Phil12_S11_Correlationals&probabilistic_reasoning(5-5-2011)

Phil12_S11_Correlationals&probabilistic_reasoning(5-5-2011)

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Correlations and Probabilistic Reasoning Phil 12: Logic and Decision Making Spring 2011 UC San Diego 5/5/2011 Thursday, May 5, 2011
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Paper 1 Due by 11am, Thursday May 12th Save as Word fle (.docx or .doc) or .rtF ±ile name: A0# lastname firstname Phil12 Paper1 - e.g., A02 Herschbach Mitch Phil12 Paper1 Submit to http://www.dropitto.me/mherschbach - Use upload password: phil12paper1s11 Will walk through it next lecture Thursday, May 5, 2011
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Clicker question Which allows for better predictions of the value of one variable from the value of the other? 0 5 10 15 20 25 30 0 5 10 15 0 5 10 15 20 25 30 0 5 10 15 A B C. Not sure Thursday, May 5, 2011
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4 0 5 10 15 20 25 30 0 5 10 15 r = 0.336 r 2 = 0.113 0 5 10 15 20 25 30 0 5 10 15 r = 1 r 2 = 1 y = 0.7214x + 8.4749 y = 0.7214x + 8.4749 Visualizing correlations Thursday, May 5, 2011
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Visualizing correlations - 1 0 1 2 - 1 0 1 2 3 r = 0.5919 http://demonstrations.wolfram.com/VisualizingCorrelations/ Thursday, May 5, 2011
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From samples to populations Is the correlation found in the sample representative of the whole population? Strategy: try to reject the null hypothesis in terms of the results in the sample - If result for the sample is statistically signiFcant (at a chosen level), one infers that the null hypothesis is false - If the result for the sample is not statistically signiFcant (at the chosen level), one cannot reject the null hypothesis Thursday, May 5, 2011
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Statistical signifcance At what level is the correlation statistically signifcant? - p < .05: less than 1 chance in 20 that the result is due to chance Factors in drawing the sample - p < .01: less than 1 chance in 100 that the result is due to chance Factors in drawing the sample Choose signifcance level (p < some value) according to how important it is not to be wrong Statistical signifcance and importance are very diFFerent things Thursday, May 5, 2011
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Two dangers H o is true H o is false Did not reject H o Correct failure to reject Type II error ( β ) Did reject H o Type I error ( α ) Correct rejection Thursday, May 5, 2011
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α and β levels α -level is the probability of rejecting the null hypothesis when it is true - SigniFcance level (criterial p-value) β -level is the probability of failing to reject the null hypothesis when it is false Statistical power of the test = 1- β - the probability that the researcher will correctly reject the null when the null is indeed false Thursday, May 5, 2011
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Summary: how to minimize error To minimize Type I error ( overconfdence ): - Use higher signifcance levels--instead oF requiring only p<.05, require p<.01 or even p<.001 To minimize Type II error ( humility ): - To minimize: Use a larger sample, which has a greater chance oF fnding a signifcant diFFerence iF one is to be Found Thursday, May 5, 2011
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Science without Error? One can reduce the risk of type I and type II errors to
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This note was uploaded on 06/07/2011 for the course PHIL 101 taught by Professor Brown during the Spring '08 term at San Diego.

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Phil12_S11_Correlationals&probabilistic_reasoning(5-5-2011)

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