Monday, August 27, 2012

Getting Ready for AP STATISTICS: LEVELS OF MEASUREMENT

Data can be separated into categories according to what is being measured and what information can be determined from the data.  Different levels of measurement are appropriate for different arithmetic and statistical operations. For example, it makes no sense to find the mean, median, or mode of a list of Social Security numbers.

NOMINAL

The nominal level of measurement is the lowest of the four ways to characterize data because it holds the least potential for instructive analysis. Nominal means "in name only" and nominal data deal with names, categories, or labels -- qualitative groups (see previous post: Getting Ready for AP STATISTICS: VOCABULARY BASICS).

Because data at the nominal level are qualitative, they can't be ordered in a meaningful way, and it makes no sense to calculate things such as the mean or standard deviation.

Examples:
Colors
Yes or no responses to a survey
Favorite class subject
Gender
Makes of cars

Some number groups can be nominal:  the numbers assigned to marathon runners, for example, are used to identify or name the entrants.

ORDINAL

The next level is called the ordinal level of measurement. Data at this level CAN be put in some order, but the differences between elements are not meaningful.

Letter grades in your classes are an example of ordinal measurement.  In some schools, a minimum of 94% is required for an A, but another school may count a 90% as an A.  It is not surprising that colleges have difficulty comparing applicants through letter grades alone, or even through class rank.  Both measures tell nothing about the difference between separate elements within a group.

As with the nominal level, data at the ordinal level should not be used in calculations.

Examples:
Movie ratings (G,P-G,PG13,R,NC17)
The Tonight Show’s “TOP 10” of anything
IQ scores

INTERVAL

The third level of measurement is the Interval level.  It deals with data that CAN BE ORDERED, and in which differences between the data DO make sense.  It can be used meaningfully in calculations, but Interval level data DOES NOT HAVE A STARTING POINT.

Temperature for example can be put in increasing or decreasing order and the difference between 20 degrees and 80 degrees makes sense.  Zero degrees, however, does NOT mean a total absence of temperature.  Without a starting point, ratios of element values are meaningless.  An 80 degree day is not four times as hot as a 20 degree day.

Examples:
Temperature
Sea level
A college student's checking account balance (hopefully that's only a joke)

RATIO

The fourth and highest level of measurement is the ratio level where data possess all of the features of the other three levels and also a ZERO VALUE, so it makes sense to compare the ratios of measurements. Phrases such as "four times" and "twice" are meaningful at the ratio level.

Examples:
Monthly precipitation
Any system of measurement (length, weight, distance)

Since organizing data is a constant task in statistics, let's encapsulate characteristics of the four levels of measurement.

Notice that each level of measurement meets the criteria for the previous levels plus one more.

As you get further along in the curriculum, you will be introduced to essential statistical operations.  The level of measurement is an important factor in determining which
computations are viable.  Save the chart below for future reference and check your textbook glossary to reference each of the computations in the left column.

WHAT'S NEXT IN STATISTICS?
Now that we have some background and terminology, we can start developing a statistical survey.  Get a jump start on the classroom by thinking of a study you might want to conduct as a practical application.  Are you in another class (like American Politics during this election year) which would give extra credit for completing the survey?  What is your population?  What sample would be appropriate?  What would you measure?  How would you measure it?  Based on the chart above, what statistical computations would be possible?  Later in the curriculum, we'll investigate the information that can be garnered from the calculations.  For now....have fun!!

1 comment:

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