Chapter 10: Common Miscellaneous Statistical Tests

This chapter will discuss common tests for nominal data (binomial, chi square [I], chi square [II], McNemar, and the Cochran Q), ordinal data (Kolmogorov-Smirnov, Mann-Whitney U, sign, Wilcoxon, Kruskal-Wallis, and Friedman), and interval data ( t test [I], t test [II], t test [III], and Scheffe's test).

BINOMIAL TEST

Some of the statistical tests you will be studying are used to analyze data with many categories or outcomes . However, when only two categories are present, the binomial test (sometimes called a test of proportion) is applicable . The two categories could be, for example: grades in a pass/fail course, party affiliation as broken down into either Republican or Democrat, evaluation of a product as good or bad, a decision about a process as go or no go, outcome in tossing a coin heads or tails , or outcome in rolling a six or not a six on a die.

The proportion of cases in one category is referred to as P and in the other category as Q. The value of P + Q always equals one. If you know the value of P, you find Q by subtracting P from one. The requirements for the binomial test are:

1. Nominal data

2. One- group test

3. Two categories only

4. Sample size can be less than five

5. Independent observations

6. Simple random sample

7. Data in frequency form

The general formula for the binomial is:

The terms are binomial coefficients and are computed by the following formula:

The meanings of the symbols are as follows : ! = factorial, N = number of trials or sample size, X = number of favorable outcomes for a series of trials, P = probability of favorable outcome in a single trial, Q = (1 - P) = probability of unfavorable outcome in a single trial.