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Independentmeasures ttest
Explanations > Social Research > Analysis > Independentmeasures ttest Description  Example  Discussion  See also
DescriptionThe 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 independentmeasures ttest (or independent ttest) is used when measures from the two samples being compared do not come in matched pairs. It is used when groups are independent and all people take only one test (typically a posttest). In design notation, this is:
The requirement for Variance homogeneity test may be measured with Levene's test. Results for this can be given in SPSS along with the ttest results. 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 / = D_{g} / SE_{g} D_{g} = AVERAGE(X_{t})  AVERAGE(X_{c}) where X_{t} are the measures in the treatment group and X_{c} are the measures in the control group. Note that any minus sign is removed, so that 't' remains positive. SE_{g} = SQRT( VAR(X_{t})/n_{t }+ VAR(X_{c})/n_{c}) where n is the number of people in the group and VAR(X) is the variance of X. VAR(X) = SUM((XAVERAGE(X))^{2})/(n1)
A single group can also be compared with a measure, M, taken elsewhere. t = (AVERAGE(X)  M) / (STDEV(X) / SQRT(n) ) Where STDEV(X) is the standard deviation of the group. InterpretationThe resultant tvalue is then looked up in a ttest table 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 an 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. ExampleThe results of two sets of measures are as follows:
Looking up the tvalue in the ttest table, with degrees of freedom = 15+152 = 28, the whole row is greater than t (0.32) so no significance can be claimed.
DiscussionIf the samples can be matched, such as in beforeandafter measurement, then you should use the matchedpair ttest. See also

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