{"id":481,"date":"2024-10-18T01:57:56","date_gmt":"2024-10-18T01:57:56","guid":{"rendered":"https:\/\/pressbooks.ccconline.org\/mat1260\/?post_type=chapter&p=481"},"modified":"2024-12-11T18:35:32","modified_gmt":"2024-12-11T18:35:32","slug":"3-1-explanatory-and-response-variables","status":"publish","type":"chapter","link":"https:\/\/pressbooks.ccconline.org\/mat1260\/chapter\/3-1-explanatory-and-response-variables\/","title":{"raw":"3.1: Explanatory and Response Variables","rendered":"3.1: Explanatory and Response Variables"},"content":{"raw":"
\r\n\r\nWhile it is fundamentally important to know how to describe the distribution of a single variable, most studies pose research questions that involve exploring the relationship between\u00a0two<\/em>\u00a0variables using the collected data.\r\n\r\n<\/div>\r\n

Here are a few examples of such research questions with the two variables highlighted:<\/p>\r\n\r\n

\r\n
\r\n

Examples<\/span><\/h2>\r\n
    \r\n \t
  1. \r\n

    Is there a relationship between\u00a0gender<\/em>\u00a0and\u00a0test scores<\/em>\u00a0on a particular standardized test?<\/p>\r\n

    Other ways of phrasing the same research question include the following:<\/p>\r\n\r\n

      \r\n \t
    • Is performance on the test related to gender?<\/li>\r\n \t
    • Is there a gender effect on test scores?<\/li>\r\n \t
    • Are there differences in test scores between males and females?<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t
    • How is the\u00a0number of calories<\/em>\u00a0in a hot dog related to (or affected by) the\u00a0type of hot dog<\/em>\u00a0(beef, meat or poultry)? In other words, are there differences in the number of calories among the three types of hot dogs?<\/li>\r\n \t
    • Is there a relationship between the\u00a0type of light<\/em>\u00a0a baby sleeps with (no light, night-light, lamp) and whether or not the child develops\u00a0nearsightedness<\/em>?<\/li>\r\n \t
    • Are the\u00a0smoking habits<\/em>\u00a0of a person (yes, no) related to the person\u2019s\u00a0gender<\/em>?<\/li>\r\n \t
    • How well can we predict a student\u2019s freshman year\u00a0GPA<\/em>\u00a0from his\/her\u00a0SAT score<\/em>?<\/li>\r\n \t
    • What is the relationship between driver\u2019s\u00a0age<\/em>\u00a0and sign legibility\u00a0distance<\/em>\u00a0(the maximum distance at which the driver can read a sign)?<\/li>\r\n \t
    • Is there a relationship between the\u00a0time<\/em>\u00a0a person has practiced driving while having a learner\u2019s permit and\u00a0whether or not this person passed the driving test<\/em>?<\/li>\r\n \t
    • Can you predict a person\u2019s\u00a0favorite type of music<\/em>\u00a0(classical, rock, jazz) on the basis of his\/her\u00a0IQ level<\/em>?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

      In most studies involving two variables, each of the variables has a role. We distinguish between:<\/p>\r\n\r\n

        \r\n \t
      • The\u00a0explanatory<\/em>\u00a0variable (also commonly referred to as the\u00a0independent variable<\/em>)\u2014the variable that claims to explain, predict, or affect the response; and<\/li>\r\n \t
      • The\u00a0response<\/em>\u00a0variable (also commonly referred to as the\u00a0dependent variable<\/em>)\u2014the outcome of the study.<\/li>\r\n<\/ul>\r\n

        Typically, the explanatory (or independent) variable is denoted by\u00a0X<\/em>, while the response (or dependent) variable is denoted by\u00a0Y<\/em>.<\/p>\r\n\r\n

        Explanatory and Response Variables<\/span><\/h2>\r\n
        \r\n
        \r\n

        In this course, we use the terms\u00a0explanatory<\/em>\u00a0and\u00a0response<\/em>\u00a0variables instead of\u00a0independent<\/em>\u00a0and\u00a0dependent<\/em>\u00a0variables.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

        Now, let\u2019s go back to some of the examples and classify the two relevant variables according to their roles in the study.<\/p>\r\n\r\n

        \r\n
        \r\n
        \r\n

        Example 1<\/h3>\r\n<\/header>\r\n
        \r\n\r\nWe want to explore whether the outcome of the study\u2014the score on a test\u2014is affected by the test-taker\u2019s gender.\r\n
        \r\n\r\n\r\n\r\n\r\n\r\n
        Therefore:<\/td>\r\n<\/tr>\r\n
        Gender<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable<\/td>\r\n<\/tr>\r\n
        Test score<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
        \r\n

        Example 2<\/h3>\r\n<\/header>\r\n
        \r\n
        \r\n
        In this study, we explore whether the nearsightedness of a person can be explained by the type of light that person slept with as a baby.<\/div>\r\n<\/div>\r\n
        \r\n
        \r\n\r\n\r\n\r\n\r\n\r\n
        Therefore:<\/td>\r\n<\/tr>\r\n
        Light type<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable<\/td>\r\n<\/tr>\r\n
        Nearsightedness<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
        \r\n
        \r\n
        \r\n

        Example 3<\/h3>\r\n<\/header>\r\n
        \r\n

        Here we are examining whether a student\u2019s SAT score is a good predictor for the student\u2019s GPA freshman year.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
        Therefore:<\/td>\r\n<\/tr>\r\n
        SAT score<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable<\/td>\r\n<\/tr>\r\n
        GPA of freshman year<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
        \r\n
        \r\n
        \r\n

        Example 4<\/h3>\r\n<\/header>\r\n
        \r\n\r\nHere we are examining whether a person\u2019s outcome on the driving test (pass\/fail) can be explained by the length of time this person has practiced driving prior to the test.\r\n
        \r\n\r\n\r\n\r\n\r\n\r\n
        Therefore:<\/td>\r\n<\/tr>\r\n
        Time<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable<\/td>\r\n<\/tr>\r\n
        Driving test outcome<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
        \r\n
        \r\n
        \r\n
        \r\n
        \r\n
        \r\n

        Many Students Wonder...<\/h3>\r\n<\/header>\r\n
        \r\n
        \r\n
        Question:\u00a0<\/em><\/strong>Is the role classification of variables always clear? In other words, is it always clear which of the variables is the explanatory and which is the response?<\/div>\r\n
        <\/div>\r\n
        Answer:\u00a0<\/em><\/strong>No. There are studies in which the role classification is not really clear. This mainly happens in cases when both variables are categorical or both are quantitative. An example is a study that explores the relationship between students' SAT Math and SAT Verbal scores. In cases like this, any classification choice would be fine (as long as it is consistent throughout the analysis).<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n

        If we further classify each of the two relevant variables according to\u00a0type<\/em>\u00a0(categorical or quantitative), we get the following four possibilities for\u00a0role-type classification<\/em>:<\/p>\r\n\r\n

          \r\n \t
        1. Categorical explanatory and quantitative response<\/li>\r\n \t
        2. Categorical explanatory and categorical response<\/li>\r\n \t
        3. Quantitative explanatory and quantitative response<\/li>\r\n \t
        4. Quantitative explanatory and categorical response<\/li>\r\n<\/ol>\r\n

          This role-type classification can be summarized and easily visualized in the following table (note that the explanatory variable is always listed first):<\/p>\r\n\"It<\/span><\/span>\r\n

          This role-type classification serves as the infrastructure for this entire section. In each of the four cases, different statistical tools (displays and numerical measures) should be used to explore the relationship between the two variables. This suggests the following important principle:<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n
          Principle<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
          \r\n
          \r\n
          \r\n

          When confronted with a research question that involves exploring the relationship between two variables, the first and most crucial step is to determine which of the four cases represents the data structure of the problem. In other words, the first step should be classifying the two relevant variables according to their role and type, and only then can we determine what statistical tools should be used to analyze them.<\/p>\r\n\r\n<\/div>\r\n<\/div><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

          Now let\u2019s go back to our examples and determine which of the four cases represents the data structure of each:<\/p>\r\n\r\n

          \r\n
          \r\n
          \r\n

          Example 1<\/h3>\r\n<\/header>\r\n
          \r\n
          \r\n
          \r\n\r\n\r\n\r\n\r\n\r\n
          Gender<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable, and it is\u00a0categorical<\/em>.<\/td>\r\n<\/tr>\r\n
          Test score<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable, and it is\u00a0quantitative<\/em>.<\/td>\r\n<\/tr>\r\n
          Therefore, this is an example of\u00a0case C\u2192Q<\/em>.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
          \r\n
          \r\n
          \r\n

          Example 2<\/h3>\r\n<\/header>\r\n
          \r\n
          \r\n
          \r\n\r\n\r\n\r\n\r\n\r\n
          Light Type<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable, and it is\u00a0categorical<\/em>.<\/td>\r\n<\/tr>\r\n
          Nearsightedness<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable, and it is\u00a0categorical<\/em>.<\/td>\r\n<\/tr>\r\n
          Therefore, this is an example of\u00a0case C\u2192C<\/em>.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
          \r\n
          \r\n
          \r\n

          Example 3<\/h3>\r\n<\/header>\r\n
          \r\n
          \r\n
          \r\n\r\n\r\n\r\n\r\n\r\n
          SAT Score<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable, and it is\u00a0quantitative<\/em>.<\/td>\r\n<\/tr>\r\n
          GPA of Freshman Year<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable, and it is\u00a0quantitative<\/em>.<\/td>\r\n<\/tr>\r\n
          Therefore, this is an example of\u00a0case Q\u2192Q<\/em>.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
          \r\n
          \r\n
          \r\n

          Example 4<\/h3>\r\n<\/header>\r\n
          \r\n
          \r\n
          \r\n\r\n\r\n\r\n\r\n\r\n
          Time<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable, and it is\u00a0quantitative<\/em>.<\/td>\r\n<\/tr>\r\n
          Driving Test Outcome<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable, and it is\u00a0categorical<\/em>.<\/td>\r\n<\/tr>\r\n
          Therefore, this is an example of\u00a0case Q\u2192C<\/em>.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
          \r\n
          \r\n
          \r\n

          Did I get this?<\/h3>\r\n<\/header>\r\n
          \r\n

          In the following three problem, you are presented with a brief description of a study involving two variables. Based on the role-type classification of the two variables, you are asked to determine which of the four cases represents the data structure of the problem.<\/p>\r\n

          For your convenience, here again is the role-type classification table:<\/p>\r\n\"<\/span><\/span>\r\n\r\n[h5p id=\"41\"]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"

          \n

          While it is fundamentally important to know how to describe the distribution of a single variable, most studies pose research questions that involve exploring the relationship between\u00a0two<\/em>\u00a0variables using the collected data.<\/p>\n<\/div>\n

          Here are a few examples of such research questions with the two variables highlighted:<\/p>\n

          \n
          \n

          Examples<\/span><\/h2>\n
            \n
          1. \n

            Is there a relationship between\u00a0gender<\/em>\u00a0and\u00a0test scores<\/em>\u00a0on a particular standardized test?<\/p>\n

            Other ways of phrasing the same research question include the following:<\/p>\n

              \n
            • Is performance on the test related to gender?<\/li>\n
            • Is there a gender effect on test scores?<\/li>\n
            • Are there differences in test scores between males and females?<\/li>\n<\/ul>\n<\/li>\n
            • How is the\u00a0number of calories<\/em>\u00a0in a hot dog related to (or affected by) the\u00a0type of hot dog<\/em>\u00a0(beef, meat or poultry)? In other words, are there differences in the number of calories among the three types of hot dogs?<\/li>\n
            • Is there a relationship between the\u00a0type of light<\/em>\u00a0a baby sleeps with (no light, night-light, lamp) and whether or not the child develops\u00a0nearsightedness<\/em>?<\/li>\n
            • Are the\u00a0smoking habits<\/em>\u00a0of a person (yes, no) related to the person\u2019s\u00a0gender<\/em>?<\/li>\n
            • How well can we predict a student\u2019s freshman year\u00a0GPA<\/em>\u00a0from his\/her\u00a0SAT score<\/em>?<\/li>\n
            • What is the relationship between driver\u2019s\u00a0age<\/em>\u00a0and sign legibility\u00a0distance<\/em>\u00a0(the maximum distance at which the driver can read a sign)?<\/li>\n
            • Is there a relationship between the\u00a0time<\/em>\u00a0a person has practiced driving while having a learner\u2019s permit and\u00a0whether or not this person passed the driving test<\/em>?<\/li>\n
            • Can you predict a person\u2019s\u00a0favorite type of music<\/em>\u00a0(classical, rock, jazz) on the basis of his\/her\u00a0IQ level<\/em>?<\/li>\n<\/ol>\n<\/div>\n<\/div>\n

              In most studies involving two variables, each of the variables has a role. We distinguish between:<\/p>\n

                \n
              • The\u00a0explanatory<\/em>\u00a0variable (also commonly referred to as the\u00a0independent variable<\/em>)\u2014the variable that claims to explain, predict, or affect the response; and<\/li>\n
              • The\u00a0response<\/em>\u00a0variable (also commonly referred to as the\u00a0dependent variable<\/em>)\u2014the outcome of the study.<\/li>\n<\/ul>\n

                Typically, the explanatory (or independent) variable is denoted by\u00a0X<\/em>, while the response (or dependent) variable is denoted by\u00a0Y<\/em>.<\/p>\n

                Explanatory and Response Variables<\/span><\/h2>\n
                \n
                \n

                In this course, we use the terms\u00a0explanatory<\/em>\u00a0and\u00a0response<\/em>\u00a0variables instead of\u00a0independent<\/em>\u00a0and\u00a0dependent<\/em>\u00a0variables.<\/p>\n<\/div>\n<\/div>\n

                Now, let\u2019s go back to some of the examples and classify the two relevant variables according to their roles in the study.<\/p>\n

                \n
                \n
                \n
                \n

                Example 1<\/h3>\n<\/header>\n
                \n

                We want to explore whether the outcome of the study\u2014the score on a test\u2014is affected by the test-taker\u2019s gender.<\/p>\n

                \n\n\n\n\n\n
                Therefore:<\/td>\n<\/tr>\n
                Gender<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable<\/td>\n<\/tr>\n
                Test score<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n
                \n
                \n

                Example 2<\/h3>\n<\/header>\n
                \n
                \n
                In this study, we explore whether the nearsightedness of a person can be explained by the type of light that person slept with as a baby.<\/div>\n<\/div>\n
                \n
                \n\n\n\n\n\n
                Therefore:<\/td>\n<\/tr>\n
                Light type<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable<\/td>\n<\/tr>\n
                Nearsightedness<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
                \n
                \n
                \n
                \n

                Example 3<\/h3>\n<\/header>\n
                \n

                Here we are examining whether a student\u2019s SAT score is a good predictor for the student\u2019s GPA freshman year.<\/p>\n\n\n\n\n\n
                Therefore:<\/td>\n<\/tr>\n
                SAT score<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable<\/td>\n<\/tr>\n
                GPA of freshman year<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
                \n
                \n
                \n
                \n

                Example 4<\/h3>\n<\/header>\n
                \n

                Here we are examining whether a person\u2019s outcome on the driving test (pass\/fail) can be explained by the length of time this person has practiced driving prior to the test.<\/p>\n

                \n\n\n\n\n\n
                Therefore:<\/td>\n<\/tr>\n
                Time<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable<\/td>\n<\/tr>\n
                Driving test outcome<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n
                \n
                \n
                \n
                \n
                \n
                \n
                \n

                Many Students Wonder…<\/h3>\n<\/header>\n
                \n
                \n
                Question:\u00a0<\/em><\/strong>Is the role classification of variables always clear? In other words, is it always clear which of the variables is the explanatory and which is the response?<\/div>\n
                <\/div>\n
                Answer:\u00a0<\/em><\/strong>No. There are studies in which the role classification is not really clear. This mainly happens in cases when both variables are categorical or both are quantitative. An example is a study that explores the relationship between students’ SAT Math and SAT Verbal scores. In cases like this, any classification choice would be fine (as long as it is consistent throughout the analysis).<\/div>\n<\/div>\n<\/div>\n<\/div>\n

                If we further classify each of the two relevant variables according to\u00a0type<\/em>\u00a0(categorical or quantitative), we get the following four possibilities for\u00a0role-type classification<\/em>:<\/p>\n

                  \n
                1. Categorical explanatory and quantitative response<\/li>\n
                2. Categorical explanatory and categorical response<\/li>\n
                3. Quantitative explanatory and quantitative response<\/li>\n
                4. Quantitative explanatory and categorical response<\/li>\n<\/ol>\n

                  This role-type classification can be summarized and easily visualized in the following table (note that the explanatory variable is always listed first):<\/p>\n

                  \"It<\/span><\/span><\/p>\n

                  This role-type classification serves as the infrastructure for this entire section. In each of the four cases, different statistical tools (displays and numerical measures) should be used to explore the relationship between the two variables. This suggests the following important principle:<\/p>\n\n\n\n\n\n
                  Principle<\/th>\n<\/tr>\n<\/thead>\n
                  \n
                  \n
                  \n

                  When confronted with a research question that involves exploring the relationship between two variables, the first and most crucial step is to determine which of the four cases represents the data structure of the problem. In other words, the first step should be classifying the two relevant variables according to their role and type, and only then can we determine what statistical tools should be used to analyze them.<\/p>\n<\/div>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                  Now let\u2019s go back to our examples and determine which of the four cases represents the data structure of each:<\/p>\n

                  \n
                  \n
                  \n
                  \n

                  Example 1<\/h3>\n<\/header>\n
                  \n
                  \n
                  \n\n\n\n\n\n
                  Gender<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable, and it is\u00a0categorical<\/em>.<\/td>\n<\/tr>\n
                  Test score<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable, and it is\u00a0quantitative<\/em>.<\/td>\n<\/tr>\n
                  Therefore, this is an example of\u00a0case C\u2192Q<\/em>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
                  \n
                  \n
                  \n
                  \n

                  Example 2<\/h3>\n<\/header>\n
                  \n
                  \n
                  \n\n\n\n\n\n
                  Light Type<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable, and it is\u00a0categorical<\/em>.<\/td>\n<\/tr>\n
                  Nearsightedness<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable, and it is\u00a0categorical<\/em>.<\/td>\n<\/tr>\n
                  Therefore, this is an example of\u00a0case C\u2192C<\/em>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
                  \n
                  \n
                  \n
                  \n

                  Example 3<\/h3>\n<\/header>\n
                  \n
                  \n
                  \n\n\n\n\n\n
                  SAT Score<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable, and it is\u00a0quantitative<\/em>.<\/td>\n<\/tr>\n
                  GPA of Freshman Year<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable, and it is\u00a0quantitative<\/em>.<\/td>\n<\/tr>\n
                  Therefore, this is an example of\u00a0case Q\u2192Q<\/em>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
                  \n
                  \n
                  \n
                  \n

                  Example 4<\/h3>\n<\/header>\n
                  \n
                  \n
                  \n\n\n\n\n\n
                  Time<\/em>\u00a0is the\u00a0explanatory<\/em>\u00a0variable, and it is\u00a0quantitative<\/em>.<\/td>\n<\/tr>\n
                  Driving Test Outcome<\/em>\u00a0is the\u00a0response<\/em>\u00a0variable, and it is\u00a0categorical<\/em>.<\/td>\n<\/tr>\n
                  Therefore, this is an example of\u00a0case Q\u2192C<\/em>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
                  \n
                  \n
                  \n
                  \n

                  Did I get this?<\/h3>\n<\/header>\n
                  \n

                  In the following three problem, you are presented with a brief description of a study involving two variables. Based on the role-type classification of the two variables, you are asked to determine which of the four cases represents the data structure of the problem.<\/p>\n

                  For your convenience, here again is the role-type classification table:<\/p>\n

                  \"Categorical<\/span><\/span><\/p>\n

                  \n