Chapter 1. Tutorial 1.1: Identifying individuals and variable types

1.1 Problem Statement

[1-99] // 30

[140-230] // 207

[0-.1,3] // 0.002

[-99 - -1] // -2

{Male, Female} // Male or Female

{Illness, Injury, Other} // Illness, Injury, or Other

For every patient admitted to the emergency room, a hospital collects certain information, including age, sex, and whether admitted for illness, injury, or other. The hospital compiles all of this information into a monthly data set for analysis.

Describe the details of such a data set. Be careful with typing/spelling for word answers.

1.2 Step 1

questions

Question 1.1

The individuals in this data set are NFy5CnQVb1pN5qT4.

The hospital collects data on patients. Did you make a typo or forget to make this a plural (we wanted a description of individuals, not an individual)?

Individuals are those from whom data are collected in any study. They can be people, things (such as car models – if, for example, we are studying gas mileage), or much larger items – such as an entire farm field, if we were studying crop yields.

Question 1.2

Variables are characteristics of the individuals in a study that may change from one individual to the next. Think of a variable as a general category for which we will be collecting data (answers about the individuals). Which of these would be variables in the data set? Check all that apply.

female 3hMJDRP6OS+3EJIb

age wg8JNehuALfILP6S

male 3hMJDRP6OS+3EJIb

reason admitted wg8JNehuALfILP6S

Jane Smith 3hMJDRP6OS+3EJIb

injury 3hMJDRP6OS+3EJIb

Male and Female are possible values for the variable Sex (which can change from one patient to another). Injury is one possible value for the variable Reason admitted. Jane Smith would be a patient.

Very Good. The only options that are general categories to describe the individual patients are Age and Reason admitted. The other items in the list are variable values (such as male and female, which are possible values for Sex) or an individual identifier (Jane Smith as one patient).

1.3 Step 2

questions

Question 1.3

Values for the variable age would most likely be measured in iysRanajfRnegCOh.

Good! Age is typically recorded in years.

Did you make a typo? When someone asks you how old you are, your response is typically given in years (and not a singular year).

Question 1.4

p6U7DzLNSnaiJu7kugUGWri4xbLAod89HheGHkKy/SNdNo5xadF2JJbW/9t3Kn3rgNnV+DAvQtMMFGY6TznVjj610eCyGp6f18bXSa5yrsw=

It is impossible for a person to have a negative age and it is similarly impossible to be 212 years old (the oldest verified person in modern times was 122 years, 164 days when she died). A person who was 0.052 years old would be a newborn 19 days old – that age would certainly be given in days, and not as a decimal fraction of a year.

The only reasonable value for age is 98. It is not possible for a person to be either -40 or 212 years old. A patient who was 0.052 years old would most likely have their age given as 19 days.

Question 1.5

Age is a bT1It096HHJSeN4WwKgRFLPe+F52BCE8z9ce0SyDQwo= variable.

Age is quantitative, because arithmetic operations make sense.

Age is quantitative, because arithmetic operations make sense (you can legitimately say that a 20-year-old person is half as old as a 40-year-old, for example). You can also legitimately find an “average age” for people in a group. Categorical variables (also called qualitative variables) are those that have values for which arithmetic makes no sense. You can’t reasonably add “brown” and “brown” when talking about hair color, for example.

1.4 Step 3

questions

Question 1.6

Sex is a i07S7cpyGau95GY+32pJtQ70rCI+tZsBd6lcvV68FkE= variable with possible values gWA4HK2eMOB3LY9dVtWFmA== and 7j/I/W60NIHpAec8X4z1iw==.

Very good. Sex [JBM1] is categorical because its possible values are male and female (and arithmetic makes no sense for those values). [JBM1]Have them change Gender to Sex in the question, as Sex is the correct variable (gender is far more complicated, and they mean sex).

Did you make a typo? Sex is categorical because its possible values are male and female (and arithmetic makes no sense for those values).

Question 1.7

Match the items listed on the left with the correct description on the right. You may use some descriptions more than once.

Item	Description
Sex	bpTJsiEyh7mm1ay32J+pdEs9IM2CcKAfua+Jh0tuMc5lA3WhpfNDq/eP0xoOSj0qgSPlnHXj9IsW15UTV2mohYpHJcjmduxYfe1f3PJs/HGWyrT8T/lVvnbnSVncZyJHP2OqB7EvM7vTFdVR9cU6t+t9n68Hg5dkCwB2VDIF0mj6ogQ/uyUhVByJIIqCpiKZYghgRx4mvF0AwlXlNiSdoVc9th9G96Fv/NdN/PIQsyor3srcOzrNTbex9l65fSzkyFrWP7ib+jT7Xi0FitNUcw==
$gen	EgGB+tQj5SaBupkOBKQIzKbt/U5vTBKupRhm7FfsZU9eYPw0u4x0rtXi/UP2o4USIRrTJCeZqdMLbOkgB1ZB3gBE04SKEjbRf0WXuwYREXkhbrH16zWmEMc6l4eTRoe/5nMHQFnhuYn/zUlgFvdGYkXvbkS3c/VtdiItC+FNEQf1NxV/gbPtERkppqWLpoDepL5EG1NtCp+Z0cv/AL768PU+t2ZBtR+LzWYGynayiMhosYVjNqfnT/S1aNcmXmo3stH4cYagFhqHwss4ke1nGA==
$n	+coCspJ//gRwnYCBR9neyo+LyzDRbf6KQdNZq7iWR6geIVJ2R3lPqibz0VLtg8n/2myTLAqGpw//sbYqAS4ye/rtT2C5rSVH0wkaH/c0jblHK6E0uDHNw7Q72BJTXYzyag3ZYrb4kECR6jhnezx4avTlGdILZR1b5Ayvd0dIikPIB02S1yEG1du0O3vOA/d+UHHMm2S6ZCUIsRYCdXJZtG6gxvNl7ExpMDVGfoQQHSQ0ArGVkEBAx103ORheILuWsvzheJtnFBL/VrcHvZhF+Q==
$ill	EgGB+tQj5SaBupkOBKQIzKbt/U5vTBKupRhm7FfsZU9eYPw0u4x0rtXi/UP2o4USIRrTJCeZqdMLbOkgB1ZB3gBE04SKEjbRf0WXuwYREXkhbrH16zWmEMc6l4eTRoe/5nMHQFnhuYn/zUlgFvdGYkXvbkS3c/VtdiItC+FNEQf1NxV/gbPtERkppqWLpoDepL5EG1NtCp+Z0cv/AL768PU+t2ZBtR+LzWYGynayiMhosYVjNqfnT/S1aNcmXmo3stH4cYagFhqHwss4ke1nGA==
Jane Smith	TmPny1V8aOdm/nX8KtE/BpUSvjyw5jOFnfPzIs3gg2QumPN0UZxxpvNQQnr0TeCHTKiYloRmmLTB049W6eSWmJ7k1srCwXfqTsol/pnEaaU808rDv5Wn5LFG2iZnTYIhr+AxMhFt+0jK9mE8QLudz6Nt3Hv+Ie8QqqLLoW25bJZXNgZh1Hb+sTx54ebj203dI6elvnPAZgqfWXULmwvXSv3i8zx3pKAdR65lSuQh3ddQXH1G/3v4tfW0r5dguYg6Fuy8p5SaTJwAhvwpiie75A==
Age	xJ1tLNsXBnadU5OcaztYP1qVKG8xFh0AwtmAk5gphO73Lj6ZMoGRlQloKB2KpwfGuayQFH1MGcaUE6kPMOyrEoXOF13MA9eyN1T7NB4iU/uayYX5uiUgPvm+LYE/1amFtxzVKZXq7i73YgG9h9AcSVgyVasTrj0AlKMsbD61+VS4I3MZpnue3vtnDYN51knunXoEXj+qoDx4lDdpvs2lbo1wiu5OhGeeIYb4GAVOfTHsRg1MrOLTK1whL6J+teMEbE+e1StCFz8U2MzcLVq4WQ==
Reason admitted	bpTJsiEyh7mm1ay32J+pdEs9IM2CcKAfua+Jh0tuMc5lA3WhpfNDq/eP0xoOSj0qgSPlnHXj9IsW15UTV2mohYpHJcjmduxYfe1f3PJs/HGWyrT8T/lVvnbnSVncZyJHP2OqB7EvM7vTFdVR9cU6t+t9n68Hg5dkCwB2VDIF0mj6ogQ/uyUhVByJIIqCpiKZYghgRx4mvF0AwlXlNiSdoVc9th9G96Fv/NdN/PIQsyor3srcOzrNTbex9l65fSzkyFrWP7ib+jT7Xi0FitNUcw==
Patients admitted to the ER	kz8dwC3MCwH8CnXuLTFAYsMZtkV5knIiNi/BFFOPRAJ3PeY82Jh7AtCSKATNMi2X+KF+EoBuO0qA/ymxEPIW7No8nrXdwkR9O1i1BIITzO9ZSQ7vG85Q5YNu5ULEUXpD1NeETnqvRJHm4g/C5PiyqQuJBVjS4yRV9TnrqYSuWYct+W4+komSfoZ7yuBf3JzP4XTs22YnMwoNc7VBYxDjHu7nwbnapALrIaM2f1AtYesnIBwizpONztQCt/Gp1ZIsTxbqDHtNIIqsPn0LN6GBcw==

Table

You’ve got it. Age is a quantitative variable because its possible values (like 70) are numbers for which arithmetic makes sense. Illness is a possible value of the categorical variable Reason admitted (you cannot do arithmetic with values like illness and injury). Male is a possible value of the categorical variable Sex[JBM1] . Jane Smith would be one particular patient (individual) from whom data were collected. [JBM1]Again, have them change Gender to Sex.

Sorry. Remember, the individuals are those (collectively) from whom we collect data (information). Quantitative variables are general category names for the information collected. A variable (such as weight) is quantitative because its values are numbers for which arithmetic makes sense. A variable (like hair color) is qualitative (categorical) because its values are words like “brown” or “blond.”