This material is from section 1.4. Be sure to read this section in the textbook for more detailed examples and explanations.

The type of data that is being analyzed determines the type of analysis that makes sense. For example, it doesn't make sense to calculate a numerical average telephone number for a group, nor does it make sense to use a bar chart to represent this kind of data. So, before we can study how to represent data, we must learn to identify the type of data we have.

Quantitative vs. categorical data

Quantitative data is numerical data that comes from a measurement or count. Some examples include the cost of something, the heights of a group of people, and the annual revenues for a sample of companies.

Categorical data, also sometimes called qualitative data, can be thought of as descriptive data. Things like eye colors, the sizes of businesses in a sample (small, med, large), or the industries a business operates in each are examples of categorical data.

Numbers, like phone numbers or the number of a course (MTH 212 for instance) can also be categorical, since they are not measured values.

Time-series vs. cross-sectional data

Most data we work with in this course will be cross-sectional. This means that it represents a particular snapshot in time. For example, if I went and collected data for the price of gas at randomly selected gas stations across the state this week, that would represent cross-sectional data.

If instead I collected the price of gas at these stations every month, over a period of several months, the resulting data would be time-series data. The analysis of time-series data is quite complex once you get past simply studying trends on a line graph and beyond the scope of this course. For now, you should just be able to recognize the difference between the two types of data.

Levels of measurement

One final way that we can truly dig into a data set is by determining the level of measurement for the data of interest. For some levels of measurement, only some of our statistical techniques will make sense.

The levels of measurement are as follows. Each variable of interest can be categorized as being at one of these levels of measurement.

Nominal

Think: simply labels or names. There is not a natural ordering to the data.

Example: Jersey Numbers. Player #10 is not better than player #23 and Player #40 is not necessarily twice as good as Player #20.

Ordinal

Think: order makes sense. There is a natural ordering to the data. The data can be ranked or ordered.

Example: Suppose we had measurements of how much people like horror films: very much, somewhat, not that much, and not at all.

Differences between data entries have no mathematical meaning at the ordinal level of measurement.

Example: In college rankings, is the difference between the college ranked #1 and that ranked #3 the same as the difference between #11 and #13?

No. The first two teams might be really close but teams #11 and #13 may be very different.

Interval

Think: order makes sense and the differences have mathematical meaning. However, there is no "true zero".

Example: Temperature on the Celsius or Fahrenheit scale. Zero is simply a number on this scale. Also note difference of 20 to 30 degrees same as 40 to 50.

A "true zero" is a zero that means zero. For example, if you have zero dollars, you truly have no money. Conversely, if it is zero degrees outside, it is just cold. (This is different from the Kelvin scale, where zero is a true zero.)

Ratio

Think: order makes sense and the differences have mathematical meaning. However, there IS a "true zero".

Most data we work with will be ratio data. All the common mathematical calculations make sense at this level.

Example: Temperature on the Kelvin Scale; Weight, Bank Account Values, Counts

When deciding if you have ratio data, don't think about the situation. Instead, think about the data itself. For example, the price of a car is ratio data. You may think this doesn't make sense, since a $0 car is not possible. However, IF the car was $0, it would be free since $0 truly means "no dollars". This can be a way to help you think about the levels of measurement.

This is the last part of the notes for week 1. You are now ready to work on this week's homework assignment.