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# Section 14.

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CPE 15.2.1 Freshman and sophomores and blood and guts films. There are 500 out and out. 200 (or a ... loving for thrillers. Discriminating at = .01. Reject the invalid ...
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Slide 1

﻿Part 14 Chi Square -  2 Chi square

Slide 2

Chi Square Chi Square is a non-parametric measurement used to test the invalid speculation. It is utilized for ostensible information. It is equal to the F test that we utilized for single variable and factorial examination. Chi square

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… Chi Square Nominal information puts every member in a classification. Classes are best when fundamentally unrelated and thorough. This implies every last member fits in one and stand out classification Chi Square takes a gander at frequencies in the classes. Chi square

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Expected frequencies and the invalid theory ... Chi Square looks at the normal frequencies in classes to the watched frequencies in classifications. "Expected frequencies"are the frequencies in every cell anticipated by the invalid theory Chi square

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… Expected frequencies and the invalid speculation ... The invalid theory: H 0 : f o = f e There is no distinction between the watched recurrence and the recurrence anticipated (expected) by the invalid. The trial speculation: H 1 : f o  f e The watched recurrence contrasts fundamentally from the recurrence anticipated (expected) by the invalid. Chi square

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Calculating  2 For every cell: Calculate the deviations of the saw from the normal. Square the deviations. Separate the squared deviations by the normal worth. Chi square

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Calculating  2 Add them up. At that point, gaze upward  2 in Chi Square Table df = k - 1 (one specimen  2 ) OR df= (Columns-1) * (Rows-1) (2 or more examples) Chi square

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Critical estimations of  2 df 1 2 3 4 5 6 7 8 .05 3.84 5.99 5.82 9.49 11.07 12.59 14.07 15.51 .01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 df 9 10 11 12 13 14 15 16 .05 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 .01 21.67 23.21 24.72 26.22 27.69 29.14 30.58 32.00 df 17 18 19 20 21 22 23 24 .05 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 .01 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 df 25 26 27 28 29 30 .05 37.65 38.89 40.14 41.34 42.56 43.77 .01 44.31 45.64 46.96 48.28 49.59 50.89

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Critical estimations of  2 df 1 2 3 4 5 6 7 8 .05 3.84 5.99 5.82 9.49 11.07 12.59 14.07 15.51 .01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 df 9 10 11 12 13 14 15 16 .05 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 .01 21.67 23.21 24.72 26.22 27.69 29.14 30.58 32.00 df 17 18 19 20 21 22 23 24 .05 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 .01 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 df 25 26 27 28 29 30 .05 37.65 38.89 40.14 41.34 42.56 43.77 .01 44.31 45.64 46.96 48.28 49.59 50.89 Degrees of flexibility

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Critical estimations of  2 df 1 2 3 4 5 6 7 8 .05 3.84 5.99 5.82 9.49 11.07 12.59 14.07 15.51 .01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 df 9 10 11 12 13 14 15 16 .05 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 .01 21.67 23.21 24.72 26.22 27.69 29.14 30.58 32.00 df 17 18 19 20 21 22 23 24 .05 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 .01 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 df 25 26 27 28 29 30 .05 37.65 38.89 40.14 41.34 42.56 43.77 .01 44.31 45.64 46.96 48.28 49.59 50.89 Critical qualities  = .05

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Critical estimations of  2 df 1 2 3 4 5 6 7 8 .05 3.84 5.99 5.82 9.49 11.07 12.59 14.07 15.51 .01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 df 9 10 11 12 13 14 15 16 .05 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 .01 21.67 23.21 24.72 26.22 27.69 29.14 30.58 32.00 df 17 18 19 20 21 22 23 24 .05 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 .01 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 df 25 26 27 28 29 30 .05 37.65 38.89 40.14 41.34 42.56 43.77 .01 44.31 45.64 46.96 48.28 49.59 50.89 Critical qualities  = .01

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Example If there were 5 degrees of opportunity, how huge would  2 must be for noteworthiness at the .05 level? Chi square

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Critical estimations of  2 df 1 2 3 4 5 6 7 8 .05 3.84 5.99 5.82 9.49 11.07 12.59 14.07 15.51 .01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 df 9 10 11 12 13 14 15 16 .05 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 .01 21.67 23.21 24.72 26.22 27.69 29.14 30.58 32.00 df 17 18 19 20 21 22 23 24 .05 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 .01 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 df 25 26 27 28 29 30 .05 37.65 38.89 40.14 41.34 42.56 43.77 .01 44.31 45.64 46.96 48.28 49.59 50.89

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Another case If there were 2 degrees of opportunity, how enormous would  2 must be for criticalness at the .05 level? Note: Unlike most different tables you have seen, the basic qualities for Chi Square get bigger as df increment. This is on account of you are summing over more cells, each of which for the most part adds to the aggregate watched estimation of chi square. Chi square

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Critical estimations of  2 df 1 2 3 4 5 6 7 8 .05 3.84 5.99 5.82 9.49 11.07 12.59 14.07 15.51 .01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 df 9 10 11 12 13 14 15 16 .05 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 .01 21.67 23.21 24.72 26.22 27.69 29.14 30.58 32.00 df 17 18 19 20 21 22 23 24 .05 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 .01 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 df 25 26 27 28 29 30 .05 37.65 38.89 40.14 41.34 42.56 43.77 .01 44.31 45.64 46.96 48.28 49.59 50.89

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 2 = 13.33 One specimen case from the cpe: Party: 75% male, 25% female There are 40 swimmers. Since 75% of individuals at gathering are male, 75% of swimmers ought to be male. So expected quality for guys is .750 X 40 = 30. For ladies it is .250 x 40 = 10.00 Observed 20 Expected 30 10 O-E - 10 (O-E) 2 100 (O-E) 2/E 3.33 10 Male Female df = k-1 = 2-1 = 1 Chi square

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 2 (1, n=40) = 13.33 Critical estimations of  2 df 1 2 3 4 5 6 7 8 .05 3.84 5.99 5.82 9.49 11.07 12.59 14.07 15.51 .01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 df 9 10 11 12 13 14 15 16 .05 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 .01 21.67 23.21 24.72 26.22 27.69 29.14 30.58 32.00 df 17 18 19 20 21 22 23 24 .05 27.59 28.87 30.14 31.41 32.67 33.92 35.17 36.42 .01 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 df 25 26 27 28 29 30 .05 37.65 38.89 40.14 41.34 42.56 43.77 .01 44.31 45.64 46.96 48.28 49.59 50.89 Exceeds basic quality at  = .01 Reject the invalid speculation. Sexual orientation affects who goes swimming. Ladies go swimming more than anticipated. Men go swimming not exactly anticipated.

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Freshmen Sophomores 2 test case Freshman and sophomores who like blood and gore flicks. 150 50 Likes thrillers 100 200 Dislikes blood and gore movies Chi square

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Freshmen Sophomores … CPE 15.2.1 Freshman and sophomores and blood and gore flicks. There are 500 out and out. 200 (or an extent of .400 are green beans, 300 (.600) are sophmores. (Extents show up in brackets in the edges.) Multiplying by column aggregates yield the accompanying expected recurrence for the principal cell. (This time we utilize the equation: (Prop column n col )=Expected Frequency). (EF shows up in brackets in every cell.) (100) 200 (.400) 150 50 (

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