Vocabulary of Statistics Part Two

Variable classifications Qualitative variables: can be placed into distinct categories, according to some characteristic or attribute. for example: gender, religion, etc. Quantitative variables: numerical and can be ordered or ranked. for example: age, height, weight

Quantitative variables Can be further divided into two groups: Discrete – assigned specific values, i.e. 1,2,3 and are said to be countable Continuous – can assume any value between any two specific values. Temperature, for example, can be anything between any two given temps.

Borders Usually, continuous data are rounded to the nearest given unit. A recorded height of 73 inches may be any measure from 72.5 inches to 73.5 inches. Boundaries are written for convenience as 72.5 – 73.5 but are understood to mean all values up to but not including 73.5

Variables can also be classified by how they are categorized, counted or measured. For example, can the data be organized into specifics such as area of residence? Can it be ranked? Or are they measurements? There are four measurement scales…

Nominal Level of Measurement Classifies data into mutually exclusive (non-overlapping) exhausting categories in which no order or ranking can be imposed. A sample of subjects taught by teachers Male/Female Zip-Codes

Ordinal Level of Measurement Classifies data into categories that can be ranked, however, precise definitions between the ranks do not exist. Grades Top 25 football polls Class Ranking

Interval Level of Measurement Ranks data, and precise differences between units of measure do exist, there is no meaningful zero. IQ scores Temperatures (IQ scores don’t measure someone with “zero intelligence” and 0° F does not mean no heat at all)

Ratio Level of Measurement Possesses all the characteristics of interval measurement, and there exists a true zero. In addition, true ratios exist when the same variable is measured on two different members of the population. Height Weight Number of phone calls received

There is not complete agreement among statisticians about the classification of data into one of the four categories. Some researchers classify IQ as ratio, rather than interval. Also, data can be altered so they fit into a different category, for example, if wages are classified into low, average, and high then a ratio becomes an ordinal.

Assignment