Independent Samples Hypothesis Testing

(Chapter 10)

Step 1. State statistical hypotheses

              (a) Two-tailed

                        H₀:  m₁ = m₂  or  (m₁ - m₂) = 0

                        H₁:  m₁ ¹ m₂  or  (m₁ - m₂) ¹ 0

              (b) One-tailed (right)

                        H₀:  m₁ < m₂  or  (m₁ - m₂) < 0

                        H₁:  m₁ > m₂  or  (m₁ - m₂) > 0

              (c) One-tailed (left)

                        H₀:  m₁ > m₂  or  (m₁ - m₂) > 0

                        H₁:  m₁ < m₂  or  (m₁ - m₂) < 0

Step 2.  Decision rule & rejection region

              Need to know: type of test, a, and df total

              df₁ = n₁ – 1 

              df₂ = n₂ – 1

              df total = df₁ + df₂ = (n₁ + n₂) – 2

Step 3.  Compute t

Step 4.  Make decision & state conclusions.         

Example:  A psychologist tested the effectiveness of subliminal self-help tapes. Fifty participants were randomly assigned to receive either a tape containing subliminal messages intended to improve performance on the math subtest of the SAT or a blank tape. All participants were asked to play the tape every night, while they were sleeping, for one month. At the end of the month, all participants completed the math sections of the SAT. Descriptive statistics for each group were as follows:

          Experimental Group (Subliminal Tape)       Control Group (Blank Tape)

Mean                              550                                            525

Standard Deviation          75                                              50  

n                                      26                                              24

Did the students who listened to the subliminal tapes have higher SAT scores than those who listened to the blank tapes?