{"id":2916,"date":"2024-07-26T22:16:05","date_gmt":"2024-07-27T02:16:05","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&p=2916"},"modified":"2024-07-27T02:38:12","modified_gmt":"2024-07-27T06:38:12","slug":"chi-squared-test-example","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/chi-squared-test-example\/","title":{"raw":"Chi-Squared Test Example","rendered":"Chi-Squared Test Example"},"content":{"raw":"
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Learning Objectives<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nSolve a Chi-Squared Test for Independence problem both with manual and Excel calculations.\r\n\r\n<\/div>\r\n<\/div>\r\nLet us now 'dive in' to an example where we use a Chi-Squared Test for Independence. Before we do, let us recap the steps we need to perform the Chi-Squared Test for Independence:\r\n
    \r\n \t
  1. State H0<\/sub> and HA<\/sub><\/li>\r\n \t
  2. Calculate the expected frequencies (values)<\/li>\r\n \t
  3. Calculate the \u03c72<\/sup> test statistic<\/li>\r\n \t
  4. Compute the p-value<\/li>\r\n \t
  5. Make a decision<\/li>\r\n \t
  6. Draw a conclusion<\/li>\r\n<\/ol>\r\n

    Example 67.1<\/h2>\r\nProblem Setup:<\/strong> Analysts who work on the popular game 'Fortnight<\/a>' are trying to determine who they should target their in-app purchases to. In particular, they want to promote a premium add-on pack to users. They are wondering if the level of the player in the app might influence their likelihood to purchase the add-on. See the table below for the purchase results per level for randomly selected players:<\/span><\/span>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Level<\/th>\r\nPurchased Add-On<\/th>\r\nDid Not Purchase<\/th>\r\nTotal<\/th>\r\n<\/tr>\r\n
    Bronze<\/th>\r\n60<\/td>\r\n40<\/td>\r\n100<\/strong><\/td>\r\n<\/tr>\r\n
    Silver<\/th>\r\n67<\/td>\r\n63<\/td>\r\n130<\/strong><\/td>\r\n<\/tr>\r\n
    Gold or Higher<\/th>\r\n49<\/td>\r\n41<\/td>\r\n90<\/strong><\/td>\r\n<\/tr>\r\n
    Total<\/th>\r\n176<\/strong><\/th>\r\n144<\/strong><\/th>\r\n320<\/strong><\/th>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nQuestion<\/strong><\/span>: Does the player's level affect whether they will purchase the premium add-on pack? Test at the 5% level of significance.\r\n\r\nYou Try<\/strong><\/span>: Try setting up and solving this problem yourself. Click the sections below to reveal the solutions when you are ready or need help.\r\n

    1. The Hypotheses<\/h1>\r\nThe hypotheses for a contingency table question are always the same format. The Null hypothesis reflects the idea that there is no difference between the groups with respect to preference (i.e., independence). The alternative reflects the idea that there is a difference between the groups with respect to preference (i.e., dependence). There are\u00a0two common methods to state the hypotheses:\r\n

    Method 1<\/h2>\r\nLet us examine the percent of players from each level who do purchase the add-on and do the analysis on them:\r\n