MA121: Introduction to Statistics

Learning Objectives

1. Describe how a variable such as height should be recorded
2. Choose a good response scale for a questionnaire

Most statistical analyses require that your data be in numerical rather than verbal form (you can't punch letters into your calculator). Therefore, data collected in verbal form must be coded so that it is represented by numbers. To illustrate, consider the data in Table 1.

Can you conduct statistical analyses on the above data or must you re-code it in some way? For example, how would you go about computing the average height of the 5 students. You cannot enter students' heights in their current form into a statistical program - the computer would probably give you an error message because it does not understand notation such as 5'4". One solution is to change all the numbers to inches. So, 5'4" becomes $(5 \times 12)+4=64$, and 6'1" becomes ($6 \times 12)+1=73$, and so forth. In this way, you are converting height in feet and inches to simply height in inches. From there, it is very easy to ask a statistical program to calculate the mean height in inches for the 5 students.

You may ask, "Why not simply ask subjects to write their height in inches in the first place?" Well, the number one rule of data collection is to ask for information in such a way as it will be most accurately reported. Most people know their height in feet and inches and cannot quickly and accurately convert it into inches "on the fly". So, in order to preserve data accuracy, it is best for researchers to make the necessary conversions.

Let's take another example. Suppose you wanted to calculate the mean amount of computer experience for the five students shown in Table 1. One way would be to convert the verbal descriptions to numbers as shown in Table 2. Thus, "Very Little" would be converted to "1" and "Little" would be converted to "2".