TWO TYPES OF ERRORS


You can make two types of mistakes when testing a hypothesis about two means. You can claim that the two means are not equal in the population when in fact they are. Or you can fail to say that a difference exists when it actually does. Statisticians, being very methodical people, have given these two types of errors particularly descriptive, easy-to-remember names . They call the first error (claiming that two means are not equal when in fact they are) a Type 1 error. The second type of error (not finding a difference when one really exists) is called a Type 2 error.

It may be easy to remember that you call the two kinds of error Type 1 and Type 2, but how do you remember which is which? Perhaps you can remember it this way. The Type 1 error is the error you are tempted to make. When you say, proudly, "There is a difference. Something is happening here. I have found a relationship," you are taking the chance of making a Type 1 error.

If you can remember what the Type 1 error is, then it is pretty easy to figure out that the Type 2 error is the one you are not tempted to make, saying "Nothing is happening here" when a difference really is present in the population.

USING SOFTWARE TO GENERATE THE OUTPUT FROM THE T TEST PROCEDURE

The computation of the t test differs depending on whether you assume that in the population the two groups have the same variances or not. If you can assume that the two variances are equal, use the numbers in the columns labeled pooled variance estimate. If you cannot assume that the two variances are equal, use the t test labeled separate variance estimate. The ratio of the variances in the two samples is shown in the column labeled F value. Next to the F value, most software shows the probability that you would see a difference at least as large as the one observed in the sample if the variances are equal in the population and if the distribution of the variable is normal. (The F test for equality of variances is quite sensitive to departures from normality, while the t test is not. If the data are not from normal populations, the observed significance level for the F statistic may be unreliable.) If the observed significance level is large, you have little reason to worry about your variances. If the number is small, you should use the t test marked separate variance estimate. In general, it is a good idea to use the separate variance t test whenever you suspect that the variances are unequal .




Six Sigma and Beyond. Statistics and Probability
Six Sigma and Beyond: Statistics and Probability, Volume III
ISBN: 1574443127
EAN: 2147483647
Year: 2003
Pages: 252

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