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Chapter 7

Chapter 7. Introduction to the t Test Part 2: Dependent Samples Oct. 3, 2013. t Test for Dependent Means. Unknown population mean and variance Two scores for each person Repeated measures design aka “Paired Samples t-test” in SPSS Same procedure as t test for single sample, except

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Chapter 7

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  1. Chapter 7 Introduction to the t Test Part 2: Dependent Samples Oct. 3, 2013

  2. t Test for Dependent Means • Unknown population mean and variance • Two scores for each person • Repeated measures design • aka “Paired Samples t-test” in SPSS • Same procedure as t test for single sample, except • Use difference scores • Assume that the comparison mean is 0

  3. t Test for Dependent Means • Difference scores • For each person, subtract one score from the other • Carry out hypothesis testing with the difference scores • Find S2 for difference scores, Find SM for difference scores • Comparison population of difference scores will always have a mean of 0 • That is, the relevant µ for the comparison with M will be 0. • This will always be stated in your null hypothesis for a dependent samples t-test

  4. Example • #5 in Ch. 7 – program to decrease litter: Note: use alpha = .01

  5. (cont.) • Research hyp: there will be a decrease in litter from time1 to time 2 (2 < 1…or 1 - 2 > 0) • Null hyp: there will be no difference/effect (2 = 1, or 1 - 2 = 0) • Will need Difference scores for each city, need S2 and SM based on difference scores • S2 =  (X-M)2 / N-1 • SM = sqrt (S2 / N)

  6. (cont.) M = 5  (X-M)2 = 50

  7. (cont.) • Find S2 and SM • Find observed t from sample: • Critical t? Draw distribution… • Compare obtained t and critical… • Conclusion?

  8. Effect Size for t Test for Dependent Means • If calculating before data collection, 2 will always be 0, 1 is the expected mean difference in our sample (pre/post-test),  is expected SD of difference scores • If calculating after data collection, 2 is still 0, 1 is the actual mean difference (pre/post-test),  is actual SD of difference scores (use S) • Use same effect size standards as earlier, small d = |.2|, medium d = |.5|, large d >= |.8|

  9. Approximate Power for t Test for Dependent Means (.05 significance level) Note: Table 7-9 shows power in body of table, you need to know N (rows), and effect size (columns)

  10. Approximate Sample Size Needed for 80% Power(.05 significance level – Table 7-10) This table shows N needed for 80% power (rule of thumb) given different expected effect sizes.

  11. SPSS: Dependent Means t-test • Using SATS data, assume ‘sats4’ is pre-semester rating of difficulty of statistics, ‘sats5’ is post-semester rating of difficulty • Is there a difference in pre/post semester? • Research hyp: Post should be lower than pre (diff >0) • Null hyp: No difference in pre/post (diff = 0) • Analyze  Compare Means  Paired Samples t-test • Pop-up window, under ‘paired variables’, select‘Sats4’ for var1, ‘Sats5’ for var2,  OK

  12. (cont.) • In output, 1st section is “Paired Samples Stats”, look for means for ‘sats4’ and ‘sats5’ – this is what we’re comparing • In 3rd section, “Paired Samples Test”, note mean difference score, t observed, df, and ‘sig (2-tail)’. • Mean difference score is compared to 0 • Sig (2 tail) should be compared to alpha level (e.g., .05). • If ‘sig’ value < alpha reject Null • This example?

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