This means that we don't have enough evidence to claim that the variables Frequency and Gender are not independent.

• Other measures of association:

The values of the significances (greater than 0.05) and the low values of the directional measures confirm the lack of association between Gender and Frequency.

We see the results found with StaTtool:

Finally we show a histogram of the frequency of each category, for each gender:

INFLUENCE OF INCOME OVER FREQUENCY:

We need to test the following hypotheses:

\[\begin{align} & {{H}_{0}}:\text{ Gender and Frequency are independent} \\ & {{H}_{A}}:\text{ Gender and Frequency are NOT}\text{ independent} \\ \end{align}\]

• We'll use again a crosstabulation and the Chi-Square test. We have the following summary of the analysis.

• The crosstab between Frequency and Income is shown below:

• The results of the Chi-Square Test are shown below:

The significance of the test is

\[p=0.177\]

Since the p-value is not less than 0.05, we fail to reject the null hypothesis of independence. This means that we don't have enough evidence to claim that the variables Frequency and Income are not independent.

• Other measures of association: In this case both variables are ordinal, therefore, we can get some different statistics.

Even though the Chi-Square test showed not enough evidence of dependence between the variables, the significances for the Directional Measures and the Symmetric measures are less than 0.05, which indicates a certain degree of association. But the low values of the statistics show a rather weak of association between Income and Frequency.

• Now we show the work with StaTtool

Distance from Expected	Income 1	Income 2	Income 3	Income 4
1	1.4077	0.8605	0.0365	1.9078
2	0.0314	0.3456	0.0342	1.6709
3	1.1745	0.4024	0.0446	0.9749
4	1.0541	0.0305	0.4042	1.3726
5	0.2703	2.5118	0.3654	1.1486
6	0.5676	0.8148	0.0371	2.4122

Finally we show a histogram of the frequency of each category, for each Income Category:

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