{"id":110,"date":"2024-08-21T12:03:37","date_gmt":"2024-08-21T12:03:37","guid":{"rendered":"http:\/\/localhost\/researchmethods\/?post_type=content&#038;p=110"},"modified":"2026-08-26T11:39:54","modified_gmt":"2026-08-26T11:39:54","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 &#8211; Tests for categorical variables and frequency tables"},"content":{"rendered":"\n<div class=\"wp-block-group has-base-background-color has-background has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"margin-top:0;margin-bottom:0;padding-top:var(--wp--preset--spacing--70);padding-bottom:var(--wp--preset--spacing--70)\">\n<div class=\"wp-block-group alignwide is-layout-flow wp-block-group-is-layout-flow\"><nav style=\"--separator: &quot;\/&quot;\" class=\"wp-block-breadcrumbs\" aria-label=\"Breadcrumbs\"><ol><li><a href=\"https:\/\/routledgelearning.com\/researchmethods\/\">Home<\/a><\/li><li><a href=\"https:\/\/routledgelearning.com\/researchmethods\/student-resources\/\">Student Resources<\/a><\/li><li><span aria-current=\"page\">Chapter 18 &#8211; Tests for categorical variables and frequency tables<\/span><\/li><\/ol><\/nav>\n\n<h1 class=\"alignwide wp-block-post-title has-large-font-size\">Chapter 18 &#8211; Tests for categorical variables and frequency tables<\/h1>\n\n\n<p class=\"wp-block-paragraph\">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<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"margin-top:0;margin-bottom:0;padding-top:var(--wp--preset--spacing--60);padding-bottom:var(--wp--preset--spacing--60)\">\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:75%\">\n<h2 id=\"aioseo-exercises\" class=\"wp-block-heading\">Exercises<\/h2>\n\n\n\n<h3 id=\"aioseo-exercise-18-1\" class=\"wp-block-heading\">Exercise 18.1<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>A 2 x 2 chi-square analysis<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>&nbsp;<\/td><td>No jaywalker<\/td><td>At least two jaywalkers<\/td><td>&nbsp;<\/td><\/tr><tr><td>Target disobeys light<\/td><td>16<\/td><td>27<\/td><td>43<\/td><\/tr><tr><td>Target obeys light<\/td><td>43<\/td><td>33<\/td><td>76<\/td><\/tr><tr><td>&nbsp;<\/td><td>59<\/td><td>60<\/td><td>119<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">1. Calculate the expected frequencies for a chi-square analysis. Copy the table below and enter your results.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>&nbsp;<\/td><td>No jaywalker<\/td><td>At least two jaywalkers<\/td><td>&nbsp;<\/td><\/tr><tr><td>Target disobeys light<\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><td>43<\/td><\/tr><tr><td>Target obeys light<\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><td>76<\/td><\/tr><tr><td>&nbsp;<\/td><td>59<\/td><td>60<\/td><td>119<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">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 <strong><em>jaywalkers<\/em><\/strong> with two values, \u2018none\u2019 and \u2018twoplus\u2019. You need a second variable, <strong><em>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 <strong><em>count<\/em><\/strong>. Then select <strong><em>Data\/Weight<\/em><\/strong> <strong><em>cases<\/em><\/strong> and drop the variable <strong><em>count<\/em><\/strong> into the <strong><em>weight cases<\/em><\/strong> box to the right.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><em>c<\/em>2 (1, N = 119)<\/td><td>&nbsp;<\/td><\/tr><tr><td><em>p<\/em>&nbsp;value<\/td><td>&nbsp;<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Show answer<\/summary>\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>&nbsp;<\/td><td>No jaywalker<\/td><td>At least two jaywalkers<\/td><td>&nbsp;<\/td><\/tr><tr><td>Target disobeys light<\/td><td>21.3<\/td><td>21.7<\/td><td>43<\/td><\/tr><tr><td>Target obeys light<\/td><td>37.7<\/td><td>38.3<\/td><td>76<\/td><\/tr><tr><td>&nbsp;<\/td><td>59<\/td><td>60<\/td><td>119<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><em>\u03c7<\/em><sup>2<\/sup> (1, N = 119)<\/td><td>4.122&nbsp;&nbsp;<\/td><\/tr><tr><td><em>p<\/em>&nbsp;value<\/td><td>.042<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/details>\n\n\n\n<h3 id=\"aioseo-exercise-18-2\" class=\"wp-block-heading\">Exercise 18.2<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>A loglinear analysis<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Males<\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><\/tr><tr><td>&nbsp;<\/td><td>No jaywalker<\/td><td>At least two jaywalkers<\/td><td>Five or more jaywalkers<\/td><td>&nbsp;<\/td><\/tr><tr><td>Target disobeys light<\/td><td>21<\/td><td>25<\/td><td>38<\/td><td>&nbsp; 84<\/td><\/tr><tr><td>Target obeys light<\/td><td>38<\/td><td>35<\/td><td>22<\/td><td>&nbsp; 95<\/td><\/tr><tr><td>&nbsp;<\/td><td>59<\/td><td>60<\/td><td>59<\/td><td>179<\/td><\/tr><tr><td>Females<\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><td>&nbsp;<\/td><\/tr><tr><td>&nbsp;<\/td><td>No jaywalker<\/td><td>At least two jaywalkers<\/td><td>Five or more jaywalkers<\/td><td>&nbsp;<\/td><\/tr><tr><td>Target disobeys light<\/td><td>22<\/td><td>23<\/td><td>29<\/td><td>&nbsp; 74<\/td><\/tr><tr><td>Target obeys light<\/td><td>39<\/td><td>37<\/td><td>31<\/td><td>107<\/td><\/tr><tr><td>&nbsp;<\/td><td>61<\/td><td>60<\/td><td>60<\/td><td>181<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>Show answer<\/summary>\n<p class=\"wp-block-paragraph\">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 <em>\u03c7<\/em><sup>2<\/sup> (4) = 5.40, p = .248; two-way effects were significant, likelihood ratio <em>\u03c7<\/em><sup>2<\/sup> (5) = 11.968, p = .035; the three-way effect was not significant, <em>\u03c7<\/em><sup>2<\/sup> (2) = 1.554, <em>p<\/em> = .46. Only the jaywalkers x obedience interaction was significant <em>\u03c7<\/em><sup>2<\/sup> (2) = 10.845, <em>p<\/em> = .004. More people crossed against the light when there were more jaywalkers present.<strong><\/strong><\/p>\n<\/details>\n\n\n\n<h3 id=\"aioseo-exercise-18-3\" class=\"wp-block-heading\">Exercise 18.3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Have a go at this short quiz to test your understanding and identify any gaps in your knowledge.<\/p>\n\n\n\n<div class=\"wp-block-group has-base-element-background-color has-background has-global-padding is-layout-constrained wp-container-core-group-is-layout-0910e091 wp-block-group-is-layout-constrained\" style=\"border-width:1px;padding-top:var(--wp--preset--spacing--40);padding-right:var(--wp--preset--spacing--40);padding-bottom:var(--wp--preset--spacing--40);padding-left:var(--wp--preset--spacing--40)\">\n<div class=\"wp-block-group alignwide is-layout-flow wp-block-group-is-layout-flow\"><script>\n                            if (window.qmn_quiz_data === undefined) {\n                                    window.qmn_quiz_data = new Object();\n                            }\n                    <\/script><script>window.qmn_quiz_data[\"16\"] = {\"quiz_id\":\"16\",\"quiz_name\":\"exercise183\",\"disable_answer\":0,\"ajax_show_correct\":0,\"progress_bar\":0,\"contact_info_location\":\"0\",\"qpages\":{\"1\":{\"id\":\"1\",\"quizID\":\"16\",\"pagekey\":\"mdik3wAw\",\"hide_prevbtn\":\"0\"}},\"skip_validation_time_expire\":0,\"timer_limit_val\":0,\"disable_scroll_next_previous_click\":0,\"disable_scroll_on_result\":0,\"disable_first_page\":\"0\",\"enable_result_after_timer_end\":0,\"enable_quick_result_mc\":0,\"end_quiz_if_wrong\":0,\"form_disable_autofill\":0,\"disable_mathjax\":0,\"enable_quick_correct_answer_info\":\"0\",\"quick_result_correct_answer_text\":\"Correct! 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table.\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 1\\\";s:14:\\\"featureImageID\\\";s:0:\\\"\\\";s:15:\\\"featureImageSrc\\\";s:0:\\\"\\\";s:11:\\\"matchAnswer\\\";s:6:\\\"random\\\";s:14:\\\"case_sensitive\\\";s:0:\\\"\\\";s:16:\\\"image_size-width\\\";s:0:\\\"\\\";s:17:\\\"image_size-height\\\";s:0:\\\"\\\";s:8:\\\"autofill\\\";s:0:\\\"\\\";s:10:\\\"limit_text\\\";s:1:\\\"0\\\";s:23:\\\"limit_multiple_response\\\";s:1:\\\"0\\\";s:17:\\\"file_upload_limit\\\";s:1:\\\"0\\\";s:16:\\\"file_upload_type\\\";s:0:\\\"\\\";s:15:\\\"min_text_length\\\";s:0:\\\"\\\";}\",\"category\":\"\",\"linked_question\":\"\",\"deleted\":\"0\",\"deleted_question_bank\":\"0\",\"answers\":[[\"True\",0,0],[\"False\",0,1]]},\"111\":{\"question_id\":\"111\",\"quiz_id\":\"16\",\"question_name\":\"Degrees of freedom for a 3 X 4 chi-square test are\",\"answer_array\":\"a:2:{i:0;a:3:{i:0;s:1:\\\"6\\\";i:1;d:0;i:2;i:1;}i:1;a:3:{i:0;s:2:\\\"12\\\";i:1;d:0;i:2;i:0;}}\",\"answer_one\":\"\",\"answer_one_points\":\"0\",\"answer_two\":\"\",\"answer_two_points\":\"0\",\"answer_three\":\"\",\"answer_three_points\":\"0\",\"answer_four\":\"\",\"answer_four_points\":\"0\",\"answer_five\":\"\",\"answer_five_points\":\"0\",\"answer_six\":\"\",\"answer_six_points\":\"0\",\"correct_answer\":\"0\",\"question_answer_info\":\"Degrees of freedom are (R-1) X (C-1) = (3-1) X (4-1) = 2 X 3 = 6\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 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occur\",\"answer_array\":\"a:2:{i:0;a:3:{i:0;s:4:\\\"True\\\";i:1;d:0;i:2;i:0;}i:1;a:3:{i:0;s:5:\\\"False\\\";i:1;d:0;i:2;i:1;}}\",\"answer_one\":\"\",\"answer_one_points\":\"0\",\"answer_two\":\"\",\"answer_two_points\":\"0\",\"answer_three\":\"\",\"answer_three_points\":\"0\",\"answer_four\":\"\",\"answer_four_points\":\"0\",\"answer_five\":\"\",\"answer_five_points\":\"0\",\"answer_six\":\"\",\"answer_six_points\":\"0\",\"correct_answer\":\"0\",\"question_answer_info\":\"Expected frequencies are the frequencies that would occur if the null hypothesis were true, given the marginal totals.\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 3\\\";s:14:\\\"featureImageID\\\";s:0:\\\"\\\";s:15:\\\"featureImageSrc\\\";s:0:\\\"\\\";s:11:\\\"matchAnswer\\\";s:6:\\\"random\\\";s:14:\\\"case_sensitive\\\";s:0:\\\"\\\";s:16:\\\"image_size-width\\\";s:0:\\\"\\\";s:17:\\\"image_size-height\\\";s:0:\\\"\\\";s:8:\\\"autofill\\\";s:0:\\\"\\\";s:10:\\\"limit_text\\\";s:1:\\\"0\\\";s:23:\\\"limit_multiple_response\\\";s:1:\\\"0\\\";s:17:\\\"file_upload_limit\\\";s:1:\\\"4\\\";s:16:\\\"file_upload_type\\\";s:21:\\\"image,application\\\/pdf\\\";s:15:\\\"min_text_length\\\";s:0:\\\"\\\";}\",\"category\":\"\",\"linked_question\":\"\",\"deleted\":\"0\",\"deleted_question_bank\":\"0\",\"answers\":[[\"True\",0,0],[\"False\",0,1]]},\"113\":{\"question_id\":\"113\",\"quiz_id\":\"16\",\"question_name\":\"Chi-square becomes larger the more that observed frequencies depart from expected frequencies\",\"answer_array\":\"a:2:{i:0;a:3:{i:0;s:4:\\\"True\\\";i:1;d:0;i:2;i:1;}i:1;a:3:{i:0;s:5:\\\"False\\\";i:1;d:0;i:2;i:0;}}\",\"answer_one\":\"\",\"answer_one_points\":\"0\",\"answer_two\":\"\",\"answer_two_points\":\"0\",\"answer_three\":\"\",\"answer_three_points\":\"0\",\"answer_four\":\"\",\"answer_four_points\":\"0\",\"answer_five\":\"\",\"answer_five_points\":\"0\",\"answer_six\":\"\",\"answer_six_points\":\"0\",\"correct_answer\":\"0\",\"question_answer_info\":\"As the Os become further from the Es so each value of (O-E)2\\\/E becomes larger as does the sum of these which is chi-square.\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 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measurement\",\"answer_array\":\"a:2:{i:0;a:3:{i:0;s:4:\\\"True\\\";i:1;d:0;i:2;i:1;}i:1;a:3:{i:0;s:5:\\\"False\\\";i:1;d:0;i:2;i:0;}}\",\"answer_one\":\"\",\"answer_one_points\":\"0\",\"answer_two\":\"\",\"answer_two_points\":\"0\",\"answer_three\":\"\",\"answer_three_points\":\"0\",\"answer_four\":\"\",\"answer_four_points\":\"0\",\"answer_five\":\"\",\"answer_five_points\":\"0\",\"answer_six\":\"\",\"answer_six_points\":\"0\",\"correct_answer\":\"0\",\"question_answer_info\":\"Chi-square can only be used when the scale of each variable is categorical. Each observation is assigned to a category on that variable.\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 5\\\";s:14:\\\"featureImageID\\\";s:0:\\\"\\\";s:15:\\\"featureImageSrc\\\";s:0:\\\"\\\";s:11:\\\"matchAnswer\\\";s:6:\\\"random\\\";s:14:\\\"case_sensitive\\\";s:0:\\\"\\\";s:16:\\\"image_size-width\\\";s:0:\\\"\\\";s:17:\\\"image_size-height\\\";s:0:\\\"\\\";s:8:\\\"autofill\\\";s:0:\\\"\\\";s:10:\\\"limit_text\\\";s:1:\\\"0\\\";s:23:\\\"limit_multiple_response\\\";s:1:\\\"0\\\";s:17:\\\"file_upload_limit\\\";s:1:\\\"4\\\";s:16:\\\"file_upload_type\\\";s:21:\\\"image,application\\\/pdf\\\";s:15:\\\"min_text_length\\\";s:0:\\\"\\\";}\",\"category\":\"\",\"linked_question\":\"\",\"deleted\":\"0\",\"deleted_question_bank\":\"0\",\"answers\":[[\"True\",0,1],[\"False\",0,0]]},\"115\":{\"question_id\":\"115\",\"quiz_id\":\"16\",\"question_name\":\"Very low frequencies are not a problem in a chi-square analysis.\",\"answer_array\":\"a:2:{i:0;a:3:{i:0;s:4:\\\"True\\\";i:1;d:0;i:2;i:0;}i:1;a:3:{i:0;s:5:\\\"False\\\";i:1;d:0;i:2;i:1;}}\",\"answer_one\":\"\",\"answer_one_points\":\"0\",\"answer_two\":\"\",\"answer_two_points\":\"0\",\"answer_three\":\"\",\"answer_three_points\":\"0\",\"answer_four\":\"\",\"answer_four_points\":\"0\",\"answer_five\":\"\",\"answer_five_points\":\"0\",\"answer_six\":\"\",\"answer_six_points\":\"0\",\"correct_answer\":\"0\",\"question_answer_info\":\"They are if more than 20% of cells contain values less than 5. Although some debate exists about how serious the problem is, the safest approach with such frequencies (e.g. any cell of less than 5 in a 2 X 2 analysis) is to conduct a Fisher\\u2019s exact test.\",\"comments\":\"1\",\"hints\":\"\",\"question_order\":\"1\",\"question_type\":\"0\",\"question_type_new\":\"0\",\"question_settings\":\"a:15:{s:8:\\\"required\\\";i:0;s:12:\\\"answerEditor\\\";s:4:\\\"text\\\";s:14:\\\"question_title\\\";s:10:\\\"Question 6\\\";s:14:\\\"featureImageID\\\";s:0:\\\"\\\";s:15:\\\"featureImageSrc\\\";s:0:\\\"\\\";s:11:\\\"matchAnswer\\\";s:6:\\\"random\\\";s:14:\\\"case_sensitive\\\";s:0:\\\"\\\";s:16:\\\"image_size-width\\\";s:0:\\\"\\\";s:17:\\\"image_size-height\\\";s:0:\\\"\\\";s:8:\\\"autofill\\\";s:0:\\\"\\\";s:10:\\\"limit_text\\\";s:1:\\\"0\\\";s:23:\\\"limit_multiple_response\\\";s:1:\\\"0\\\";s:17:\\\"file_upload_limit\\\";s:1:\\\"4\\\";s:16:\\\"file_upload_type\\\";s:21:\\\"image,application\\\/pdf\\\";s:15:\\\"min_text_length\\\";s:0:\\\"\\\";}\",\"category\":\"\",\"linked_question\":\"\",\"deleted\":\"0\",\"deleted_question_bank\":\"0\",\"answers\":[[\"True\",0,0],[\"False\",0,1]]}},\"first_page\":false,\"questions_settings\":[]}\n                    <\/script>\t\t<div class='qsm-quiz-container qsm-quiz-container-16 qmn_quiz_container mlw_qmn_quiz qsm_auto_pagination_enabled quiz_theme_default  '>\n\t\t\t\t\t\t\t\t<form name=\"quizForm16\" id=\"quizForm16\" action=\"\/researchmethods\/wp-json\/wp\/v2\/content\/110\/\" method=\"POST\" class=\"qsm-quiz-form qmn_quiz_form mlw_quiz_form\" novalidate enctype=\"multipart\/form-data\">\n\t\t\t\t<input type=\"hidden\" name=\"qsm_hidden_questions\" id=\"qsm_hidden_questions\" value=\"\">\n\t\t\t\t<input type=\"hidden\" name=\"qsm_nonce\" id=\"qsm_nonce_16\" value=\"2fd727bbb5\">\n\t\t\t\t<input type=\"hidden\" name=\"qsm_unique_key\" id=\"qsm_unique_key_16\" value=\"6a8f8c857db6e\">\n\t\t\t\t<div id=\"mlw_error_message\" class=\"qsm-error-message qmn_error_message_section\"><\/div>\n\t\t\t\t<span id=\"mlw_top_of_quiz\"><\/span>\n\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-1\" data-apid=\"1\" data-qpid=\"1\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-110 slide0 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 1 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>Chi-square can be used with related data<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question110-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question110\" id=\"question110_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question110_1\">\n\t\t\t\t\tTrue\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question110-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question110\" id=\"question110_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question110_2\">\n\t\t\t\t\tFalse\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question110_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question110\" id=\"question110_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_110\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-2\" data-apid=\"2\" data-qpid=\"2\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-111 slide1 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 2 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>Degrees of freedom for a 3 X 4 chi-square test are<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question111-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question111\" id=\"question111_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question111_1\">\n\t\t\t\t\t6\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question111-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question111\" id=\"question111_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question111_2\">\n\t\t\t\t\t12\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question111_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question111\" id=\"question111_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_111\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-3\" data-apid=\"3\" data-qpid=\"3\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-112 slide2 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 3 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>Expected frequencies are the frequencies the researcher expects to occur<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question112-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question112\" id=\"question112_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question112_1\">\n\t\t\t\t\tTrue\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question112-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question112\" id=\"question112_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question112_2\">\n\t\t\t\t\tFalse\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question112_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question112\" id=\"question112_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_112\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-4\" data-apid=\"4\" data-qpid=\"4\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-113 slide3 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 4 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>Chi-square becomes larger the more that observed frequencies depart from expected frequencies<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question113-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question113\" id=\"question113_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question113_1\">\n\t\t\t\t\tTrue\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question113-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question113\" id=\"question113_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question113_2\">\n\t\t\t\t\tFalse\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question113_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question113\" id=\"question113_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_113\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-5\" data-apid=\"5\" data-qpid=\"5\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-114 slide4 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 5 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>Data used in a chi-square analysis are at a nominal level of measurement<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question114-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question114\" id=\"question114_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question114_1\">\n\t\t\t\t\tTrue\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question114-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question114\" id=\"question114_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question114_2\">\n\t\t\t\t\tFalse\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question114_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question114\" id=\"question114_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_114\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t\t\t\t<div class=\"qsm-auto-page-row qsm-question-page qsm-apc-6\" data-apid=\"6\" data-qpid=\"6\" style=\"display: none;\">\n\t\t\t\t\t\t\t\t<div class=\"quiz_section qsm-question-wrapper question-type-0  question-section-id-115 slide5 \">\n\t\t\t\t\t\t<div class='mlw_qmn_new_question'>Question 6 <\/div>\n\t\t\t<div class='mlw_qmn_question  qsm_remove_bold' >\n\t\t<p>Very low frequencies are not a problem in a chi-square analysis.<\/p>\n\t<\/div>\n\t\t<fieldset>\n\t\t<legend><\/legend>\n\t<div class='qmn_radio_answers mlwRequiredRadio'>\n\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question115-1 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question115\" id=\"question115_1\" value=\"0\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question115_1\">\n\t\t\t\t\tTrue\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<div class=\"qmn_mc_answer_wrap  mrq_checkbox_class\" id=\"question115-2 \">\n\t\t\t\t\t\t\t\t\t\t\t<input type='radio' class='qmn_quiz_radio qmn-multiple-choice-input ' name=\"question115\" id=\"question115_2\" value=\"1\" \/>\n\t\t\t\t\t<label class=\"qsm-input-label\" for=\"question115_2\">\n\t\t\t\t\tFalse\t\t\t\t\t<\/label>\n\t\t\t\t\t \t\t\t\t<\/div>\n\t\t\t\t\t \t\t\t<label style=\"display: none !important;\" for=\"question115_none\">None<\/label>\n\t\t\t<input type=\"radio\" style=\"display: none;\" name=\"question115\" id=\"question115_none\" checked=\"checked\" value=\"\" \/>\n\t\t\t\t<\/div>\n\t<\/fieldset>\n\t<input type=\"hidden\" name=\"answer_limit_keys_115\" value=\"\" \/>\n\t\t\t\t<\/div><!-- .quiz_section -->\n\t\t\t\t\t\t\t\t<\/div><!-- .qsm-auto-page-row -->\n\t\t\t\t\t\t\t<input type=\"hidden\" name=\"qmn_question_list\" value=\"110Q111Q112Q113Q114Q115Q\" \/>\n\t\t\t\t\t<div class=\"qsm-auto-page-row quiz_section quiz_end empty_quiz_end qsm-d-none\" >\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<div id=\"mlw_error_message_bottom\" class=\"qsm-error-message qmn_error_message_section\"><\/div>\n\t\t\t\t\t<input type=\"hidden\" name=\"qmn_all_questions_count\" id=\"qmn_all_questions_count\" value=\"6\" \/>\n\t\t\t\t\t<input type=\"hidden\" name=\"total_questions\" id=\"total_questions\" value=\"6\" \/>\n\t\t\t\t\t<input type=\"hidden\" name=\"timer\" id=\"timer\" value=\"0\" \/>\n\t\t\t\t\t<input type=\"hidden\" name=\"timer_ms\" id=\"timer_ms\" value=\"0\"\/>\n\t\t\t\t\t<input type=\"hidden\" class=\"qmn_quiz_id\" name=\"qmn_quiz_id\" id=\"qmn_quiz_id\" value=\"16\" \/>\n\t\t\t\t\t<input type='hidden' name='complete_quiz' value='confirmation' \/>\n\t\t\t\t\t\t\t\t\t<\/form>\n\t\t\t\t\t\t<\/div>\n\t\t<div style=\"display: none;\" class=\"qsm-popup qsm-popup-slide\" id=\"modal-4\" aria-hidden=\"false\"><div class=\"qsm-popup__overlay\" tabindex=\"-1\" data-micromodal-close=\"\"><div class=\"qsm-popup__container qmn_quiz_container\" role=\"dialog\" aria-modal=\"true\"><div class=\"qsm-popup__content\"><img decoding=\"async\" src=\"https:\/\/routledgelearning.com\/researchmethods\/wp-content\/plugins\/quiz-master-next\/assets\/clock.png\" alt=\"clock.png\"\/><p class=\"qsm-time-up-text\"> Time&#8217;s up<\/p><\/div><footer class=\"qsm-popup__footer\"><button class=\"qsm-popup-secondary-button qmn_btn\" data-micromodal-close=\"\" aria-label=\"Close this dialog window\" onclick=\"location.reload();\">Cancel<\/button><\/footer><\/div><\/div><\/div><\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 id=\"aioseo-weblinks\" class=\"wp-block-heading\">Weblinks<\/h2>\n\n\n\n<h3 id=\"aioseo-categorical-variables-and-frequency-tables-weblinks\" class=\"wp-block-heading\">Categorical variables and frequency tables<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">If you want to use Vassarstats for a chi-square calculation you\u2019ll find it under the \u2018Clinical Research Calculators\u2019 tab on the left of the main screen in Vassarstats \u2013 see Chapter 17 links.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using Google you\u2019ll find plenty of chi-square calculators that are easy to use. Here are a few I found:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"http:\/\/www.socscistatistics.com\/tests\/chisquare2\/Default2.aspx%0d\"><u>Chi Square Calculator &#8211; Up To 5&#215;5, With Steps (socscistatistics.com)<\/u><\/a>&nbsp;&nbsp; (deals with up to 5&#215;5 tables).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.mathsisfun.com\/data\/chi-square-calculator.html\">https:\/\/www.mathsisfun.com\/data\/chi-square-calculator.html<\/a> &#8211; easier to use and deals with up to 10&#215;10 tables.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"http:\/\/www.quantpsy.org\/chisq\/chisq\">http:\/\/www.quantpsy.org\/chisq\/chisq<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Fischer\u2019s exact test can be done here:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"http:\/\/graphpad.com\/quickcalcs\/contingency1.cfm\">http:\/\/graphpad.com\/quickcalcs\/contingency1.cfm<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">and on the social science site: <a href=\"https:\/\/www.socscistatistics.com\/\">Social Science Statistics (socscistatistics.com)<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:25%\">\n<div class=\"wp-block-group is-vertical is-nowrap is-layout-flex wp-container-core-group-is-layout-b3ff8204 wp-block-group-is-layout-flex wp-container-1 is-position-sticky\">\n<p class=\"wp-block-paragraph\"><strong>On this page<\/strong><\/p>\n\n\n\n<nav class=\"wp-block-table-of-contents\"><ol><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/researchmethods\/student-resources\/chapter-18-tests-for-categorical-variables-and-frequency-tables\/#aioseo-exercises\">Exercises<\/a><\/li><li><a class=\"wp-block-table-of-contents__entry\" href=\"https:\/\/routledgelearning.com\/researchmethods\/student-resources\/chapter-18-tests-for-categorical-variables-and-frequency-tables\/#aioseo-weblinks\">Weblinks<\/a><\/li><\/ol><\/nav>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>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. Exercises Exercise 18.1 A 2 x 2 chi-square analysis 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 [&hellip;]<\/p>\n","protected":false},"featured_media":0,"parent":121,"menu_order":0,"template":"single-chapter","format":"standard","meta":{"_acf_changed":false},"categories":[],"class_list":["post-110","content","type-content","status-publish","format-standard","hentry"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO Pro 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"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. 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