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# Scientific Study Politic POL 051

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This 73 page Class Notes was uploaded by Pierre Huel on Tuesday September 8, 2015. The Class Notes belongs to POL 051 at University of California - Davis taught by Bradford Jones in Fall. Since its upload, it has received 34 views. For similar materials see /class/187571/pol-051-university-of-california-davis in Political Science at University of California - Davis.

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Date Created: 09/08/15

Brad Jones1 1Department of Political Science University of California Davis November 6 2007 he Scientific Study of Polil39 Jones Today Two Varia bles Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal gt Normal distribution has been good to us Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal gt Normal distribution has been good to us gt It is now useful to think about the standard error of the normal Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal gt Normal distribution has been good to us gt It is now useful to think about the standard error of the normal gt Remember standard error is the standard deviation of the sampling distribution Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal gt Normal distribution has been good to us gt It is now useful to think about the standard error of the normal gt Remember standard error is the standard deviation of the sampling distribution gt Conventionally this thing is given by am Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal b Normal distribution has been good to us It is now useful to think about the standard error of the normal V gt Remember standard error is the standard deviation of the sampling distribution Conventionally this thing is given by am Here a is the population standard error V V Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal b Normal distribution has been good to us It is now useful to think about the standard error of the normal V gt Remember standard error is the standard deviation of the sampling distribution Conventionally this thing is given by am Here a is the population standard error V V gt which we usually do not know Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal gt However we can estimate this through our sample data Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal gt However we can estimate this through our sample data gt The best estimate of a is 5 Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal gt However we can estimate this through our sample data gt The best estimate of a is s gt s is our standard deviation we39ve seen this before 2 702 T Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal gt However we can estimate this through our sample data gt The best estimate of a is s gt s is our standard deviation we39ve seen this before 2 702 T gt In the previous slides used the notation 6 Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal gt However we can estimate this through our sample data gt The best estimate of a is s gt s is our standard deviation we39ve seen this before gt In the previous slides used the notation 6 gt Assume s 6 Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal gt However we can estimate this through our sample data gt The best estimate of a is s gt s is our standard deviation we39ve seen this before 2 702 T gt In the previous slides used the notation 6 gt Assume s 6 gt Once we estimate 0 however we have to move to a different distribution Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Inference and the Normal gt However we can estimate this through our sample data gt The best estimate of a is s gt s is our standard deviation we39ve seen this before 2 702 T gt In the previous slides used the notation 6 gt Assume s 6 gt Once we estimate 0 however we have to move to a different distribution gt t distribution Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables All these distributions gt No worries the t is very similar to the z and therefore the normal Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables All these distributions gt No worries the t is very similar to the z and therefore the normal gt Basic difference 1 has fatter tails Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables All these distributions gt No worries the t is very similar to the z and therefore the normal gt Basic difference 1 has fatter tails gt In the limit as n a 00 t approaches a normal therefore 2 Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables Artwork Jone POL 51 The Sclenllflc Study of Pollllch Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test gt Let39s start out with the a one sample t test Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test gt Let39s start out with the a one sample t test gt The test statistic looks like 1 7 iii ll Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test gt Let39s start out with the a one sample t test gt The test statistic looks like 1 7 iii ll gt Here In is taken to mean the population mean Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables lhe t test gt Let39s start out with the a one sample t test gt The test statistic looks like tiyi sxN39 gt Here In is taken to mean the population mean gt u could be a hypothesized value Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables lhe t test gt Let39s start out with the a one sample t test gt The test statistic looks like tiyi sxN39 gt Here In is taken to mean the population mean gt u could be a hypothesized value gt Let39s look at an example using some hypothetical data on test scores Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypothetical example gt Suppose that in the past I39ve administered the same test repeated times Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypothetical example gt Suppose that in the past I39ve administered the same test repeated times gt From past exams I know the mean has been 80 percent Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypothetical example gt Suppose that in the past I39ve administered the same test repeated times gt From past exams I know the mean has been 80 percent gt Let39s say I give the exam to another class The class mean is 759 percent Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypothetical example gt Suppose that in the past I39ve administered the same test repeated times gt From past exams I know the mean has been 80 percent gt Let39s say I give the exam to another class The class mean is 759 percent gt Question is this class significantly different from past classes Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypothetical example gt Suppose that in the past I39ve administered the same test repeated times gt From past exams I know the mean has been 80 percent gt Let39s say I give the exam to another class The class mean is 759 percent gt Question is this class significantly different from past classes gt That is is Y 759 significantly different from u 80 Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypothetical example gt Suppose that in the past I39ve administered the same test repeated times V From past exams I know the mean has been 80 percent V Let39s say I give the exam to another class The class mean is 759 percent V Question is this class significantly different from past classes That is is Y 759 significantly different from u 80 V V Note I39m treating the population mean as 80 and evaluating deviation Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypothetical example gt Suppose that in the past I39ve administered the same test repeated times V From past exams I know the mean has been 80 percent V Let39s say I give the exam to another class The class mean is 759 percent V Question is this class significantly different from past classes That is is Y 759 significantly different from u 80 Note I39m treating the population mean as 80 and evaluating deviation V V gt Enter onesample t test Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypotheses gt Classical hypothesis testing means evaluating statements about the world probabilistically Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypotheses gt Classical hypothesis testing means evaluating statements about the world probabilistically gt The null is what we evaluate Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypotheses gt Classical hypothesis testing means evaluating statements about the world probabilistically gt The null is what we evaluate gt Null ho X 80 What am I saying Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypotheses gt Classical hypothesis testing means evaluating statements about the world probabilistically gt The null is what we evaluate gt Null ho X 80 What am I saying gt Alternative ha Yy 80 Now what am I saying Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypotheses gt Classical hypothesis testing means evaluating statements about the world probabilistically gt The null is what we evaluate gt Null ho Y 80 What am I saying gt Alternative ha Yy 80 Now what am I saying gt That statement was two sided What about onesided alternatives Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypotheses gt Classical hypothesis testing means evaluating statements about the world probabilistically gt The null is what we evaluate gt Null ho Y 80 What am I saying gt Alternative ha Yy 80 Now what am I saying gt That statement was two sided What about onesided alternatives gt Alternative 1 ha Tgt 80 Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Hypotheses gt Classical hypothesis testing means evaluating statements about the world probabilistically The null is what we evaluate Null ho Y 80 What am I saying Alternative ha Yy 80 Now what am I saying That statement was two sided What about onesided alternatives Alternative 1 ha 7 gt 80 Alternative 2 ha 7 lt 80 VVVV V V Jones POL 51 The Scientific Study of Politics l I a o u mg R stat 1 51 package Th1 is my computer code aw Mawa Maw wawwwwwww lbrarystats Dalgaard example modlfled p 83 hyposcoreltrc3245769982937472317681846679889261 76818589917069697278818290100 meanhypoltmeanhypoScore meanhypo sdhypoltsdhyposcore sdhypo t test hypo score mu80 tscoreltmean hypo 80Sd hyposqrt31 tscore mm Mawa Maw MMHMMHMMHM Jone POL 51 The Sclenll Ic Study 0 Po lllch l I hls output gt llbrarystats gt gt Dalgaard example modlfled p 83 gt gt hyposcoreltc 7e9982937472317e81846579889261 76818589917069697278818290100 gt anhypolt1ueanhyposcore meamhypo gt me 1 00323 gt e hypoltaedlthypoeeoaex sdhypo 1 070001 gt gt gt ttesthyposcore mm80 One Sample t test data hyposcore 30 pwalue 0 1821 true mean 15 not equal to 80 vaL sample estlmates mean of x 7590323 gt tscorelt mean hypo 80Sd hyposqrt 31 tseore 86 1 71365 Jone POL 51 The Sclenu Ic Study 0 Po Illch Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt t isjust a statistic It equaled the value 137 Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt t isjust a statistic t equaled the value 137 gt Consider the 95 percent rule Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt t isjust a statistic t equaled the value 137 gt Consider the 95 percent rule gt In previous slide we saw 95 percent ci was 6978 to 8203 Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt t isjust a statistic t equaled the value 137 gt Consider the 95 percent rule gt In previous slide we saw 95 percent ci was 6978 to 8203 gt Where did this interval come from Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics t is just a statistic t equaled the value 137 Consider the 95 percent rule D D gt In previous slide we saw 95 percent ci was 6978 to 8203 gt Where did this interval come from D Roughly 7 isem Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics t is just a statistic t equaled the value 137 Consider the 95 percent rule In previous slide we saw 95 percent ci was 6978 to 8203 Where did this interval come from Roughly 7 isem Mean 7590 semz 3 Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics b b b b b b b t is just a statistic t equaled the value 137 Consider the 95 percent rule In previous slide we saw 95 percent ci was 6978 to 8203 Where did this interval come from Roughly 7 isem Mean 7590 semz 3 Thus the approximate 95 percent ci is roughly 70 and 82 R gives exact ci Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Interpretation of ci The Scienllflc Study of Polquot POL 5 Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Interpretation of ci gt Here is one way to think about this test Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Interpretation of Ci gt Here is one way to think about this test gt Does 1 fall into this interval Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Interpretation of Ci gt Here is one way to think about this test gt Does 1 fall into this interval gt AH HA Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics Interpretation of Ci Here is one way to think about this test AH HA Since it does we might conclude our sample statistic is no different from 80 D D gt Does 1 fall into this interval D D Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics Interpretation of Ci Here is one way to think about this test AH HA Since it does we might conclude our sample statistic is no different from 80 gt Why D D gt Does 1 fall into this interval D D Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Interpretation of Ci gt Here is one way to think about this test gt Does u fall into this interval gt AH HA gt Since it does we might conclude our sample statistic is no different from 80 gt Why gt The interval around my sample estimate covers the population parameter Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Interpretation of ci gt Here is one way to think about this test gt Does u fall into this interval gt AH HA gt Since it does we might conclude our sample statistic is no different from 80 gt Why gt The interval around my sample estimate covers the population parameter gt 95 percent of repeated samples will produce an interval like this one Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Interpretation of ci gt Here is one way to think about this test gt Does u fall into this interval gt AH HA gt Since it does we might conclude our sample statistic is no different from 80 gt Why gt The interval around my sample estimate covers the population parameter gt 95 percent of repeated samples will produce an interval like this one V Therefore I cannot conclude my statistic is meaningfully different from M Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt The t statistic is used to compute the probability that Y u Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt The t statistic is used to compute the probability that Y u gt Logic What39s the probability of observing a t score of 7137 or larger Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt The t statistic is used to compute the probability that Y u gt Logic What39s the probability of observing a t score of 7137 or larger gt It is 18 Jones POL 51 The Scientific Study of Politics Bradford 5 Jones CrDavis Dept of Political Science Today Two Variables The t test Mechanics gt The t statistic is used to compute the probability that Y u gt Logic What39s the probability of observing a t score of 7137 or larger gt It is 18 gt Big Small Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt The t statistic is used to compute the probability that Y u gt Logic What39s the probability of observing a t score of 7137 or larger It is 18 gt Big Small gt To reject the null hypothesis this p value should be small V Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt The t statistic is used to compute the probability that Y u gt Logic What39s the probability of observing a t score of 7137 or larger It is 18 Big Small To reject the null hypothesis this p value should be small Why Suppose p 01 VVVV Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt The t statistic is used to compute the probability that Y u gt Logic What39s the probability of observing a t score of 7137 or larger It is 18 Big Small To reject the null hypothesis this p value should be small Why Suppose p 01 The probability that the difference between Y and u could have occurred by random chance alone is only 01 Thus we39re about 99 percent confident our difference is significant VVVVV Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt The t statistic is used to compute the probability that Y u gt Logic What39s the probability of observing a t score of 7137 or larger It is 18 Big Small To reject the null hypothesis this p value should be small Why Suppose p 01 The probability that the difference between Y and u could have occurred by random chance alone is only 01 Thus we39re about 99 percent confident our difference is significant VVVVV gt Above we39re only 82 percent confident the difference could have occurred by random chance alone about 18 percent of the time Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Suppose a drug company said we39re 82 percent confident this drug has no side effects Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Suppose a drug company said we39re 82 percent confident this drug has no side effects gt Policy implications and hypothesis testing You bet Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Suppose a drug company said we39re 82 percent confident this drug has no side effects gt Policy implications and hypothesis testing You bet gt Another example Jones POL 51 The Scientific Study of P l I gt hyposcoae2ltac9285969982937492917681849579889261 76818589917o699972788182so1o gt gt meanhypo2ltameanhyposcoae2 meanhyp02 1 846129 gt 56Lhypo2ltasdhyposcoae2 sdhyp02 1 9107995 gt gt gt c testhypo scoreQ muso One Sample cacesc 2 df so pavalue 0 data hyposcore c 6456 o 286 mean 15 not equal to so 2 alternatlve hypothesls tr e fldence Anterval 846129 gt tscore2lt mean hypoQasosd hypoQSqrt31 tscore2 1 2 645609 Jone POL 51 The Sclenll Ic Study 0 Po Illch Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Here the mean is 8461 The Scienllflc Study of Polquot POL 5 Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Here the mean is 8461 gt The 95 percent ci is 81 to 88 Jon POL 5 The Scientific Study of Politic Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Here the mean is 8461 gt The 95 percent ci is 81 to 88 gt Is 1 covered by this region No Jones POL 51 The Scientific Study of P Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Here the mean is 8461 gt The 95 percent ci is 81 to 88 gt Is 1 covered by this region No gt What is the p value for the t of 265 Jones POL 51 The Scientific Study of Politics Bradford 5 Jones UCrDavis Dept of Political Science Today Two Variables The t test Mechanics gt Here the mean is 8461 gt The 95 percent ci is 81 to 88 gt Is 1 covered by this region No gt What is the p value for the t of 265 gt It is 013 Interpretation Jones POL 51 The Scientific Study of Politics

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