PPT_2_After_2nd_Midterm. - SE13 Statistics Review...

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SE13 Statistics Review Correlation Output Hypothesis test for Correlation (r) Cohen’s Guidelines for r rxy2 as a measure of “explained” variance Factors influencing size of r Common errors in interpreting r Association between Qualitative variables
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Pearson Correlation (r) Review SPSS output y = anxiety x = yrs of smoking rxy = .350 r = 0, ___________ ___________ ___________
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Hypothesis test: Pearson Correlation (r) 1. There is an association between years of smoking and anxiety.
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Hypothesis test: Pearson Correlation (r) Greek letter Rho (ρ) : Population value of r 2. Statistical Hypotheses Ho: ρxy = 0 No association between yrs smoked and anxiety
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Hypothesis Test for r 3.    = .05;  df = n – 2;  tcritical = 2.447  α  n – 2  .35    8 - 2 4.  tcalc =                        =     1 – r2        1 – .352             tcalc =  .90
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Hypothesis Test for r 5. Decision/Interpretation |  tcalc |  <  tcritical         .90    <   2.447 Do not Reject Ho There is no statistically significant  association  between yrs smoked and  anxiety
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Hypothesis Test for r 5. Decision r = .35, p = .403 p-value > α Do not reject Ho       .403   >  .05
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Interpreting r2 rxy2 = Proportion of variance in y “explained ” or “accounted ” for by x rxy2 = .352 rxy2 = .123 or 12.3 % of variance in anxiety accounted for by yrs smoking
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Interpreting r2 rxy2 Proportion of “explained” variance 1 - rxy2 Proportion of “unexplained ” variance
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Interpreting r2 Cohen’s Effect Size Guidelines for r2 Small r2  .01 Medium r2  .09 Large r2 > .25
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Factors Influencing size of r 1. Range Restriction 2. Outlying Observation
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Common Mistakes in Interpreting r 1. r = .80 is twice as strong as r = .40 2. Inferring causation from correlation
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Correlation Matrix SEE COURSE WEBSITE for SPSS output
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