Level of Measurement

In statistics, data can be classified according to the 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(s), it is important to recognize the data type, which may be qualitative (nominal and ordinal) and quantitative (interval and ratio).

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

Nominal Level of Measurement

At the 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 (discrete frequency tables), pie chart, and bar graph are usually drawn for this level of measurement.

Ordinal Level of Measurement

In the ordinal level of measurement, data classification is 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 a higher score (highest liking level) and zero shows the lowest (lowest liking level). Taking the average of these 1,000 people’s responses 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, size of the dress, and plane ticket are all quantities. The interval level of measurement allows for the degree of difference between items but not the ratio between them. There is a 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 represent the absence of heat, just that it is a 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 points are meaningful and the ratio between two numbers is meaningful. Examples of ratio levels are wages, units of production, weight, changes in stock prices, the distance between home and office, height, etc.

Many of the inferential test statistics depend on the ratio and interval level of measurement. Many authors argue that interval and ratio measures should be named as scales.

Understanding the level of measurement data is crucial for several reasons:

• Choosing Appropriate Statistical Tests: Different statistical tests are designed for different levels of measurement. Using the wrong test on data with an inappropriate level of measurement can lead to misleading results and decisions.
• Data Interpretation: The level of measurement determines how one can interpret the data and the conclusions can made. For example, average (mean) is calculated for interval and ratio data, but not for nominal or ordinal data.
• Data analysis: The level of measurement influences the types of calculations and analyses one can perform on the data.

By correctly identifying the level of measurement of the data, one can ensure that he/she is using appropriate statistical methods and drawing valid conclusions from the analysis.

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