| Student's T-test |
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Information AboutStudent's T-test |
: If the ''t'' value that is calculated is greater than the threshold chosen for Statistical Significance (usually the 0.05 level), then the null hypothesis that the two groups do not differ is rejected in favor of the alternative hypothesis, which typically states that the groups do differ.
DECIDING WHICH ''T''-TEST TO USE Whether the data points are normally distributed can be assessed by a normality test, such as Kolmogorov-Smirnov or Shapiro-Wilk . Whether the sample variances are equal can be assessed using s make the test equally easy to do with or without it. (Since all calculations are done subject to the null hypothesis, it may be very difficult to come up with a reasonable null hypothesis that accounts for equal means in the presence of unequal variances. In the usual case, the null hypothesis is that the different treatments have no effect; this makes unequal variances untenable. In this case, one should forgo the ease of using this variant afforded by the statistical packages. See also Behrens-Fisher Problem .) For novices, the most difficult issue is often whether the samples are paired (dependent) or independent. Dependent samples are sometimes described as involving "repeated measures", often arising when we make before and after measurements on the same individuals or objects. But related samples also occur in other cases. For example, to compare the height of men and women, we might recruit 100 married or cohabiting opposite-sex couples, and compare the height of each woman with her partner; this would call for a related samples test. There are repeated measures here: the ''couple'' is measured twice - once for the woman and once for the man. Alternatively, we might recruit 100 men and 100 women, with no relationship between any particular man and any particular woman; in this case we would use an independent samples test. ALTERNATIVES TO THE ''T''-TEST If a Non-parametric alternative to the ''t''-test is wanted, the usual choices are:
HISTORY The t-statistic was invented by William Sealy Gosset for cheaply monitoring the quality of beer brews. "Student" was his Pen Name . Gosset was statistician for Guinness brewery in Dublin, Ireland , hired due to Claude Guinness's innovative policy of recruiting the best graduates from Oxford and Cambridge for applying biochemistry and statistics to Guinness's industrial processes. Gosset published the t-test in Biometrika in 1908, but was forced to use a pen name by his employer who regarded the fact that they were using statistics as a trade secret. In fact, Gosset's identity was unknown not only to fellow statisticians but to his employer - the company insisted on the pseudonym so that it could turn a blind eye to the breach of its rules. Today, it is more generally applied to the confidence that can be placed in judgements made from small samples. SOURCES
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