{"id":586,"date":"2015-07-20T08:00:56","date_gmt":"2015-07-20T12:00:56","guid":{"rendered":"http:\/\/sites.berry.edu\/vbissonnette\/?page_id=586"},"modified":"2017-08-02T13:51:40","modified_gmt":"2017-08-02T17:51:40","slug":"goodness-of-fit-test","status":"publish","type":"page","link":"https:\/\/sites.berry.edu\/vbissonnette\/index\/stats-homework\/documentation\/goodness-of-fit-test\/","title":{"rendered":"Goodness of Fit Test"},"content":{"rendered":"

Your homework problem:<\/h3>\n

You suspect that a gambler’s die is “loaded,” such that its\u00a0 six outcomes are not<\/u> equally likely. You roll this die 120 times\u00a0 and get the following results:<\/p>\n\n\n\n\n
Side of Die:<\/td>\n1<\/td>\n2<\/td>\n3<\/td>\n4<\/td>\n5<\/td>\n6<\/td>\n<\/tr>\n
Observed Frequency:<\/td>\n16<\/td>\n16<\/td>\n10<\/td>\n20<\/td>\n28<\/td>\n30<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Is this a fair die? In other words, does the obtained pattern of\u00a0 frequencies deviate significantly from what you would expect by\u00a0 chance (i.e., equal probability) (alpha = .05)?<\/p>\n

If you would like some help with the hand-written work on this\u00a0 problem, then click here<\/a>.<\/p>\n

\n

In Stats Homework<\/i> pull down the Analyze<\/b> menu, choose \u00a0Analysis\u00a0of Frequency or Proportion<\/strong>, and then choose Goodness of Fit Test<\/b>.<\/p>\n

Entering Frequency Data<\/h4>\n

\"\"<\/a><\/p>\n

Click ‘Manually enter frequency data,’ enter a name for your variable, and then enter 6 for the number of categories. \u00a0Click both output options, and then click the\u00a0Next Step<\/strong> button.<\/p>\n

Working with Raw Data<\/h4>\n

\"gfit4\"<\/a><\/p>\n

It’s possible that you will work with a data set that contains the raw data for a goodness-of-fit test. \u00a0In this case, you would have a data set with 120 observations — 16 ones, 16 twos, 10 threes, 20 fours, 28 fives, and 30 sixes. \u00a0In this case, you would specify this variable in this dialog:<\/p>\n

\"\"<\/a><\/p>\n

Click ‘Analyze frequencies in a variable,’ and click the variable name. \u00a0Then click all of the output options and the\u00a0Next Step<\/strong> button.<\/p>\n

\"gfit6\"<\/a><\/p>\n

If you are working with raw data, this table will already be filled in for you. \u00a0If you are entering frequencies manually, then it will be blank. \u00a0Enter your category labels and your observed frequencies.<\/p>\n

Next, specify whether or not you expect equal frequencies under your null hypothesis. \u00a0If yes, click the first option and then click\u00a0Compute<\/strong>. \u00a0If no, click the second option and then click the\u00a0Next Step<\/strong> button (the Compute button changes into the Next Step button when you choose this option). \u00a0If you expect unequal frequencies, you will be presented with a third dialog that will ask you to enter these.<\/p>\n

Output<\/h4>\n

\"gfit7\"<\/a><\/p>\n

Descriptive Statistics<\/b>. This table lists the observed and expected\u00a0frequencies for each outcome category, along with the total observed and expected frequencies (these should match). In addition, this table presents each outcome category’s contribution to the Chi Square statistic, and the total Chi Square statistic.<\/p>\n

Inferential Statistics<\/b>. This table presents the Chi Square statistic (14.80), its df<\/i> (5), and the p<\/i> value for the obtained value of Chi Square (.01).<\/p>\n

Effect Size Statistic<\/strong>. \u00a0This output includes the value of Cohen’s W (.35), which is interpreted much like the value of a correlation coefficient.<\/p>\n

Critical Values<\/b>. These are the values from a statistical table of critical values<\/a> for the Chi Square test.\u00a0In our case, we are conducting a test with alpha = .05.\u00a0So, we would compare the value of our obtained Chi Square (14.80) to 11.070.\"\"<\/a>Bar Chart.<\/strong> This chart will illustrate the frequencies that you analyzed with the goodness-of-fit test.\u00a0 It can plot the frequencies or the relative frequencies, and it offers you a number of options for customizing the chart to your needs.<\/p>\n

\n

See the Hand-Written Work<\/a><\/p>\n

Return to Table of Contents<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Your homework problem: You suspect that a gambler’s die is “loaded,” such that its\u00a0 six outcomes are not equally likely. You roll this die 120 times\u00a0 and get the following […]<\/p>\n","protected":false},"author":34,"featured_media":0,"parent":282,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"site-container-style":"default","site-container-layout":"default","site-sidebar-layout":"default","site-transparent-header":"default","disable-article-header":"default","disable-site-header":"default","disable-site-footer":"default","disable-content-area-spacing":"default","footnotes":""},"class_list":["post-586","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/586","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/users\/34"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/comments?post=586"}],"version-history":[{"count":15,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/586\/revisions"}],"predecessor-version":[{"id":1380,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/586\/revisions\/1380"}],"up":[{"embeddable":true,"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/pages\/282"}],"wp:attachment":[{"href":"https:\/\/sites.berry.edu\/vbissonnette\/wp-json\/wp\/v2\/media?parent=586"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}