100 Statistical Tests

Gopal K Kanji, Author

• Publisher: SAGE Publications Ltd
• Year: 2006
• Print ISBN: 9781412923767, 9781412923750
• eBook ISBN: 9781446222508
• Edition: 3
• Topic: Ciencias sociales
• Subtopic: Investigación y metodología de las ciencias sociales

?This is a very valuable book for statisticians and users of statistics. It contains a remarkable number of statistical tests which are currently available and useful for practical purposes? - Statistical Papers

This expanded and updated Third Edition of Gopal Kanji?s best-selling resource on statistical tests covers all the most commonly used tests with information on how to calculate and interpret results with simple datasets.

Each entry begins with a short summary statement about the test?s purpose, and contains details of the test objective, the limitations (or assumptions) involved, a brief outline of the method, a worked example and the numerical calculation.

This new edition also includes:

" A brand new introduction to statistical testing with information to guide the reader through the book so that even non-statistics students can find information quickly and easily

" Real-world explanations of how and when to use each test with examples drawn from wide range of disciplines.

" A useful Classification of Tests table

" All the relevant statistical tables for checking critical values

100 Statistical Tests: Third Edition is the one indispensable guide for users of statistical materials and consumers of statistical information at all levels and across all disciplines.

The Test

Test 1 Z-test for a population mean (variance known)

Object

To investigate the significance of the difference between an assumed population mean μ₀ and a sample mean

Limitations

1. It is necessary that the population variance σ² is known. (If σ² is not known, see the t-test for a population mean (Test 7).)
2. The test is accurate if the population is normally distributed. If the population is not normal, the test will still give an approximate guide.

Method

From a population with assumed mean μ₀ and known variance σ², a random sample of size n is taken and the sample mean

calculated. The test statistic

may be compared with the standard normal distribution using either a one- or two-tailed test, with critical region of size α.

Example

For a particular range of cosmetics a filling process is set to fill tubs of face powder with 4 gm on average and standard deviation 1 gm. A quality inspector takes a random sample of nine tubs and weighs the powder in each. The average weight of powder is 4.6 gm. What can be said about the filling process?

A two-tailed test is used if we are concerned about over- and under-filling.

In this Z = 1.8 and our acceptance range is –1.96 < Z < 1.96, so we do not reject the null hypothesis. That is, there is no reason to suggest, for this sample, that the filling process is not running on target.

On the other hand if we are only concerned about over-filling of the cosmetic then a one-tailed test is appropriate. The acceptance region is now Z < 1.645. Notice that we have fixed our probability, which determines our acceptance or rejection of the null hypothesis, at 0.05 (or 10 per cent) whether the test is one- or two-tailed. So now we reject the null hypothesis and can reasonably suspect that we are over-filling the tubs with cosmetic.

Quality control inspectors would normally take regular small samples to detect the departure of a process from its target, but the basis of this process is essentially that suggested above.

Numerical calculation

μ₀ = 4.0, n = 9,

= 4.6, σ = 1.0

Z = 1.8

Critical value Z_0.05 = 1.96 [Table 1].

H₀: μ = μ₀, H₁: μ ≠ μ₀ (Do not reject the null hypothesis H₀.)

H₀: μ = μ₀, H₁: μ = μ₀ (Reject H₀.)

Test 2 Z-test for two population means (variances known and equal)

Object

To investigate the significance of the difference between the means of two populations.

Limitations

1. Both populations must have equal variances and this variance σ² must be known. (If σ² is not known, see the t-test for two population means (Test 8).)
2. The test is accurate if the populations are normally distributed. If not normal, the test may be regarded as approximate.

Method

Consider two populations with means μ₁ and μ₂. Independent random samples of size n₁ and n₂ are taken which give sample means

and

. The test statistic

may be compared with the standard normal distribution using either a one- or two-tailed test.

Example

Two teams of financial sales persons are compared to see if it is likely that the instruction each has received could have led to differing success rates. A sample of nine transactions (which involves the whole team) yields an average success rate of 1.2. Similarly a sample of 16 transactions for the second team yields a success rate of 1.7. The variances for both teams are equal to 2.0750 (standard deviation 1.4405). The success rate is calculated using a range of output measures for a transaction.

If we are only interested to know ...

Table of contents

• Cover Page
• Half Title Page
• Title Page
• Copyright Page
• feedback
• Contents
• Acknowledgements
• Preface
• List of Common Symbols
• Introduction to the Book
• . Introduction to Statistical Testing
• Examples of Test Procedures
• List of Tests
• Classification of Tests
• The Tests
• List of Tables
• Tables
• References
• Index