Chapter 13

Nonparametric Tests

Back to List | Introduction | Data Sets - A Review | Random Number Sequences | Exercises

Introduction

This project is in two parts. The first part, in which you will refamiliarize yourself with data sets used in earlier projects, considers the use of nonparametric tests vs. the parametric ones you saw earlier. The second part looks at randomness and how you detect it.

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Data Sets - A Review

The following data sets from previous projects will be used in the exercises. They are listed here for you to review your understanding of the information they contain.

  1. The heart rate/body temperature data for men and women.
  2. The speed of light measurements.
  3. The home run chase data.

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Random Number Sequences

Many mathematical and statistical software packages as well as pocket calculators come equipped with a random number generator. A random number generator is just what its name implies. It is a function that spits out a random number every time it is executed. If the function is executed repeatedly, the resulting sequence of numbers is a random sequence. Since such a function is created with a computer program, it excuses a sequence of lines of code and is therefore not really random. The function does however simulate randomness and is properly called a pseudorandom number generator.

A pseudorandom number generator underlies the Java applet you looked at when doing the Project on the Central Limit Theorem. This applet is located at http://www.stat.sc.edu/~west/javahtml/CLT.html and allows you to simulate the rolling of dice. You can use this applet to simulate a coin toss or any experiment where there are equally likely 1/0 outcomes. Simply roll 1 die once and call the roll a success or 1 if the roll is four, five or six and a failure or 0 if the roll is a one, two or three. In this way you can generate a sequence of 0s and 1s.

For example with the number of dice set to 1 and Number of rolls set to 1, hit the Roll the dice button. Record a 0 or a 1 depending on whether you rolled a 1-3 or a 4-6. Hit the Roll the dice button again and record the result and so on. A sequence of rolls might look like

Roll: 5 Sequence: 1

Roll: 3 Sequence: 1, 0

Roll: 6 Sequence: 1, 0, 1

Roll: 3 Sequence: 1, 0, 1, 0

Roll: 1 Sequence: 1, 0, 1, 0, 0

and so on. You will be generating such a sequence for the exercises so be sure you understand the process.

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Exercises

In all tests, use an appropriate nonparametric hypothesis testing method with a level of significance of .

Discuss your choice of test and associated computations and conclusion.

1.  

Using the heart rate/temperature data, test to determine if men and women are similar or significantly different with respect to these two physical measurements.

2.  

Retest the Michelson speed of light data with respect to the known value of 299,734.5 Km/s.

3.  

Who hits longer home runs: Mark McGwire or Sammy Sosa? Use the 1998 data.

4.  

Generate a sequence of 0s and 1s using the dice rolling applet as described. Use this sequence to test for randomness with a 5% cutoff criterion. The sequence can be as long as you like but be sure to use a fairly long sequence so as to be confident in the test. Summarize your test and its conclusion.

5.  

The following data set contains three sequences of 0s and 1s as generated by the pseudorandom number generators in each of three leading software packages. Test each for randomness using a 5% cutoff and summarize your results.

Software Package #1

Software Package #2

Software Package #3

0

1

0

0

0

0

1

1

1

1

1

0

0

0

1

1

0

1

1

1

1

0

0

1

1

1

1

1

1

0

1

0

0

1

1

1

0

0

0

0

1

1

1

1

1

0

1

1

1

1

0

1

0

0

0

0

0

1

1

1

0

0

1

1

1

1

0

0

0

1

1

0

1

1

1


   


© 2000 by Addison Wesley Longman
A division of Pearson Education