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ttest
Explanations > Social Research > Analysis > ttest Description  Example  Discussion  See also
DescriptionThe ttest (or student's ttest) gives an indication of the separateness of two sets of measurements, and is thus used to check whether two sets of measures are essentially different (and usually that an experimental effect has been demonstrated). The typical way of doing this is with the null hypothesis that means of the two sets of measures are equal. The ttest assumes:
It is used when there is random assignment and only two sets of measurement to compare. There are two main types of ttest:
A singlesample ttest compares a sample against a known figure, for example where measures of a manufactured item are compared against the required standard. CalculationThe value of t may be calculated using packages such as SPSS. The actual calculation for two groups is: t = experimental effect / variability = difference between group means / InterpretationThe resultant tvalue is then looked up in a ttable to determine the probability that a significant difference between the two sets of measures exists and hence what can be claimed about the efficacy of the experimental treatment. EffectThe tvalue can also be converted to a Pearson rvalue to measure effect, which can be calculated as: r = SQRT( t^{2} / (t^{2} + DF)) where DF is the degrees of freedom. In a ttest, DF = N_{1} + N_{2}  2. ReportingReporting a ttest might look something like this: On average, the reported relationship between holidays in the south (M=24.1, SE=1.5) were significantly preferred than holidays in the north (M=20.1, SE=1.2), t(22)=2.3, p<.05, r=.44. In this, 'M' is the mean and 'SE' the standard error of each sample. In 't(X)=Y', X is the degrees of freedom and Y is the tmetric. 'p' is the probability of a type1 error and 'r' is the effect. DiscussionThe ttest was described by 1908 by William Sealy Gosset for monitoring the brewing at Guinness in Dublin. Guinness considered the use of statistics a trade secret, so he published his test under the penname 'Student'  hence the test is now often called the 'Student's ttest'. The ttest is a basic test that is limited to two groups. For multiple groups, you would have to compare each pair of groups, for example with three groups there would be three tests (AB, AC, BC), whilst with seven groups there would need to be 21 tests. The basic principle is to test the null hypothesis that the means of the two groups are equal. A significant problem with this is that we typically accept significance with each ttest of 95% (p=0.05). For multiple tests these accumulate and hence reduce the validity of the results.
See alsoMatchedpair ttest, Pearson correlation


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