
Paried ttest procedure demonstrated with an exampleThe idea and demo exampleA common experiment design is to have a test and control conditions. While the regular twosample ttest assumes independence, paired ttest assumes that the two samples are dependent. For example, in an experiment where the response time is measured with or without taking a drug. Each subject could have been measured twice, once in the absence of the drug (control value) and the other after taking the drug (treatment value). The question is whether the response time differs between the two conditions? The model is response (continuous) ~ drug (categorical: 2 levels) The data is "response.csv". Open the data set from SAS. Or import with the following command. data response; infile "H:\sas\data\response.csv" dlm=',' firstobs=2; input control treatment; run; Checking assumptionsPaired sample ttest assumes that
When the assumptions are not met, other methods are possible based on the two samples:
Comparing two dependent samples with paired ttestThe regular ttest cannot be used here since the groups are no longer independent. In stead, a paried ttest is more appropiate. Compare two sample with paired ttest proc ttest data=response sides=2 alpha=0.05 h0=0; title "Paired sample ttest example"; paired Control * Treatment; run; The output is shown below. Paired sample ttest example The TTEST Procedure Difference: control  treatment N Mean Std Dev Std Err Minimum Maximum 6 7.3333 4.1312 1.6865 15.0000 4.0000 Mean 95% CL Mean Std Dev 95% CL Std Dev 7.3333 11.6687 2.9979 4.1312 2.5787 10.1322 DF t Value Pr > t 5 4.35 0.0074 As a significance level of 0.05, the hypothesis is whether the response time is significantly different in the treatment than control group.
We can state that response times are longer under the treatment than the control group Note that SAS only perform a two side test, meaning the hypothesis is to compare a significant difference between two groups. If one wants to test whether one group is greater(smaller) than the other, pvalue must be divided by 2. For example, the pvalue/2=0.0074/2=0.00342 < 0.05, hence the concluse for the one side test is still to reject the hypothesis. 
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