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Testing Hypotheses II

Testing Hypotheses II. Lesson 10. A Directional Hypothesis (1-tailed). Does reading to young children increase IQ scores? m = 100, s = 15, n = 25 sample mean also same z obs will be the same as 2-tailed test Differences from nondirectional hypotheses critical region ~.

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Testing Hypotheses II

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  1. Testing Hypotheses II Lesson 10

  2. A Directional Hypothesis (1-tailed) • Does reading to young children increase IQ scores? • m = 100, s = 15, n = 25 • sample mean also same • zobs will be the same as 2-tailed test • Differences from nondirectional • hypotheses • critical region ~

  3. A Directional Hypothesis 1. State hypotheses • H1: m > 100 • Reading to young children will increase IQ scores. • H0: m< 100 • Reading to young children will decrease or not change IQ scores. ~

  4. A Directional Hypothesis 2. Set criterion for rejecting H0 • a = .05, level of significance • directional (one-tailed) test • zCV = +1.645 • critical value for area = .05 • in upper tail ~

  5. -2 -1 0 +1 +2 +1.645 Critical Regions a = .05 zCV = + 1.645 f

  6. 3. Collect sample & compute statistics n = 25

  7. -2 -1 0 +1 +2 +1.645 Critical Regions a = .05 zCV = + 1.645 f

  8. 4. Interpret Results • Is zobsin the critical region? • yes • reject H0, accept H1 • These data suggest that reading to young children does increase IQ. • Difference is statistically significant • but not for 2-tailed test • lower criterion than 2-tailed ~

  9. Significance of Result • If reject H0 • Statistical significance • difference between groups is ... greater than expected by chance alone • Does NOT say it is meaningful • Even very small effects can be statistically significant • How? ~

  10. Significance of Result • If fail to reject H0 • Data are inconclusive • Does not mean that there is no difference • Why might there be a Type II error? ~

  11. Practical Significance • Extent to which difference is important • Magnitude of effect • Independent of statistical significance • Effect size • APA recommends it be reported • Pearson’s correlation coefficient, r • Will cover later • Cohen’s d ~

  12. Effect Size: Cohen’s d • Standardized measure • Units of standard deviation • General form • For z test:

  13. Evaluating Effect Size: Cohen’s d • Cohen’s d • Small: d = 0.2 • Medium: d = 0.5 • High: d = 0.8 For t-test:

  14. Significance Testing: Issues • Focus on H0 rather than data • H0 is always false • Small differences can be statistically significant • Focus on results of single study rather than accumulation • Focus on a, ignoring b • Focuson p-values misleading • Dichotomyvs continuum ~

  15. Significance Testing: Alternatives • Criticized by some scientists • As inappropriate • Alternatives • Confidence intervals • Effect size • Meta-analysis ~

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