Download
1 / 12
120 likes | 256 Vues
This chapter delves into the paired samples t-test, an essential statistical method for comparing two related scores from the same participants. It covers the calculation of difference scores, hypothesis testing, and assumptions of the test. You'll learn how to calculate the mean and variance of these difference scores and how to conduct the test using SPSS, including interpreting output results. The chapter also presents a practical example related to litter reduction over time and discusses effect sizes and power analysis for informed decision-making in research.
E N D
Chapter 7 Introduction to the t Test Part 2: Dependent Samples Sept. 30, 2014
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
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
Example • #5 in Ch. 7 – program to decrease litter: Note: use alpha = .01
(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)
(cont.) M = 5 (X-M)2 = 50
(cont.) • Find S2 and SM • Find observed t from sample: • Critical t? Draw distribution… • Compare obtained t and critical… • Conclusion?
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|
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)
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.
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
(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?
