{"id":110,"date":"2024-08-21T12:03:37","date_gmt":"2024-08-21T12:03:37","guid":{"rendered":"https:\/\/routledgelearning.com\/researchmethods\/?post_type=content&p=110"},"modified":"2024-09-12T14:25:00","modified_gmt":"2024-09-12T14:25:00","slug":"chapter-18-tests-for-categorical-variables-and-frequency-tables","status":"publish","type":"content","link":"https:\/\/routledgelearning.com\/researchmethods\/student-resources\/chapter-18-tests-for-categorical-variables-and-frequency-tables\/","title":{"rendered":"Chapter 18 – Tests for categorical variables and frequency tables"},"content":{"rendered":"\n
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\n\tHome\n<\/span><\/div>\n\n

Chapter 18 – Tests for categorical variables and frequency tables<\/h1>\n\n\n

This chapter discusses the use of the chi-square test to analyze categorical data, and the analysis of multi-way tables using log-linear analysis.<\/p>\n<\/div>\n<\/div>\n\n\n\n

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Exercises<\/h2>\n\n\n\n

Exercise 18.1<\/h3>\n\n\n\n

A 2 x 2 chi-square analysis<\/strong><\/p>\n\n\n\n

Individual passers-by, approaching a pedestrian crossing, are targeted by observers who record whether the person crosses against the red man under two conditions, when no one at the crossing disobeys the red man and when at least two people disobey. The results are recorded in the table below.<\/p>\n\n\n\n

 <\/td>No jaywalker<\/td>At least two jaywalkers<\/td> <\/td><\/tr>
Target disobeys light<\/td>16<\/td>27<\/td>43<\/td><\/tr>
Target obeys light<\/td>43<\/td>33<\/td>76<\/td><\/tr>
 <\/td>59<\/td>60<\/td>119<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

1. Calculate the expected frequencies for a chi-square analysis. Copy the table below and enter your results.<\/p>\n\n\n\n

 <\/td>No jaywalker<\/td>At least two jaywalkers<\/td> <\/td><\/tr>
Target disobeys light<\/td> <\/td> <\/td>43<\/td><\/tr>
Target obeys light<\/td> <\/td> <\/td>76<\/td><\/tr>
 <\/td>59<\/td>60<\/td>119<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

2. Now conduct the chi-square analysis. The data set is available here. However if you are learning SPSS it is a good idea to set this up for yourself. Don\u2019t forget to weight cases as described on XXX of the book. To weight cases here you need a variable called jaywalkers<\/em><\/strong> with two values, \u2018none\u2019 and \u2018twoplus\u2019. You need a second variable, obeys<\/em><\/strong>, with two values \u2018no\u2019 and \u2018yes\u2019. Make your datasheet show one case for each possible combination and enter the data from the observed data table above into the appropriate rows in a third column variable called count<\/em><\/strong>. Then select Data\/Weight<\/em><\/strong> cases<\/em><\/strong> and drop the variable count<\/em><\/strong> into the weight cases<\/em><\/strong> box to the right.<\/p>\n\n\n\n

Now enter your result into the spaces below. In each case use three places of decimals and don\u2019t worry if you\u2019re a fraction out. This could be because of rounding decimals in your calculations.<\/p>\n\n\n\n

c<\/em>2 (1, N = 119)<\/td> <\/td><\/tr>
p<\/em> value<\/td> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Show answer<\/summary>\n
 <\/td>No jaywalker<\/td>At least two jaywalkers<\/td> <\/td><\/tr>
Target disobeys light<\/td>21.3<\/td>21.7<\/td>43<\/td><\/tr>
Target obeys light<\/td>37.7<\/td>38.3<\/td>76<\/td><\/tr>
 <\/td>59<\/td>60<\/td>119<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\u03c7<\/em>2<\/sup> (1, N = 119)<\/td>4.122  <\/td><\/tr>
p<\/em> value<\/td>.042<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/details>\n\n\n\n

Exercise 18.2<\/h3>\n\n\n\n

A loglinear analysis<\/strong><\/p>\n\n\n\n

Suppose that the research in Exercise 18.1 is extended to include an extra condition of five or more jaywalkers and to include a new variable of gender. The table below gives fictitious data for such an observational study. Conduct a loglinear analysis on the data outlining all significant results in your results report.<\/p>\n\n\n\n

Males<\/td> <\/td> <\/td> <\/td> <\/td><\/tr>
 <\/td>No jaywalker<\/td>At least two jaywalkers<\/td>Five or more jaywalkers<\/td> <\/td><\/tr>
Target disobeys light<\/td>21<\/td>25<\/td>38<\/td>  84<\/td><\/tr>
Target obeys light<\/td>38<\/td>35<\/td>22<\/td>  95<\/td><\/tr>
 <\/td>59<\/td>60<\/td>59<\/td>179<\/td><\/tr>
Females<\/td> <\/td> <\/td> <\/td> <\/td><\/tr>
 <\/td>No jaywalker<\/td>At least two jaywalkers<\/td>Five or more jaywalkers<\/td> <\/td><\/tr>
Target disobeys light<\/td>22<\/td>23<\/td>29<\/td>  74<\/td><\/tr>
Target obeys light<\/td>39<\/td>37<\/td>31<\/td>107<\/td><\/tr>
 <\/td>61<\/td>60<\/td>60<\/td>181<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Show answer<\/summary>\n

A three-way backward elimination loglinear analysis was performed on the frequency data in the table above produced by combining frequencies for jaywalkers, obedience and gender. One-way effects were not significant, likelihood ratio \u03c7<\/em>2<\/sup> (4) = 5.40, p = .248; two-way effects were significant, likelihood ratio \u03c7<\/em>2<\/sup> (5) = 11.968, p = .035; the three-way effect was not significant, \u03c7<\/em>2<\/sup> (2) = 1.554, p<\/em> = .46. Only the jaywalkers x obedience interaction was significant \u03c7<\/em>2<\/sup> (2) = 10.845, p<\/em> = .004. More people crossed against the light when there were more jaywalkers present.<\/strong><\/p>\n<\/details>\n\n\n\n

Exercise 18.3<\/h3>\n\n\n\n

Have a go at this short quiz to test your understanding and identify any gaps in your knowledge.<\/p>\n\n\n\n

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