Basic Statistics and Data Analysis

Lecture notes, MCQS of Statistics

Level of Measurement | Basic Statistics | MCQs Statistics

The Level of Measurements

In statistics, data can be classified according to level of measurement, dictating the calculations that can be done to summarize and present the data (graphically), it also helps to determine, what statistical tests should be performed. For example, suppose there are six colors of candies in a bag and you assign different numbers (codes) to them in such a way that brown candy has a value of 1, yellow 2, green 3, orange 4, blue 5, and red a value of 6. From this bag of candies, adding all the assigned color values and then dividing by the number of candies, yield an average value of 3.68. Does this mean that the average color is green or orange? Of course not. When computing statistic, it is important to recognize the data type, which may be qualitative (nominal and ordinal) and quantitative (Interval and ratio).

The level of measurements has been developed in conjunction with the concepts of numbers and units of measurement. Statisticians classified measurements according to levels. There are four level of measurements, namely, nominal, ordinal, interval and ratio, described below.

Nominal Level of Measurement

In nominal level of measurement, the observation of a qualitative variable can only be classified and counted. There is no particular order to the categories. Mode, frequency table, pie chart and bar graph are usually drawn for this level of measurement.

Ordinal Level of Measurement

In ordinal level of measurement, data classification are presented by sets of labels or names that have relative values (ranking or ordering of values). For example, if you survey 1,000 people and ask them to rate a restaurant on a scale ranging from 0 to 5, where 5 shows higher score (highest liking level) and zero shows the lowest (lowest liking level). Taking the average of these 1,000 people’s response will have meaning. Usually graphs and charts are drawn for ordinal data.

Interval Level of Measurement

Numbers also used to express the quantities, such as temperature, dress size and plane ticket are all quantities. The interval level of measurement allows for the degree of difference between items but no the ratio between them. There is meaningful difference between values, for example 10 degrees Fahrenheit and 15 degrees is 5, and the difference between 50 and 55 degrees is also 5 degrees. It is also important that zero is just a point on the scale, it does not represents the absence of heat, just that it is freezing point.

Ratio Level of Measurement

All of the quantitative data is recorded on the ratio level. It has all the characteristics of the interval level, but in addition, the zero point is meaningful and the ratio between two numbers is meaningful. Examples of ratio level are wages, units of production, weight, changes in stock prices, distance between home and office, height etc.
Many of the inferential test statistics depends on ratio and interval level of measurement. Many author argue that interval and ratio measures should be named as scale.

For Examples about Level of Measurements Visits: Examples of Levels of Measurements

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The Author

Muhammad Imdadullah

Student and Instructor of Statistics and business mathematics.
Currently Ph.D. Scholar (Statistics), Bahauddin Zakariya University Multan.

Like Applied Statistics and Mathematics and Statistical Computing.
Statistical and Mathematical software used are: SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel.

Like to use type-setting LaTeX for composing Articles, thesis etc.

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