# Kruskal- Wallis test , scatter plot, regression equation

18.6 A business that is interested in starting an on-line shopping service is interested in finding out whether or not there are differences in how women shop on-line. They are interested in capturing people who are already connected to the Internet, so they run a Web. based survey. They ask respondents how many purchases they have made on-line in the last three months. In addition, they ask demographic questions about gender, age, and level of education. The data for women respondents in three age categories are shown below:

21-30 30-45 45-60

2 4 3

2 5 3

3 6 4

4 6 5

4 8 6

5 9 6

8 9 9

(b) Set up the hypotheses to see if there is a difference in the number of purchases made on-line by women for the three age groups.

(c) Find the rank for each data value, and find the rank sum and average rank for each sample.

(d) Perform the Kruskal- Wallis test at the 0.05 level of significance. What can you conclude?

15.25 The British Bankers' Association wanted to look at the relationship between the amount of deposits made (in billions of £) and the number of customers that a bank had. Analysts collected data on six different large banks and found the following information:

Bank Name Deposits (£ billion) Customers (million)

Abbey National 101.7 13.6

Barclays 108.2 10.0

Lloyds 96.9 15.0

National Westminster 113.8 7.5

Woolrich 27.5 4.0

Halifax 77.1 7.6

(a) Which variable is the independent variable? Which is the dependent variable?

(b) Create a scatter plot of the data. Does it appear that the amount of deposits is related to the number of customers?

(c) Find the equation of the regression line for the data-

(d) Plot the regression line on the same plot as the data. Do you think that the line does a good job of predicting the amount of deposits? Why or why not?

(e) Calculate the standard error of the estimate, Sylx' for the regression line.

(f) At the 0.05 level, is the model significant?

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#### Solution Summary

Answers questions on Kruskal- Wallis test , scatter plot, regression equation. The hypothesis to see if there is a difference in the number of purchases made on-line by women are determined.

Non-parametric Hypothesis Tests, Correlation & Regression

Use the RENAL.sav file from Norusis and do the following:

1) Mann-Whitney U test (nonparametric)

- Use the same variables you used in the Independent Samples t-test from DATA ANALYSIS PROJECT 3 (Assignment 11).

- Conduct a Mann-Whitney U test on the scale variable with the nominal variable as a grouping variable.

- Copy and paste the output in a Word processor in RTF format.

- State the hypothesis to be tested.

- State the reject / not reject decision and conclusion.

2) Kruskal-Wallis H test (nonparametric)

- Use the same variables you used in the One-Way ANOVA from DATA ANALYSIS PROJECT 3 (Assignment 11).

- Conduct a Kruskal-Wallis H test on the scale variable with the nominal variable as a grouping variable.

- Copy and paste the output in a Word processor in RTF format.

- State the hypothesis to be tested.

- State the reject / not reject decision and conclusion.

3) Chi Square test (nonparametric)

- Choose any two nominal variables from the RENAL.sav file.

- Conduct a Chi Square test of Independence on the two variables, displaying the crosstabulation table.

- Copy and paste the output in a Word processor in RTF format.

- State the hypothesis to be tested.

- State the reject / not reject decision and conclusion.

4) Correlation & Regression

- Choose any two scale variables from the RENAL.sav file.

- Create a scatterplot with regression line.

- Conduct a linear regression analysis and test for correlation.

- Copy and paste the output in a Word processor in RTF format.

- State the hypothesis to be tested.

- Discuss the computed values of R, R-squared and the regression model.

- State the reject / not reject decision and conclusion.

- In the RTF document, you should state the variables you are analyzing, display the SPSS output, and add a brief analysis of the output. The analysis should be a brief write-up (probably about one or two paragraphs) of what you can conclude from the output and any insights you might have. Disregard APA rules for this paper, but adhere to the rules of grammar / spelling / punctuation.

- Note: Please choose variables that you actually understand. The scoring breakdown is:

- 1 point: Selected correct variables for Mann-Whitney U test

- 1 point: Mann-Whitney U test performed correctly

- 1 point: Mann-Whitney U test decision and conclusion correct

- 1 point: Selected correct variables for Kruskal-Wallis H test

- 1 point: Kruskal-Wallis H test performed correctly

- 1 point: Kruskal-Wallis H test decision and conclusion correct

- 1 point: Selected correct variables for Chi Square

- 1 point: Chi Square performed correctly

- 1 point: Chi Square crosstabulation displayed correctly

- 1 point: Chi Square decision correct

- 1 point: Chi Square conclusion correct

- 1 point: Selected correct variables for Correlation & Regression

- 1 point: Correlation & Regression performed correctly

- 1 point: Scatterplot with line displayed correctly

- 1 point: Correlation decision and conclusion correct

- 1 point: R and R-squared discussed correctly

- 1 point: Regression Model stated correctly

- 3 points: Output explained correctly and completely (you may receive partial credit here)

Copy the SPSS output into a Word file and add your analysis at the appropriate spots within the document, then save the file as a .rtf file using the NCU file naming convention and submit for credit.

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