Comparison of Two Univariate Means Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication/ Graduate Institute of Networking and Multimedia 1

Scenarios To test if the differences are significant between Teaching using Power Point vs. using chalks and blackboard only Drug vs. placebos Processing speed of MP3 player model I of brand A vs. model G of brand B Performance of students going to cram schools vs. those not

Experiment Design for Paired Comparisons 1 2 3 n . . . . . . Treatments 1 and 2 assigned at random Treatments 1 and 2 assigned at random Treatments 1 and 2 assigned at random Treatments 1 and 2 assigned at random 3

Single Response (Univariate) Case 4

Comparing Means from Two Populations Without explicitly controlling for unit-to-unit variability, as in the paired comparison case Experimental units are randomly assigned to populations Applicable to a more general collection of experimental units 5

Assumptions Concerning the Structure of Data 6

Pooled Estimate of Population Variance 7

t-Statistics for Comparing Two Populations 8

Test of Hypothesis 9