CHAPTER TWO

MEASUREMEN

T AND SCALES

2.1Introducti

on

Statis

cs is a study

discipline o

f Mat

hematics

which deals with data

collection, data findings in ed

ucational research. It is all a

bout the manipulation and interp

retation of numbers, which repr

esent information about the ar

ea under investigation. This

chapter is focused towards

discussing the process of m

easurement which affects the choice of statistical tools as well as interpretation and the conclusions, one may draw from the basic steps in educational research. The chapter will also discuss measurement, scale of measurement and steps involved in measurement process.

2.2Objectives

At the end of this chapter, you should be able to:

define measurement.
explain the types of measurement.
enumerate the steps involves in measurement process.
describe the use of rating scale in measuring behavior.

2.3Concept of Measurement

Measurement can be referred to as an act or systematic process of determining the size or amount of object or event by applying a defined rule or standard. Measurement always has two parts, Magnitude and Unit, Magnitude is the number while unit is the standard.

For example, if a length of table is 10cm, then 10 is the magnitude and centimeter (cm) is the Unit. Measurement is of two types; Physical measurement which requires the use of physical instrument such as rulers, tapes, stop clock, calendar, clinical thermometer, etc.

Psychological measurement sometimes referred to educational measurement which requires the use of educational tools such as classroom test, examination, observation etc.

2.4Process of Measurement

As Researchers in education, you are required to carry out some measurement processes.

These are steps involved in measurement processes: -

Identify a fact (phenomenon) of your study (e.g., teaching, learning, students, teachers, parents, society, school administers etc.).
Identify the aspect(s) or variable(s) of the fact (phenomenon) you intended to investigate (e.g., socioeconomic status of the parents, learning styles, teaching styles etc.).
Direct or indirect observation of the variables.
Appropriately select measurement scales.
Data collected are analyzed.
Interpret the data.

When number is assigned to represent the quantity of the variables observed direct or indirect with defined rules is known as scales of measurement or measurement scales.

2.5Measurement Scales

Scales of measurement is a defined sets of rules for assigning numerical scores to any directly or indirectly observed variable in order to know the quality or quantity of the variable. A measurement scale becomes valid if it has assignment of numbers to represent all things observed directly or indirectly.

There are four (4) levels of measurement (measurement scales)

2.5.1Nominal Scales

The lowest measurement scale is nominal scale, which classifies objects into two or more categories for identification needs. Numbers applied in this nominal scale has no magnitude or quantitative importance and cannot be used for any basic operations in mathematics (i.e., addition, subtraction, multiplication, and division). For example, the variable marital status used nominal scale; Not married = 0, Separated / Divorced = 1, Married = 2, Also if we assigned numbers to state of origin; Abia = 1, Bauchi = 2, Benue = 3 and Niger = 4, course code, MAT 224, EDU 402, EDME 408. All these are made for identification needs and cannot be added or subtracted or any other operations.

In nominal measurement, we do not play with size, order and other properties of the numbers assigned. They do not imply anything about the objects being measured or took no cognizance of the size, order and other properties of the numbers assigned. As a Researcher in education, it is good to know that two assumptions are made regarding the assignment of numbers in nominal scale. These are:

Different number is assigned for each object.
There exist a number assigned for observed or potential, quality, or quantity.

Therefore, the number values assigned in nominal scale stands for qualitative or quantitative differences in the part of the variables being measured.

2.5.2Ordinal Scales

This scale sometimes known as ranking scale, and it’s used for both classification and ranking of objects. The number values assigned aspect of the object being measured and put the object together in order from highest to lower, from most to least. In ordinal scale of measurement, we use the terms: grades position, merit awards, prize award etc. The only mathematical operation allows here or possible is correlation or association made regarding numbers assigned in the scale. These are:

Different number is assigned for each quality.
There exists a number for every observed or potential quality.
The number represent difference in some magnitude among the aspects of the variable being measured. Thus, the number values assigned in ranking scale shows the degree or difference of attribute possessed by the object.

2.5.3Interval Scales

This scale allows all mathematical operations to be carried out except division because the scale has no zero value. It is a scale that has the features of nominal and ordinal scale and as well as the quality of equal interval for the various grades.

For instance, if Ndagara, Liman, and Aliyu scored these marks, in a test; 30%, 40%, 50% respectively, there are equal difference between them. Furthermore, looking at five-point Likert Scale, a distance between the other points is equal.

Strongly Disagree (SD)

Undecided (U)

Strongly Agree (SA)

Agree

(A)

Disagree

(D)

Strongly Disagree (SD)

Undecided (U)

Strongly Agree (SA)

Agree

(A)

Disagree

(D)

This is an interval scale, there is a difference of 1 between two points, that is (SD) and (D) (3—2 = 1), (A) and (D) (4—3 = 1), (SA) and (A) (5—4 = 1). It involves assigning numbers to objects in such a way that you record equal differences in the objects of the attribute measured. Zero point is placed arbitrarily, which does not mean absence of the property measured.

The interval scale accommodates four assumptions regarding the assignment of numbers. They include:

Different number is assigned for each object.
There exists a number for every object observed or potential.
Numbers assigned indicate difference, in some magnitude among the aspects.
Numbers assigned represent equal units.

2.5.4Ratio Scales

Ratio scale is the highest and most precise measurement scale which is considered to be the most powerful among other scale of measurement because it has all the qualities of nominal, ordinal and interval scale. It has an absolute zero rather than an arbitrary origin. In other word, zero is true zero, indicating that, at that point the variable cease to exist. Addition, Subtraction, Multiplication and Division are possible in this scale. For example, we can say that weight of 8grams is twice as heavy as a weight of 4grams.

Regarding the assignment of numbers in this scale five assumption are made.

Different number is assigned for each object.
There exist a number for every observed or potential object.
The number values indicate differences in variable.
The number values assigned indicate equal units of counting.
Zero point at the beginning is true zero point.

The four measurement scales are very essential in the field of research work. To have a clear picture of the characteristics of measurement scale we can look into following table invented by Gilbert sax of university of Washington.

Scale	Definition	Understand Examples	Limitation
Nominal (least)	The scale that categorizes objects, persons, or events	Like names of places, objects, course code License plate numbers;	It cannot be used for specifying qualitative addition or difference among categories
Ordinal complex	The scale that ranks objects, persons, traits, or abilities instant recognition to equal of difference	Grade in letters (rating from excellent to fail), military rank, prize awards position and merit awards.	The Only Mathematical operation possible is corruption or comparison
Interval (most)	The Scale that has equal Differences between successive categories	The scale used variables such as, examination scores, temperature (centigrade and Fahrenheit) and calendar Date.	All Mathematical operation can be carryout in the scale except division and no zero value.
Ratio (complex)	The scale that represents highest and most precise measurement scale and has meaningful zero (0) value.	The scale is used in physical and behavioral sciences, Distance, height, and weight.	None except educational variables

2.6Rating Scales

You have learnt about measurement scales and based on your experience, To provide a suitable indication of where the observed behavior falls, rating scales for classifying behavior into categories or levels are a good idea. Since human behavior cannot be properly observed, educational researchers create rating systems that can be used.

Since values, attitudes, and beliefs are not physical objects like length, volume, mass, or weight, they are measured using rating scales. Because instruments are utilized, measurements of length, weight, height, and mass are accurate and objective. But because the outcomes are subjective and imprecise, gauging values, attitudes, and beliefs are not exact.

In education and social sciences, scales are extensively used; Likert-type, the Thurstone Scale, and the Guttmann Scale.

2.6.1The Likert-Type Rating Scale

The Likert-type rating scale, also known as the summated scale, was created by Rensis Likert and is named after him. This scale includes a collection of assertions or queries regarding the fact that is to be measured. Everyone is supposed to declare how much they agree or disagree with the statement or question. It is based on a five-point scale, however currently there exist Likert scales with less than five points. The replies are then added up or an average is calculated.

This will make it easier to assess how each person feels about the variable being assessed. For example, “I like Mathematics’‘.

A positive statement is scored with higher value while negative statement is scored with lower value, e.g.

'‘I like Mathematics’'

Other terms are used in the place of agree and disagree as the situations may demand. For examples: Excellent, Very good, Good, Average, Poor, Extremely high, Usually true, Moderately, Slightly, Never true, Very important, Important, Less important, Not important.

2.6.2The Thurstone Scale

This rating scale, which is unidimensional, is used to monitor respondents’ actions, attitudes, and feelings about a certain issue or topic. This scale includes of statements on a problem or subject, and each statement has a number value that reflects whether the respondent has a positive or unfavorable opinion of the subject. The researcher will give numerical values, and the explanation provided by these numerical values will indicate whether the respondents’ reactions to the issue are positive or negative. The scale is frequently employed in the domains of sociology and psychology.

2.6.3The Guttmann Scale

Guttmann scale is sometimes called cumulative scaling or Scalogram analysis. It is one out of three uni-dimensional measurement scaled. A researcher make use of it to test how a person responds to a specific topic and measures how extremely positive or negative a person reacts topic or issue. Whether all the items measure every feature of the variable in issue or are facets of it is referred to as the variable’s uni-dimensionality. For instance, if you are conducting research on attitudes toward mathematical literacy, you are aware that mathematics has many distinct facets. Trigonometry, geometry, algebra, abstract algebra, number theory, real analysis, etc. may be included. An individual could have a favorable attitude toward trigonometry but not geometry. Some people prefer actual analysis to abstract algebra. Two people could get the same score on this scale if they exhibit comparable patterns of interest on the same scale dimension as the issue. Alternatively, they may have been interested in the same variable’s dimension. When the items on a scale are one-dimensional, we say that they constitute a perfect scale; however, when the intensity of the items on a perfect scale varies, we claim that the scale is completely repeatable. But when the response contains mistakes or contradictions, or when the scale contains mistakes.

It is said that the scale cannot be replicated. Having a perfect repeatable scale and estimating the extent are exceedingly tough tasks of reproducibility of a scale it is known as coefficient of reproducibility and given inform of an equation as:

Coefficient of reproducibility = \\frac{\\mathrm{N}\\mathrm{u}\\mathrm{m}\\mathrm{b}\\mathrm{e}\\mathrm{r}\\mathrm{o}\\mathrm{f}\\mathrm{e}\\mathrm{r}\\mathrm{r}\\mathrm{o}\\mathrm{r}\\mathrm{s}}{\\mathrm{N}\\mathrm{u}\\mathrm{m}\\mathrm{b}\\mathrm{e}\\mathrm{r}\\mathrm{o}\\mathrm{f}\\mathrm{r}\\mathrm{e}\\mathrm{s}\\mathrm{p}\\mathrm{o}\\mathrm{n}\\mathrm{c}\\mathrm{e}\\mathrm{s}}

If the calculated value is at 0.90 and above, we say the scale is reproducible. On other way round the scale is said not reproducible.

Student Activity

Explain the word measurement.
Mention two properties of measurement.
List four (4) levels of measurement.
Write a short on the following.
Nominal scales
Ratio scales
Ordinal scale.
Enumerate three (3) assumptions required in ratio scales.
List the steps involved in the measurement process.
Mention three (3) rating scales.

References

Awotunde, P.O & Ugodulunwa, C.A (2002). An Introduction to Statistical Methods in Education. Printed and Published in Nigeria by fab Anieh (Nig) Ltd.

Dash, B. N. & Nibedita Dash (2019). Educational Measurement Statistics and Guidance Services. Dominat Publishers and Distributors PVT Ltd.

Maruf, O. I. & Aliyu, Z, (2013). Measurement and Evaluation in Education. Printed by Stevano Printing Press, General Printers, and Publishers.