Six Sigma and Beyond: Statistics and Probability, Volume III
TEST (II)
The t test (II) concerns itself with two groups. These groups are independent; that is, an individual in one group cannot be in any way related to an individual in the other group. The purpose of the t (II), or t ratio as it is called, is to determine whether the mean of one group is significantly different from the mean of the other group. The requirements of the t (II) are as follows :
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The two groups are independent.
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Measurement is at least at the interval level.
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The populations are both normally distributed.
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The populations have the same variances. (Older statistics books and articles suggest that a test of homogeneity of variance be carried out before it is permissible to use a t ratio. However, many modern statisticians feel that such a test is not worth the time and effort. Where these tests for homogeneity of variance are most needed ” on small samples with unequal sizes ” they are the least effective [Hays, 1973].)
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The samples are drawn at random.