Phil12_S11_Correlationals&amp;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
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
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
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
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
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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