Statistics for the Social Sciences: Using t-tests

Slide1Statistics for the Social SciencesPsychology 340 Fall 2006 Using t-tests

Slide2Statistics for theSocial Sciences Outline (for 2 weeks) • Review t-tests – One sample, related samples, independent samples – Additional assumptions • Levene’s test

Slide3Statistics for theSocial Sciences Testing Hypotheses – Step 1 : State your hypotheses – Step 2 : Set your decision criteria – Step 3 : Collect your data – Step 4 : Compute your test statistics • Compute your estimated standard error • Compute your t-statistic • Compute your degrees of freedom – Step 5 : Make a decision about your null hypothesis • Hypothesis testing: a five step program

Slide4Statistics for theSocial Sciences t  Test for Dependent Means • Unknown population mean and variance • Two situations – One sample, two scores for each person • Repeated measures design – Two samples, but individuals in the samples are related • Same procedure as  t  test for single sample, except – Use difference scores – Assume that the population mean is 0

Slide5Statistics for theSocial Sciences Statistical analysis follows design • The  related-samples t- test  can be used when: – 1 sample – Two scores per subject

Slide6Statistics for theSocial Sciences Statistical analysis follows design • The  related-samples t- test  can be used when: – 1 sample – Two scores per subject – 2 samples – Scores are related - OR -

Slide7Statistics for theSocial Sciences Performing your statistical test Diff. Expected by chance Estimated standard error of the  differences Test statistic What are all of these “D’s” referring to? Mean of the differences Number of difference  scores • Difference scores – For each person, subtract one score from the other – Carry out hypothesis testing with the difference scores • Population of difference scores with a mean of 0 – Population 2 has a mean of 0

Slide8Statistics for theSocial Sciences Performing your statistical test What are all of these “D’s” referring to? Difference scores 2 6 5 9 22 Person Pre-test Post-test 1 2 3 4 45 55 40 60 43 49 35 51 (Pre-test) - (Post-test) H 0 : There is no difference between pre-test and post- test H A : There is a difference between pre-test and post- test    D  = 0  D  ≠ 0

Slide9Statistics for theSocial Sciences Performing your statistical test What are all of these “D’s” referring to? Difference scores 2 6 5 9 22 = 5.5 Person Pre-test Post-test 1 2 3 4 45 55 40 60 43 49 35 51 (Pre-test) - (Post-test)

Slide10Statistics for theSocial Sciences Performing your statistical test What are all of these “D’s” referring to? Person Pre-test Post-test Difference scores 1 2 3 4 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5

Slide11Statistics for theSocial Sciences Performing your statistical test What are all of these “D’s” referring to? Person Difference scores 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5  -3.5 - 5.5 =   0.5 - 5.5 = -0.5 - 5.5 =   3.5 - 5.5 = 12.25 0.25 0.25  12.25 25 = SS D D - D (D - D) 2

Slide12Statistics for theSocial Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2  -3.5   0.5 -0.5   3.5 D - D Difference scores 12.25 0.25 0.25  12.25

Slide13Statistics for theSocial Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D  -3.5   0.5 -0.5   3.5 D - D Difference scores 12.25 0.25 0.25  12.25

Slide14Statistics for theSocial Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D ? Think back to the null hypotheses  -3.5   0.5 -0.5   3.5 D - D Difference scores 12.25 0.25 0.25  12.25

Slide15Statistics for theSocial Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D H 0 :  Memory performance at the post-test are equal to memory performance at the pre-test.  -3.5   0.5 -0.5   3.5 D - D Difference scores 12.25 0.25 0.25  12.25

Slide16Statistics for theSocial Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D This is our t obs  -3.5   0.5 -0.5   3.5 D - D Difference scores 12.25 0.25 0.25  12.25

Slide17Statistics for theSocial Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D t obs  = 0.05 Two-tailed t crit  -3.5   0.5 -0.5   3.5 D - D Difference scores 12.25 0.25 0.25  12.25

Slide18Statistics for theSocial Sciences + 3.18 = t crit - Reject H 0 Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D t obs  = 0.05 Two-tailed t crit  -3.5   0.5 -0.5   3.5 D - D Difference scores 12.25 0.25 0.25  12.25 t obs =3.8

Slide19Statistics for theSocial Sciences Performing your statistical test What are all of these “D’s” referring to? Person 1 2 3 4 Pre-test Post-test 45 55 40 60 43 49 35 51 2 6 5 9 22 D = 5.5 25 = SS D (D - D) 2 2.9 = s D 1.45 = s D t obs  = 0.05 Two-tailed t crit T obs  > t crit  so we reject the H 0  -3.5   0.5 -0.5   3.5 D - D Difference scores 12.25 0.25 0.25  12.25

Slide20Statistics for theSocial Sciences • Using SPSS Person Pre-test Post-test 1 2 3 4 45 55 40 60 43 49 35 51

Slide21Statistics for theSocial Sciences Next time • Independent samples t-tests