Ch14slideswebsitefin al7222006

Information about Ch14slideswebsitefin al7222006

Published on February 18, 2008

Author: Regina1

Source: authorstream.com

Content

Chapter 14:  Chapter 14 Chi Square - 2 Chi Square:  Chi Square Chi Square is a non-parametric statistic used to test the null hypothesis. It is used for nominal data. It is equivalent to the F test that we used for single factor and factorial analysis. … Chi Square:  … Chi Square Nominal data puts each participant in a category. Categories are best when mutually exclusive and exhaustive. This means that each and every participant fits in one and only one category. Chi Square looks at frequencies in mutually exclusive and exhaustive categories into which participants are assigned after a single measurement. Expected frequencies and the null hypothesis ...:  Expected frequencies and the null hypothesis ... Chi Square compares the expected frequencies in categories to the observed frequencies in categories. “Expected frequencies”are the frequencies in each cell predicted by the null hypothesis … Expected frequencies and the null hypothesis ...:  … Expected frequencies and the null hypothesis ... The null hypothesis: H0: fo = fe There is no difference between the observed frequency and the frequency predicted (expected) by the null. The experimental hypothesis: H1: fo  fe The observed frequency differs significantly from the frequency predicted (expected) by the null. Calculating 2:  Calculating 2 Calculate the deviations of the observed from the expected. For each cell: Square the deviations. Divide the squared deviations by the expected value. Calculating 2:  Calculating 2 Add ‘em up. Then, look up 2 in Chi Square Table df = k - 1 (one sample 2) OR df= (Columns-1) * (Rows-1) (2 or more samples) Slide8:  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 values of 2 Slide9:  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 values of 2 Degrees of freedom Slide10:  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 values of 2 Critical values  = .05 Slide11:  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 values of 2 Critical values  = .01 Example:  Example If there were 5 degrees of freedom, how big would 2 have to be for significance at the .05 level? Slide13:  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 values of 2 Using the 2 table.:  Using the 2 table. If there were 2 degrees of freedom, how big would 2 have to be for significance at the .05 level? Note: Unlike most other tables you have seen, the critical values for Chi Square get larger as df increase. This is because you are summing over more cells, each of which usually contributes to the total observed value of chi square. Slide15:  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 values of 2 One sample example: Party: 75% male, 25% female There are 40 swimmers. Since 75% of people at party are male, 75% of swimmers should be male. So expected value for males is .750 X 40 = 30. For women it is .250 x 40 = 10.00:  One sample example: Party: 75% male, 25% female There are 40 swimmers. Since 75% of people at party are male, 75% of swimmers should be male. So expected value for males is .750 X 40 = 30. For women it is .250 x 40 = 10.00 Male Female Observed 20 20 Expected 30 10 O-E -10 10 (O-E)2 100 100 (O-E)2/E 3.33 10 df = k-1 = 2-1 = 1 Slide17:  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 values of 2 2 (1, n=40)= 13.33 Men go swimming less than expected. Gender does affect who goes swimming. Exceeds critical value at  = .01 Reject the null hypothesis. Women go swimming more than expected. 2 sample example:  2 sample example Freshman and sophomores who like horror movies. Likes horror films Dislikes horror films 150 200 100 50 Slide19:  There are 500 altogether. 200 (or a proportion of .400 like horror movies, 300 (.600) dislike horror films. (Proportions appear in parentheses in the margins.) Multiplying by the proportion in the “likes horror films” row by the number in the “Freshman” column yield the following expected frequency for the first cell. The formula is: Expected Frequency = (Proprowncol). (EF appears in parentheses in each cell.) Likes horror films Dislikes horror films 150 200 (150) 100 (150) 50 (100) 200 (.400) 300 (.600) 250 250 500 (100) Computing 2 :  Computing 2 Fresh Likes Fresh Dislikes Soph Likes Soph Dislikes Observed 150 100 50 200 Expected 100 150 100 150 df = (C-1)(R-1) = (2-1)(2-1) = 1 Slide21:  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 values of 2 2 (1, n=500)= 83.33 Fresh/Soph dimension does affect liking for horror movies. Critical at  = .01 Reject the null hypothesis. Proportionally, more freshman than sophomores like horror movies The only (slightly)hard part is computing expected frequencies:  The only (slightly)hard part is computing expected frequencies In one sample case, multiply n by a hypothetical proportion based on the null hypothesis that frequencies will be random. Simple Example - 100 teenagers listen to radio stations:  Simple Example - 100 teenagers listen to radio stations H1: Some stations are more popular with teenagers than others. H0: Radio station do not differ in popularity with teenagers. Expected frequencies are the frequencies predicted by the null hypothesis. In this case, the problem is simple because the null predicts an equal proportion of teenagers will prefer each of the four radio stations. Is the observed significantly different from the expected? Slide24:  Observed Expected df = k-1 = (4-1) = 3 2(3, n=100) = 20.00, p<.01 Station 1 Station 2 Station 3 Station 4 40 30 20 10 25 25 25 25 15 5 -5 15 225 25 25 225 9.00 1.00 1.00 9.00 Differential popularity of Radio station among teenagers The only (slightly)hard part is computing expected frequencies:  The only (slightly)hard part is computing expected frequencies In the multi-sample case, multiply proportion in row by numbers in each column to obtain EF in each cell. A 3 x 4 Chi Square:  A 3 x 4 Chi Square Women, stress, and seating preferences. (and perimeter vs. interior, front vs. back Very Stressed Females Moderately Stressed Females Control Group Females Front Front Back Back Perim Inter Perim Inter 10 60 15 35 30 50 70 5 10 15 15 25 20 300 60 30 150 100 100 100 Expected frequencies:  Expected frequencies Women, stress, and perimeter versus interior seating preferences. Very Stressed Females Moderately Stressed Females Control Group Females 10 60 15 35 30 50 70 5 10 15 15 25 20 300 60 30 150 100 100 100 (20) (20) (20) Front Front Back Back Perim Inter Perim Inter Column 2:  Column 2 Women, stress, and perimeter versus interior seating preferences. Very Stressed Females Moderately Stressed Females Control Group Females 10 60 15 35 30 50 70 5 10 15 15 25 20 300 60 30 150 100 100 100 (20) (20) (20) (50) (50) (50) Front Front Back Back Perim Inter Perim Inter Column 3:  Column 3 Women, stress, and perimeter versus interior seating preferences. Very Stressed Females Moderately Stressed Females Control Group Females 10 60 15 35 30 50 70 5 10 15 15 25 20 300 60 30 150 100 100 100 (20) (20) (20) (50) (50) (50) (10) (10) (10) Front Front Back Back Perim Inter Perim Inter All the expected frequencies:  All the expected frequencies Women, stress, and perimeter versus interior seating preferences. Very Stressed Females Moderately Stressed Females Control Group Females 10 60 15 35 30 50 70 5 10 15 15 25 20 300 60 30 150 100 100 100 (20) (20) (20) (50) (50) (50) (10) (10) (10) (20) (20) (20) Front Front Back Back Perim Inter Perim Inter Slide31:  FrontP FrontI BackP BackI Observed 10 70 5 15 Expected 20 50 10 20 df = (C-1)(R-1) = (4-1)(3-1) = 6 Very Stressed FrontP FrontI BackP BackI 15 50 10 25 20 50 10 20 -5 0 0 5 25 0 0 25 1.25 0.00 0.00 1.25 Moderately Stressed FrontP FrontI BackP BackI 35 30 15 20 20 50 10 20 15 -20 5 0 225 400 25 0 11.25 8.00 2.50 0.00 Control Group Slide32:  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 values of 2 2 (6, n=300)= 41.00 There is an effect between stressed women and seating position. Critical at  = .01 Reject the null hypothesis. Slide33:  FrontP FrontI BackP BackI Observed 10 70 5 15 Expected 20 50 10 20 O-E -10 20 -5 -5 (O-E)2 100 400 25 25 (O-E)2/E 5.00 8.00 2.50 1.25 2 = 41.00 df = (C-1)(R-1) = (4-1)(3-1) = 6 Very Stressed FrontP FrontI BackP BackI 15 50 10 25 20 50 10 20 -5 0 0 5 25 0 0 25 1.25 0.00 0.00 1.25 Moderately Stressed FrontP FrontI BackP BackI 35 30 15 20 20 50 10 20 15 -20 5 0 225 400 25 0 11.25 8.00 2.50 0.00 Control Group Very stressed women avoid the perimeter and prefer the front interior. The control group prefers the perimeter and avoids the front interior. Summary: Different Ways of Computing the Frequencies Predicted by the Null Hypothesis:  Summary: Different Ways of Computing the Frequencies Predicted by the Null Hypothesis One sample Expect subjects to be distributed equally in each cell. OR Expect subjects to be distributed proportionally in each cell. OR Expect subjects to be distributed in each cell based on prior knowledge, such as, previous research. Multi-sample Expect subjects in different conditions to be distributed similarly to each other. Find the proportion in each row and multiply by the number in each column to do so. Conclusion - Chi Square:  Conclusion - Chi Square Chi Square is a non-parametric statistic,used for nominal data. It is equivalent to the F test that we used for single factor and factorial analysis. Chi Square compares the expected frequencies in categories to the observed frequencies in categories. … Conclusion - Chi Square:  … Conclusion - Chi Square The null hypothesis: H0: fo = fe There is no difference between the observed frequency and frequency predicted by the null hypothesis. The experimental hypothesis: H1: fo  fe The observed frequency differs significantly from the frequency expected by the null hypothesis. The end. Hope you found the slides helpful! RK:  The end. Hope you found the slides helpful! RK

Related presentations


Other presentations created by Regina1

Romantic Period Intro
15. 01. 2008
0 views

Romantic Period Intro

era7
17. 01. 2008
0 views

era7

English Technical Writing
19. 03. 2008
0 views

English Technical Writing

The Globalization of HIV
11. 01. 2008
0 views

The Globalization of HIV

Araki
08. 05. 2008
0 views

Araki

CLDP Presentation AU 2006
07. 05. 2008
0 views

CLDP Presentation AU 2006

P2 4 Liu Yu RFIDlab in CAISA
02. 05. 2008
0 views

P2 4 Liu Yu RFIDlab in CAISA

Lesson38 The Olympic Games
02. 05. 2008
0 views

Lesson38 The Olympic Games

2010Bid Park
30. 04. 2008
0 views

2010Bid Park

roysembel smak7
24. 04. 2008
0 views

roysembel smak7

jbartram
22. 04. 2008
0 views

jbartram

KJ1E0019
21. 04. 2008
0 views

KJ1E0019

Guides Saga
18. 04. 2008
0 views

Guides Saga

investing in costarica
17. 04. 2008
0 views

investing in costarica

Barg PAC3
10. 01. 2008
0 views

Barg PAC3

cisco systems dwdm primer oct03
11. 01. 2008
0 views

cisco systems dwdm primer oct03

Mark Regier
13. 01. 2008
0 views

Mark Regier

Coherence 1
15. 01. 2008
0 views

Coherence 1

WonnacottPhase1
16. 01. 2008
0 views

WonnacottPhase1

Micro Clim
17. 01. 2008
0 views

Micro Clim

geoterm
22. 01. 2008
0 views

geoterm

handout 186663
23. 01. 2008
0 views

handout 186663

similars
23. 01. 2008
0 views

similars

dac03 shatter
16. 01. 2008
0 views

dac03 shatter

Customer Presentation
04. 02. 2008
0 views

Customer Presentation

part3 storms
11. 02. 2008
0 views

part3 storms

Gherm
12. 02. 2008
0 views

Gherm

Strawberries and Blueberries
22. 01. 2008
0 views

Strawberries and Blueberries

2007921162811471
28. 01. 2008
0 views

2007921162811471

treasuresbg
29. 01. 2008
0 views

treasuresbg

display advertising
29. 01. 2008
0 views

display advertising

telecom
31. 01. 2008
0 views

telecom

zhizhan
06. 02. 2008
0 views

zhizhan

TT IntroAfrica VCT
10. 01. 2008
0 views

TT IntroAfrica VCT

Parsons bores
13. 02. 2008
0 views

Parsons bores

Traditional music of Japan
13. 02. 2008
0 views

Traditional music of Japan

classrocks
10. 01. 2008
0 views

classrocks

Microsoft Longhorn
20. 02. 2008
0 views

Microsoft Longhorn

ISV App Hosting for SaaS
21. 02. 2008
0 views

ISV App Hosting for SaaS

Iain Macleod Stephen Potts
29. 02. 2008
0 views

Iain Macleod Stephen Potts

poetry2007
11. 03. 2008
0 views

poetry2007

Crim Proc Sat Class 6
28. 01. 2008
0 views

Crim Proc Sat Class 6

Geology of Terrestial Planets
15. 03. 2008
0 views

Geology of Terrestial Planets

Minjun PhD Oral Exam
16. 03. 2008
0 views

Minjun PhD Oral Exam

Ontology of TB 16 9 04
20. 03. 2008
0 views

Ontology of TB 16 9 04

20070315presentation
24. 03. 2008
0 views

20070315presentation

harder2006wasteelvs
12. 02. 2008
0 views

harder2006wasteelvs

IPE Mutlinationals2005
31. 03. 2008
0 views

IPE Mutlinationals2005

39179261
08. 04. 2008
0 views

39179261

astrobiology
24. 01. 2008
0 views

astrobiology

The Panel of Chefs Of Ireland
05. 02. 2008
0 views

The Panel of Chefs Of Ireland

AMEDOC 2004 EXP RESP
15. 01. 2008
0 views

AMEDOC 2004 EXP RESP

otqh
10. 03. 2008
0 views

otqh

A C 4 US CHAPTER
13. 01. 2008
0 views

A C 4 US CHAPTER

chap5a
28. 02. 2008
0 views

chap5a

nih coprrace and trust
11. 01. 2008
0 views

nih coprrace and trust

ppt 44
14. 02. 2008
0 views

ppt 44

Morley TheLongandWindingRoa d1
04. 02. 2008
0 views

Morley TheLongandWindingRoa d1

abacus
11. 02. 2008
0 views

abacus

aaai99
25. 01. 2008
0 views

aaai99

DeCourcey Benefits 25Aug05
22. 01. 2008
0 views

DeCourcey Benefits 25Aug05

Holt
05. 02. 2008
0 views

Holt

Cmtg Dec11
09. 01. 2008
0 views

Cmtg Dec11

Modified Micro May 2003
08. 01. 2008
0 views

Modified Micro May 2003

egs poster
22. 01. 2008
0 views

egs poster