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Matchedpair ttest
Explanations > Social Research > Analysis > Matchedpair ttest Description  Example  Discussion  See also
DescriptionThe ttest gives an indication of how separate two sets of measurements are, allowing you to determine whether something has changed and there are two distributions, or whether there is effectively only one distribution. The matchedpair ttest (or paired ttest or paired samples ttest or dependent ttest) is used when the data from the two groups can be presented in pairs, for example where the same people are being measured in beforeandafter comparison or when the group is given two different tests at different times (eg. pleasantness of two different types of chocolate). In design notation, this could be is:
or
Goodness of fitThis can also be used when you have one measure and are matching against a particular frequency distribution, for which you can determine 'should' measures. The two most common distributions to test for are normal (bellshaped) and flat. In a flat distribution, all items are equally likely. The ttest can be used here to discover whether any one or more of a set of measures is significantly different from the others. This use of the chisquare test is often known as the 'Goodness of Fit' test. CalculationThe value of t may be calculated using packages such as SPSS. The actual calculation is: t = AVERAGE(X_{1}X_{2}) / ( S_{d }/ SQRT( n) ) Where S_{d} is the standard deviation of the differences and n is the number of pairs. S_{d} = SQRT( (SUM((X_{1}X_{2})^{2})  (SUM(X_{1}X_{2}))^{2}/n) / (n1) ) InterpretationThe resultant tvalue is then looked up in a ttable as below 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. The tvalue can also be interpreted as an rvalue, which can be calculated as: r = SQRT( t^{2} / (t^{2} + DF)) where DF is the degrees of freedom. ExampleThe results of two sets of measures are as follows:
Looking up the tvalue in the ttest table, with degrees of freedom = 151 = 14, the whole row is greater than t (0.97) so no significance can be claimed. DiscussionWhen measures from the two samples being compared do not come in matched pairs, the independentmeasures ttest should be used. When there are multiple samples, then ANOVA should be used. Goodnessoffit curvefitting is also available in more sophisticated forms where you have parametric data. In this case the KolmogorovSmirnov test or ShapiroWilk test may be used. See alsottest, Independentmeasures ttest

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