Statistics

# Variable and It’s Measurement  Written by
RIFAT AFROZE

Variables:
By variable we mean the characteristics which can be measured numerically and the value of which varies from individuals to individuals, item to item. It can also call as Quantitative Variable. Example: For human beings height, weight, number of siblings, sex, and marital status are all example of variables.
The characteristic which can be measured but not expressed numerically and which indicates a difference in the quality of the phenomenon is known as an attribute. It can also define as Qualitative Variable. Example: Efficiency (Efficient/inefficient), gender, eye color are attributes.

Discrete Variable:
A quantitative variable whose possible values are a finite (or countable infinity) set of numbers is called a discrete variable. Example: Number of children in each family of Dhaka city is a discrete variable.

Continuous Variable:
A quantitative variable whose possible values are some interval of numbers is called a continuous variable. Example: Age of human beings, speed of automobiles etc.

Data:
Information attained by observing values of a variable is data. Data is a plural word which comprehends the idea of collection of pieces of information. The singular word is datum.

Data Set:
Each individual piece of data is called an observation and the collection of all observation of a particular investigation is called a data set.

Measurement scales: It is very important because it relates to the types of statistics you can use to analyze your data. There are four types of measurement level used in statistical analysis and researchers can use a combination of all or use specific level for gauge any characteristics such as 1. Nominal. 2. Ordinal, 3. Interval, 4. Ratio

Nominal:
The lowest measurement level from a statistical point of view is a nominal scale. In this scale, as the name implies, is simply some placing of data into categories, without any order or structure. In research activities a YES/NO scale is a very common example of nominal scale. It has no order and there is no distance between YES and NO. The nominal scales are belongs in non-parametric group. In order to analysis nominal data we can estimate mode and cross-tabulation – with chi-square statistic.

Ordinal:
An ordinal scale is next up the list in terms of scale of measurement. The simplest ordinal scale is ranking. When a researcher asks you to rank top 5 Universities of the country, he is asking you to create an ordinal scale of preference. The difference between ordinal and nominal scale is ordinal scale used to arrange data into order rather than nominal scale. Ordinal data would use non-parametric statistics. These analysis would be include:

1. Median and mode, 2. Rank order correlation, 3. Non-parametric analysis of variance

Interval:
By Interval scale we mean a standard survey rating scale. When you are asked to rate your satisfaction about a training on a 7 point scale, from Dissatisfied to Satisfied, you are using an interval scale. It is an interval scale because it is assumed to have central points between each of the scale elements. This means that, it is possible to interpret differences in the distance along the scale. In contrast, this to an ordinal scale where we can only talk about differences in order, not differences in the degree of order.

Interval scales are also defined by metrics such as logarithms. In these cases, the distances are not equal but they are strictly definable based on the metric used. In order to analysis Interval scale data would use parametric statistical techniques:

1. Mean and standard deviation, 2. Correlation – r, 3. Regression, 4. Analysis of variance, 5. Factor analysis, 6. Advance multivariate analysis

It should be mention; you can use non-parametric techniques with interval and ratio data. But non-parametric techniques are less powerful rather the parametric ones.

Ratio: A ratio scale is the top level of measurement scale and is not often obtainable in social research. A ratio scale starts from a true zero point. In other words, we can say that when zero means absence of the characteristics then the appropriate scales to use is the ratio scales. The simplest example of a ratio scale is the measurement of weight. The analysis is same as for Interval data.

Comparative discussion on different scales of measurement: The following table can be constructed from the definition of the different scales of measurements.

 Level Arithmetic Features Example Nominal Counting Categories Religion Ordinal CountingRanking CategoriesRanks Economic status Interval CountingRankingAdditionSubtraction CategoriesRanksHas equal units IQ score Ratio CountingRankingAdditionSubtractionMultiplicationDivision CategoriesRanksHas equal unitsHas absolute zero Family size

Author: Staff Researcher, Research and Evaluation Division, BRAC, Dhaka, Bangladesh. Email: [email protected] 