T test for two independent samples
- 1. Group 1 STR November9,2010 T- Testfor twoindividual variables Usedonlywhen: o Two independentgroups(mayormay nothave equal numberof samples)are compared o Measurementsare either: 1. Interval – arbitraryzero 2. Ratio– true zero point Testswhetherthere isanysignificantdifference betweenthe populationmeansof the twogroups Advantages: o Simple,straightforward o Easy to use o Adaptable toa broad range of situations It answers: o Are these twovariablesrelated? o If we alterthe level of one,willwe therebyalterthe level of the other? o If we test different levels of one, will the results be associated with the different levels of the other group? Steps: 1. State the null hypothesis(logical antithesisof hypothesisthatisbeing examined) 2. State the alternative hypothesis(whatyouwanttoprove) 3. State the level of significance (probability that the test statistic falls within the rejection region which is usually0.05 or 0.01) 4. Setup table (mean,meansquared,summationof mean,andsummationof meansquared) 5. Compute fort (t dependsonthe directionof difference betweenthe twomeans) a. Compute formeanof the twogroups b. Compute forthe standarderror of the difference betweenmeans c. Compute fort using(a) and (b) 6. Findthe critical or tabularof t (usuallygiven) 7. Formulate youconclusion (whetherthere isasignificantdifference betweenthe twogroupor not) Example o Do two types of music, type 1 and type 2, have different effects upon the ability of college students to performa seriesof mental tasksrequiringconcentration? Steps: 1. Begin with a group, relatively homogenous group of people, with respect to age, record of academicachievement,andothersrelatingtoperformance. 2. Randomlysortthemintotwo groups 3. Expose toseriesof mental tasksunderconditionsthatare identical inbothgroupsexceptone: a. One playingtype 1 inthe background b. The other platingtype 2 inthe background 4. Measure howwell the subjectsperformintheirrespective conditions 5. The difference between the effects of the two types of music playing is the difference between the meanlevelsof the twogroups Null hypothesis:theydonothave differenteffects