1 / 23

Independent-Measures Hypothesis Testing

Independent-Measures Hypothesis Testing Unit 8 Ch 10: 1-5, 7, 9, 11, 13, 15, 19 (pp. 282-286) Comparing 2 sets of data 2 general research strategies data sets come from 2 separate groups independent samples between groups design 2 sets of data from 1 group dependent or related samples

albert
Download Presentation

Independent-Measures Hypothesis Testing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Independent-Measures Hypothesis Testing Unit 8 Ch 10: 1-5, 7, 9, 11, 13, 15, 19 (pp. 282-286)

  2. Comparing 2 sets of data • 2 general research strategies • data sets come from 2 separate groups • independent samples • between groups design • 2 sets of data from 1 group • dependent or related samples • matched-subjects (2 related groups) • within subjects design ~

  3. Independent Measures Hypothesis Test • Select 2 independent samples • are they from same population? • Experiment • select 2 samples • 1 receives treatment • are the samples the same? ~

  4. Experimental Outcomes • Do not expect to be exactly equal • sampling error • How big a difference to reject H0 ? ~

  5. Hypotheses: Independent Measures • Nondirectional • H0: m1 - m2 = 0 H1: m1 - m2 0 • or H0: m1 = m2 H1: m1m2 • Directional (depends on prediction ) • H0: m1 - m2 < 0 H1: m1 - m2 > 0 • or H0: m1<m2 H1: m1 > m2 • no value specified for either • Group 1 scores = Group 2 scores~~

  6. Sample statistic: t test: Independent Samples • Same basic structure as single sample • Independent samples [df = n1 + n2 - 2]

  7. The Test Statistic • Since m1 - m2 = 0 [df = n1 + n2 - 2]

  8. Estimated Standard Error • *Standard error of difference between 2 sample means • must calculate s2p first ~

  9. Pooled Variance (s2p) • Average of 2 sample variances • weighted average if n1n2 • if n1 =n2

  10. The Test Statistic: Assumptions 1. Samples are independent 2. Samples come from normal populations 3. Assume equal variance s21 = s22 • does not require s21 = s22 • homogeneity of variance • t test is robust • violation of assumptions • Little effect on P(rejecting H0) ~

  11. Example: Independent Samples • Is exam performance affected by how much sleep you get the night before a test? • Dependent variable? • independent variable? • Grp 1: 4 hrs sleep (n = 6) • Grp 2: 8 hrs sleep (n = 6) ~

  12. Example: n1 = n2 1. State Hypotheses H0: m1 - m2 = 0 or H0: m1= m2 H1: m1 - m2 ¹ 0 or H1: m1 ¹m2 2. Set criterion for rejecting H0: nondirectional a = .05 df = (n1 + n2 - 2) = (6 + 6 - 2) = 10 tCV.05 =

  13. Example: n1 = n2 3. select sample, compute statistics do experiment • mean exam scores for each group • Group 1: M1 = 15 ; s1 = 4 • Group 2: M2 = 19; s2 = 3 • compute • s2p • s M1-M2 • tobs~

  14. Example: n1 = n2 • compute s2p

  15. Example: n1 = n2 • compute

  16. Example: n1 = n2 • compute test statistic

  17. Example: n1 = n2 4. Decision? • Is tobs in critical region? • No, fail to reject H0 • If directional test or change level of significance • change critical value of t (tcv) • just like other tests ~

  18. Pooled Variance: n1¹n2 • Unequal sample sizes • weight each variance • bigger n ---> more weight

  19. Example: n1¹n2 Supplementary Material • What effect does the amount of sleep the night before an exam have on exam performance? • Dependent variable • independent variable • Grp 1: 4 hrs sleep (n = 6) • Grp 1: 8 hrs sleep (n = 7) ~

  20. Example: n1¹n2 1. State Hypotheses H0:m1 = m2 or m1 - m2 = 0 H1:m1¹ m2 or m1 - m2 ¹ 0 2. Set criterion for rejecting H0: nondirectional a = .05 df = (n1 + n2 - 2) = (6 + 7 - 2) = 11 tCV = + 2.201 ~

  21. Example: n1¹n2 3. select sample, compute statistics do experiment mean exam scores for each group • Group 1: M1 = 14 ; s1= 3 • Group 2: M2 = 19; s2= 2 • compute • s2pooled • sM1- M2 • tobs~

  22. Example: n1¹n2 • compute s2pooled • compute • compute test statistic [df = n1 + n2 - 2]

  23. Example: n1¹n2 4. Interpret Is tobsbeyond tCV? If yes, Reject H0.

More Related