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Non-parametric test, parametric alternative, counterparts

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1. What are the most common reasons you would select a non-parametric test over the parametric alternative?

2. Discuss the issue of statistical power in non-parametric tests (as compared to their parametric counterparts). Which type tends to be more powerful? Why?

3. For each of the following parametric tests, identify the appropriate non-parametric counterpart:

a. Dependent t-test

b. Independent samples t-test

c. Repeated measures ANOVA (one-variable)

d. One-way ANOVA (independent)

e. Pearson Correlation

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(1) If a statistical variable understudy can be represented on a ratio or at least an interval scale of measurement, then it is said to have proper units. With some assumption made about the distribution of the variable (say normality, for example), the variable is fit to be tested parametrically. The t-test, the z-test etc are a few well-known parametric testing methods. But these tests lay different restrictions on the data.

If a statistical variable is of the nominal or ordinal type only, then it does not qualify to be parametrically tested. ...

Solution Summary

Non-parametric test, parametric alternative and non-parametric counterparts are examined.

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Non-parametric Methods

1. Complete the following exercises using Non-parametric Methods:
a. Exercise 1-Sign Test
Are stock splits beneficial to stockholders? SNL Securities studied stock splits in the banking industry over an 18-month period and found that stock splits tended to increase the value of an individual's stock holding. Assume that of a sample of 20 recent stock splits, 14 led to an increase in value, four led to a decrease in value, and two resulted in no change. Suppose a sign test is to be used to determine whether stock splits continue to be beneficial for holders of bank stocks.
1) What are the null and alternative hypotheses?
2) With α = .05, what is the rejection rule?
3) What is your conclusion?
(Reference: Anderson, Sweeney, Williams, 2002, print version, section 5, p. 381, exercise 3)
b. Exercise 2-Wilcoxon-Signed Rank Test
The 1997 price/earnings ratios for a sample of 12 stocks are shown in the following list ( Barron's, December 8, 1997). Assume that a financial analyst has provided the estimated price/earnings ratio for 1998. Using a .05 level of significance, what is your conclusion about the differences between the price/earnings ratios for 1997 and 1998?

Coca-Cola 40 32
Du Pont 24 22
Eastman Kodak 21 23
General Electric 30 23
General Mills 25 19
IBM 19 19
McDonalds 20 17
Merck 29 19
Motorola 35 20
Philip Morris 17 18
Walt Disney 33 27
Xerox 20 16

(Reference: Anderson, Sweeney, Williams, 2002, print version, section 5, p. 386, exercise 16)
c. Exercise 3-Mann-Whitney-Wilcoxon Test
Samples of starting annual salaries for individuals entering the public accounting and financial planning professions follow (Fortune, June 26, 1995). Annual salaries are shown in thousands of dollars.

Public Accountant Financial Planner Public Accountant Financial Planner
25.2 24.0 30.0 28.6
33.8 24.2 25.9 24.7
31.3 28.1 34.5 28.9
33.2 30.9 31.7 26.8
29.2 26.9 26.9 23.9

1) Using a .05 level of significance, test the hypothesis that there is no difference between the starting annual salaries of public accountants and financial planners. What is your conclusion?
2) What are the sample mean annual salaries for the two professions?
(Reference: Anderson, Sweeney, Williams, 2002, print version, section 5, p. 382, exercise 19)
d. Exercise 4-Kruskall-Wallis Test
A large corporation has been sending many of its first-level managers to an off-site supervisory skills course. Four different management development centers offer this
course, and the corporation wants to determine whether they differ in the quality of training provided. A sample of 20 employees who have attended these programs has been chosen and the employees ranked in terms of supervisory skills. The results follow.

1 3 14 10 12 13
2 2 7 1 5 11
3 19 16 9 18 17
4 20 4 15 6 8

Note that the top-ranked supervisor attended course 2 and the lowest-ranked supervisor attended course 4. Use α = .05 and test to see whether there is a significant difference in the training provided by the four programs.
(Reference: Anderson, Sweeney, Williams, 2002, print version, section 5, p. 398, exercise 30)
e. Summary Exercise, Part 5
Create a table illustrating the kinds of business problems that can be analyzed with each of the non-parametric tests discussed with this exercise set. Show how you set up each problem, show key equations and your rationale for your problem analysis and then list your solution for each exercise. Also provide at least two examples of types of business problems that could be analyzed by each test in a table. Your table should list the type of non-parametric test and then list two or more examples. For full credit, list an outside reference which cites the usage of one of these tests in a business setting.

(See attached file for full problem description)

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