Scales of measurement in statistics pdf

Job classification such as; teacher, counselor, administrator, principal, minister, carpenter etc. Numbers of the license plates of automobiles also constitute a nominal scale, because automobiles are classified into various sub-classes, each showing a district or region and a serial number. It is known as a ranking level. This level is one step above of the nominal level. It has the characteristics of equivalence and order. In this scale a set of objects is assigned a value on the basis of some rule, i.

It means that categories on the ordinal scale are arranged according to the amount of trait or characteristic that each category represents. In this scale, there is a quantitative difference from category to category, and these categories are arranged according to some order. The example of such scale is that we arrange the students of a class according to their ranking in class result like 1st, 2nd, 3rd and so on.

Similarly we categorize the students as superior, above average, average, below average and inferior or may arrange them as 1, 2, 3, 4 and 5 respectively.

In ordinal scale the objects or events are ranked or ordered from lowest to highest or from highest to lowest according to the characteristic we wish to measure. Thus ordinal scale corresponds to quantitative classification of a set of objects with reference to some attribute.

In the educational institutions or hierarchy we find professional as well as administrative classifications on ordinal level. As for example, we can mention the classification as professor, the associate professor and the assistant professor in academic side.

The administrative classification can be cited as principal, administrative officer, section officer etc. Social classes in a country—lower, lower-middle, middle, upper middle and upper—constitute an ordinal scale, because in such a classification each class is higher than the classes below it and lower than the classes above it in prestige or social status.

All members of the upper class are higher to all members of the U-M; of upper-middle in turn are higher to Lower-Middle, and so on. The numbers used in identifying our observations are called Ranks. In ordinal scaling a transformation which does not change the order of the classes is completely admissible, because it does not involve any loss of information, e. The third level of measurement is known as interval level.

It has the characteristics of both nominal and ordinal level of scales. The additional characteristic it possesses is quality of interval. It means the distance or difference between any adjacent class on the scale can be known numerically.

The intervals on the scale are the same; it is a constant unit of measurement. This consistency of intervals is lacking in two previous level of scale. In other words, the intervals of the scale i. For example, the difference between 6 cm. Thus interval scale is also known as equal-interval scale. Interval scales have an arbitrary zero. That is, there is no absolute zero-point or unique origin.

With interval scales the measurement units are equal. Interval scales show that a person or item is so many units larger or smaller, heavier or lighter, brighter or duller etc. No absolute zero.

In physical sciences the concept of absolute zero is well conceived. For example, zero inch means absence of length, zero pound means absence of weight. But in psychology, education and other social sciences it is difficult to visualise a true zero in any scale used. For example a student who scores 0 zero in mathematics does not imply that he knows nothing in mathematics.

In this case, concept of zero is meaningless. In a similar way an I. Due to the absence of a true zero-point we cannot say that a child with an I. However, to describe the data, means are often of limited value unless the data follow a classic normal distribution and a frequency distribution of responses will likely be more helpful. Furthermore, because the numbers derived from Likert scales represent ordinal responses, presentation of a mean to the th decimal place is usually not helpful or enlightening to readers.

In summary, we recommend that authors determine how they will describe and analyze their data as a first step in planning educational or research projects. Then they should discuss, in the Methods section or in a cover letter if the explanation is too lengthy, why they have chosen to portray and analyze their data in a particular way. Reviewers, readers, and especially editors will greatly appreciate this additional effort.

Gail M. National Center for Biotechnology Information , U. Search database Search term. J Grad Med Educ. Artino, Jr , PhD. Author information Copyright and License information Disclaimer.

Corresponding author: Gail M. This article has been cited by other articles in PMC. Open in a separate window. Continuous Measure Example Please tell us your current pain level by sliding the pointer to the appropriate point along the continuous pain scale above.

The Controversy In the medical education literature, there has been a long-standing controversy regarding whether ordinal data, converted to numbers, can be treated as interval data. The Bottom Line Now that many experts have weighed in on this debate, the conclusions are fairly clear: parametric tests can be used to analyze Likert scale responses. Footnotes Gail M. References 1. Weighted Kappa; Nominal scale agreement with provision for scaled disagreement or partial credit.

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