# Interval scale

Interval scale |
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See also |

**Interval scale** is a scale of measurement for a variable in which the interval between observation is expressed in terms of a fixed standard of measurement (J.K.Sharma 2012, p.14).

J.K.Sharma says also that, an **interval scale** lets us perform serial arithmetical operations on the information collected from the respondents. While the nominal scale only allows us to qualitatively, exhaustive sets, the ordinal scale lets us to rank-order the preferences, and the interval scale allows us to calculate the mean and the standard deviation of the information on the variables. To put it differently, *the internal scale not only classifies individuals according to some categories and determines the order of these categories; it also measures the magnitude of the differences in the preferences between the individuals*(J.K.Sharma 2012, p.14).

## Characteristics of interval scale

An Interval Scale main qualities:

- An interval scale contains all the features of an ordinal scale, and, what is more, allows the researches to compare the variations between objects. The values in the interval scale show us how far apart the objects are with respect to a specific characteristic. The difference between the scale values 1 and 2 is the same as the difference between the scale 2 and 3.What is more, the difference between values 2 and 4 is twice the difference of that between 2 and 3(1 and 2, etc.)(J.P.Neeklankavil 2015, p.197).
- In interval scales, the subjective votes from respondents are translated into valuable and quantitative information. By designing an interval, a researcher can achieve a higher level of measurement than with ordinal scales. Sometimes the researcher has to impose equal intervals between descriptors. The researcher would assume that the variation between one descriptor and the next one on a scale using "strongly agree", "agree", "neutral", "disagree", "strongly disagree" as one unit. The values assigned to this set of responses run from 1 to 5.Respondents will treat the differences between adjacent response categories as equal(J.P.Neeklankavil 2015, p.198).

## Location of starting point

In an **interval scale**, the place of starting point(zero) is not fixed. The zero and the units of measurement units are arbitrary.
For example(J.P.Neeklankavil 2015, p.198):

- Temperature measurement for a day in a city ranged between 20°Fahrenheit(F) and 40°F. From these values, can we infer from these measurements that the high temperature of 40°F was twice as hot as the low temperature of 20°F? The answer is no. This can be proven by translating the temperature from Fahrenheit to centigrade(C). The low temperature of 20°F is equal to-7°C, and the high temperature of 40°F is equal to 4°C. The high temperature of 4°C is not as twice as hot as the low temperature of -7°C.

## Examples of Interval scale

**Temperature**: Temperature is measured in degrees Celsius or Fahrenheit. The interval between each degree is the same, so temperature is an example of an interval scale.**IQ**: IQ is measured on a scale from 0 to 200. Each increment on the scale is equal, so IQ is an example of an interval scale.**SAT scores**: SAT scores are measured on a scale of 400 to 1600. Each increment on the scale is equal, so SAT scores are an example of an interval scale.**Music notes**: Music notes are measured on a scale from C to C. Each increment on the scale is equal, so music notes are an example of an interval scale.

## Advantages of Interval scale

An interval scale provides several advantages when measuring a variable. These include:

- the ability to measure the magnitude of differences between values;
- the ability to measure the relative position of values with respect to one another;
- the ability to compare and contrast values;
- the ability to add and subtract values;
- the ability to apply statistical tests and calculations to the data;
- the ability to measure the variability of a variable;
- the ability to measure the central tendency of a variable.

## Limitations of Interval scale

Interval scales have several limitations, including:

- Interval scales do not indicate the absolute amount of a quantity, only the relative amount between two points. This makes it difficult to compare quantities measured using different scales.
- Interval scales do not have a true zero point, so it is not possible to determine the absolute value of a variable.
- Interval scales are not suitable for measuring qualitative data, as they measure only the intervals between two points and not the meaning of the data.
- Interval scales are limited in their ability to measure extreme values, as the distance between intervals is constant.
- Interval scales can be affected by bias, as they do not take into account the context of the data.

One possible approach to Interval scale measurement is to use the following methods:

- Nominal Scale - A nominal scale is a type of measurement that assigns numbers or labels to variables in order to differentiate them from one another. The numbers or labels don’t have any quantitative value, but are simply used to organize the data.
- Ordinal Scale - An ordinal scale is a type of measurement that assigns numbers or labels to different categories of a variable in order to show the relative position of each category in relation to the others. The numbers or labels can denote rank, but they don't measure the differences in the magnitude of the variable.
- Ratio Scale - A ratio scale is a type of measurement that assigns numbers or labels to different categories of a variable in order to show the relative position of each category in relation to the others. The numbers or labels denote rank and also measure the differences in the magnitude of the variable.

In summary, Interval scale is a type of measurement that assigns numbers or labels to different categories of a variable in order to show the relative position of each category in relation to the others, with the added distinction that the numbers or labels denote rank and also measure the differences in the magnitude of the variable. Other approaches related to Interval scale measurement include Nominal, Ordinal, and Ratio scales.

## References

- Ayyub B., McCuen R. (2011),
*Probability, Statistics, and Reliability for Engineers and Scientists* - Neeklankavil J. (2015),
*International Business Research*, M.E.Sharpe, p.197-198, New York - Protonotarios E., Baum B., Johnston A., Hunter G., Griggin L. (2014),
*An absolute interval scale of order for point patterns*, Royal Society - Sharma J. (2012),
*Business Statistics*, Dorling Kindersley(India)Pvt. Ldt, p.14 - Sreejsh S., Mohapatra S., Anusree M. (2013),
*Business Research Methods: An Applied Orientation*, Springer, New York

**Author:** Szymon Olejniczak