MA121: Introduction to Statistics

Example #1: How much information should I record?

Say you are volunteering at a track meet at your college, and your job is to record each runner's time as they pass the finish line for each race. Their times are shown in large red numbers on a digital clock with eight digits to the right of the decimal point, and you are told to record the entire number in your tablet. Thinking eight decimal places is a bit excessive, you only record runners' times to one decimal place. The track meet begins, and runner number one finishes with a time of 22.93219780 seconds. You dutifully record her time in your tablet, but only to one decimal place, that is 22.9. Race number two finishes and you record 32.7 for the winning runner. The fastest time in Race number three is 25.6. Race number four winning time is 22.9, Race number five is…. But wait! You suddenly realize your mistake; you now have a tie between runner one and runner four for the title of Fastest Overall Runner! You should have recorded more information from the digital clock - that information is now lost, and you cannot go back in time and record running times to more decimal places.

The point is that you should think very carefully about the scales and specificity of information needed in your research before you begin collecting data. If you believe you might need additional information later but are not sure, measure it; you can always decide to not use some of the data, or "collapse" your data down to lower scales if you wish, but you cannot expand your data set to include more information after the fact. In this example, you probably would not need to record eight digits to the right of the decimal point. But recording only one decimal digit is clearly too few.

Example #2

Pretend for a moment that you are teaching five children in middle school (yikes!), and you are trying to convince them that they must study more in order to earn better grades. To prove your point, you decide to collect actual data from their recent math exams, and, toward this end, you develop a questionnaire to measure their study time and subsequent grades. You might develop a questionnaire which looks like the following:

1. Please write your name: ____________________________
2. Please indicate how much you studied for this math exam:
   a lot……………moderate……….…….little
3. Please circle the grade you received on the math exam:
   A  B  C  D   F

Given the above questionnaire, your obtained data might look like the following:

Eyeballing the data, it seems as if the children who studied more received better grades, but it's difficult to tell. "Little," "lots," and "B," are imprecise, qualitative terms. You could get more precise information by asking specifically how many hours they studied and their exact score on the exam. The data then might look as follows:

Of course, this assumes the students would know how many hours they studied. Rather than trust the students' memories, you might ask them to keep a log of their study time as they study.