Statistics Essay Example: Scales of Measurement

In the field of statistics, there are various methods utilized to measure numerical data. For instance, in order to carry out statistical analysis, there is a need to measure a dependent variable in relation to an independent variable. As such, there are various scales of measurements that are used to measure various variables. The four main scales of measure measurement include nominal, ordinal, interval and ratio.

The nominal scale of measurement is the simplest of the four scales of measurement. The nominal level of measurement refers to quality more than quality as nominal data deals with names, labels or categories (Taylor, 2017). Even when numbers are used in the nominal scale of measurement, such numbers are only names and cannot be used to conduct any arithmetic or analysis as they do not denote quantity. Data at the nominal level cannot be ordered in any meaningful way. Nominal scales are used to collect qualitative data such as meal preferences, political affiliations, and religious preferences.

On the other hand, the ordinal scale of measurement unlike the nominal scale allows for the ordering or ranking of data. In the ordinal measurement, items of interest are ranked by ordinal numbers. Such numbers represent the position or rank of an item in a sequence and as such the interval between ranks is not a measure of distance (Volchok, 2015). For this reason, ordinal levels of measurement can only be used to count the frequency of an occurrence, calculate percentiles, quartiles and median but cannot be used to calculate mean, median, standard deviation or variance.

Unlike nominal and ordinal levels of measurement, interval scale of measurement is used to measure quantitative data. Similar to the ordinal scale of measurement, the interval level also has an innate order, however, unlike the ordinal level, the distance between two observations has meaning (Volchok, 2015). For this reason, data at the interval scale can be utilized in calculations of mean, variance, standard deviations. However, as interval scales lack an absolute zero, they cannot be used to calculate ratios, proportions or percentages.

The last level of measurement is the ratio level. Similar to the interval and ordinal level of measurement, the ratio scale of measurement also possesses an inherent order. Also, like the interval level, the distance between two intervals is meaningful and can be measured. However, unlike the interval level, the ratio scale possesses an absolute zero and as such, it can be used to calculate numerical relationships between values using percentages, ratios, and fractions (Taylor, 2017). In statistical analysis, ratio scale of measurement can be utilized to calculate geometric and harmonic mean, median, standard deviation, variance as well as hypothesis tests and regression and correlation analyses.

References

Taylor, C. (2017, April 13). What Are the Levels of Measurement in Statistics? Retrieved from ThoughtCo: https://www.thoughtco.com/levels-of-measurement-in-statistics-3126349

Volchok, E. (2015, April 13). Measurement & Measurement Scales. Retrieved from Queensborough Community College: http://media.acc.qcc.cuny.edu/faculty/volchok/Measurement_Volchok/Measurement_Volchok5.html