What is the scale of measurement for the color of a karate belt?

Date: 2015-10-07; view: 722.

For each tourist entering the United States, the U.S. Immigration and Naturalization Service computer is fed the tourist's nationality and length of intended stay. Characterize each variable as quantitative or qualitative.

A quantitative variable can be described by a number for which arithmetic operations such as averaging make sense.

A qualitative (or categorical) variable simply records a quality. If a number is used for distinguishing members of different categories of a qualitative variable, the number assignment is arbitrary.

The tourist's nationality is a qualitative variable since it conveys a quality (British, French, Italian). The length of intended stay is a quantitative variable: it conveys a quantity – the length of intended stay is counted in days, months or years.

The field of statistics deals with measurements – some quantitative and others qualitative. The measurements are the actual numerical values of a variable.

There are four generally used scales of measurement: nominal scale, ordinal scale, interval scale, and ratio scale.

The nominal scale is the scale of measurement for the color of a karate belt.

Nominal Scale. In the nominal scale of measurement, numbers are used simply as labels for groups or classes. If our data set consists of blue, green, and red items, we may designate blue as 1, green as 2, and red as 3. In this case, the numbers 1, 2, and 3 stand only for the category to which a data point belongs. “Nominal” stands for “name” of category. The nominal scale of measurement is used for qualitative rather than quantitative data.

Ordinal scale. In the ordinal scale of measurement, data elements may be ordered according to their relative size or quality. Four products ranked by a consumer may be ranked as 1, 2, 3, and 4, where the 4 is the best and 1 is the worst. In this scale of measurement we do not know how much better one product is than others, only that it is better.

Interval scale. . In the interval scale of measurement, we can assign a meaning to distances between any two observations. The data are on the interval of numbers, and distances between elements can be measured in units.

Ratio scale. The ratio scale is the strongest scale of measurement. Here not only do distances between paired observations have a meeting, but also there is a meaning to rations of distances. Salaries are measured on a ratio scale: A salary of $50,000 is twice as large as a salary of $25,000.