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Session2_HMA278_2010 - HMA278/HAYG421 Session2...

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Click to edit Master subtitle style HMA278/HAYG421  Design and Measurement 2 Session 2 Diane Mainwaring
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Brief Review of Last Session Limitations of hypothesis testing. Power analysis  Comparing the relationship between two metric  variables for subgroups Describing the Relationship Between two  Categorical Variables Testing Significance using Chi-Square Session 2
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Describing the distribution of a single metric  variable Describing the relationship between two metric  variables Introduction to power analysis Review last Session
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lS u m a 4 .0 5 .0 0 M e 1 R q u ju s q u S td .E o f th e E s t im a P re d a . Regression Note that R is always reported as a positive  value, even when the relationship is  negative.
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A N O V A b 1 6 9 0 .8 6 0 .0 0 0 a 2 5 2 9 3 R e g re s s R e s id u a T o ta l M o 1 S u m u a d M e a S q u F S ig P re d ic to rs a . D e p e n d b . o e f ic ie n ts a 2 5 .7 2 0 .0 0 0 .0 6 9 0 .7 2 3 .0 0 0 (C o n s ta A G E M o 1 B S td .E n d a e f ic ie B e S ta n d rd z e C o e f ic n ts t S ig D e p e n a .
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There was a weak, linear relationship between age  and hours spent watching television per week, with  older individuals tending to watch less television.  The relationship between age and time spent  watching TV was significant (r=-0.29, n=200,  p<.001).  Example
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Effect Size:  Proportion of variation in scores  (dependent variable) that can be explained by the  differences in level of the independent variable. Significance versus Importance Power Analysis  Issues related to Hypothesis    Testing continued
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Effect Size Obj118 r = –0.82
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r  =   0.23
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Correlation between age and enthusiasm   r = 0.64, n = 10, p = 0.046  Correlation between age and self esteem   r = 0.12, n = 1000, p < .001 Correlation between age and experience   r = 0.78, n = 1000, p < .001 Significance versus Importance
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Samples of size 10 POP CORR SAMP 1 SAMP 2 SAMP3 SAMP 4 SAMP5 A 0.80 0.87 ** 0.97 ** 0.57 0.69 ** 0.80 ** B 0.64 0.71 * 0.91 ** 0.43 0.75 * 0.68 * C 0.26 0.09 0.66 ** 0.34 0.52 0.63 D 0.10 0.13 0.55 –0.06 –0.42 0.42
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Samples of size 50 POP CORR SAMP 1 SAMP 2 SAMP 3 SAMP 4 SAMP 5 A 0.80 0.82 ** 0.79 ** 0.91 ** 0.83 ** 0.64 ** B 0.64 0.72 ** 0.67 ** 0.63 ** 0.78 ** 0.50 ** C 0.26 0.27 0.60 ** –0.11 0.42 ** 0.37 ** D 0.10 0.12 0.10 0.01 0.13 –0.11
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Samples of size 100 POP CORR SAMP 1 SAMP 2 SAMP 3 SAMP 4 SAMP 5 A 0.80 0.80 ** 0.81 ** 0.84 ** 0.81 ** 0.75 ** B 0.64 0.70 ** 0.71 ** 0.76 ** 0.64 ** 0.66 ** C 0.26 0.27 ** 0.28 ** 0.26 ** 0.15 0.22 * D 0.10 0.19 ** –0.01 0.25 * 0.23 * 0.05
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Samples of size 1000 Obj123
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Question How closely do the sample  correlations reflect the correlations in  the population?
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Consider Sample 5, population D (r=0.42) and Sample  3 population B ( r=0.43). In population D, population correlation = 0.10 In population B, population correlation = 0.64 What do we do if the  correlation is not significant?
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