Advanced Statistics Demystified
Offering exercises at the end of each chapter as well as two final exams, this self-teaching guide provides an effective, anxiety-soothing, and totally painless way to learn advanced statistics.
TABLE OF CONTENTS Advanced Statistics Demystified
Chapter 6: Chi-Squared Tests
6-1 Categorical Data and the Multinomial Experiment
A binomial experiment consists of a sequence of n trials. On each trial, one of two outcomes can occur. The two outcomes are usually referred to as failure and success. If p 1 is the probability of success and p 2 is the probability of failure, then p 1 + p 2 = 1 and p 1 and p 2 do not change from trial to trial.
Example 6-1:
Suppose we flip a fair coin ten times and we are interested in the number of heads and tails that occur. In this case p 1 = p 2 = 0.5. We expect np 1 = 10(0.5) = 5 heads and np 2 = 10(0.5) = 5 tails to occur. Now suppose we perform the experiment and n 1 heads and n 2 tails occur. The test statistic ( n 1 - np 1) 2/ np 1 + ( n 2 - np 2) 2/ np 2 has an approximate chi-squared distribution with 1 degree of freedom when np 1 ? 5 and np 2 ? 5. Suppose we wish to test the following hypotheses concerning the coin:
| H 0: p 1 = 0.5, p 2 = 0:5 | H a: The probabilities are not equal to 0.5 |
SOLUTION
You flip the coin and obtain 9 heads...
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