With the change of focus in instruction from content to learning outcomes came the need to redefine and clarify the terms used to determine the progress of students towards the attainment of the desired learning outcomes. These are ** measurement**, evaluation, and assessment.

Measurement is the process of determining or describing the attributes or characteristics of physical objects generally in terms of quantity. When we measure, we use some standard instruments to find out how long, heavy, hot, voluminous, cold, fast or straight some things are. Such instruments may be ruler, scale, thermometer, or pressure gauge. When we measure, we are actually collecting quantitative information relative to some established standards. To measure is to apply a standard measuring device to an object, group of objects, events or situations according to the procedure determined by one who is skilled in the use of such device.

Sometimes, we can measure physical quantities by combining directly measurable quantities to form derived quantities. For example, to find the area of a rectangular piece of paper, we simply multiply the lengths of the sides of the paper. In the field of education, however, the quantities and qualities of interest are abstract, unseen and cannot be touched and so

the measurement process becomes difficult; hence, the need to specify the learning outcomes to be measured.

For instance, knowledge of the subject matter is often measured through standardized test results. In this case, the measurement procedure is ** testing**. The same concept can be measured in another way. We can ask a group of experts to rate a student’s (or a teacher’s) knowledge of the subject matter in a scale of 1 to 5 with 1 being the lowest and 5 the highest. In this procedure, knowledge of the subject matter is measured through

*.*

**perceptions**## Types of Measurement

Measurements can, therefore, be objective (as in testing) or subjective (as in perceptions). In the example cited, testing produces objective measurements while expert ratings provide subjective measurements. Objective measurements are more stable than subjective measurements in the sense that repeated measurements of the same quantity or quality of interest will produce more or less the same outcome. For this reason, many people prefer objective measurements over subjective measurements whenever they are available. However, there are certain facets of the quantity or quality of interest that cannot be successfully captured by objective procedures but which can be done by subjective methods e.g. aesthetic appeal of a product or project of a student, student’s performance in a drama, etc. It follows that it may be best to use both methods of assessment whenever the constraints of time and resources permit.

Whether one uses an objective or subjective assessment procedure, the underlying principle in educational measurement

is summarized by the following formula:

*Measurement of Quantity or Quality of Interest = True value plus random error.*

Each measurement of the quantity of interest has two components: a true value of the quantity and a random error component. The objective in educational measurement is to estimate or approximate, as closely as possible, the true value of the quantity of interest, e.g. true knowledge of the subject matter. This is a tall order and one which will occupy most of our time in this particular course.

Objective measurements are measurements that do not depend on the person or individual taking the measurements.

Regardless of who is taking the measurement, the same measurement values should be obtained when using an objective assessment procedure. In contrast, subjective measurements often differ from one assessor to the next even if the same quantity or quality is being measured.

## Measuring Indicators, Variables and Factors

An educational variable (denoted by an English alphabet, like X) is a measurable characteristic of a student. Variables may be directly measurable as in X = age or X = height of a student. However, many times, a variable cannot be directly measured like when we want to measure “class participation” of a student. For those variables where direct measurements are not feasible, we introduce the concept of indicators.

An indicator, I, denotes the presence or absence of a measured characteristic. Thus:

I = 1, if the characteristic is present

= 0, if the characateristic is absent

For the variable X= class participation, we can let I_{1}, I_{2} …, I_{11} denote the participation of a student in n class recitations and let X = sum of the I’s divided by it recitations. Thus, if there were n = 10 recitations and the student participated in 5 of these 10, then X = 5/10 or 50%. Indicators are the building blocks of educational measurement upon which all other forms of measurement are built. A group of indicators constitute a variable. A group of variables form a construct or a factor. The variables which form a factor correlate highly with each other but have low correlations with variables in another group.

*Example*: The following variables were measured in a battery of tests:

*XI = computational skills **X2 = reading skills **X3 = vocabulary **X4 = logic and reasoning **X5 = sequences and series **X6 = manual dexterity*

*These variables can be grouped as follows: *

*Group 1 : (Xl, X4 X5) = mathematical ability factor **Group 2 : (X2, x3) = language ability factor **Group 3 : (x6 ) = psychomotor ability factor*

*The first group is called a “mathematical ability” factor, the second group is called a “language ability” factor while the third group (with only one variable) is called a “Psychomotor ability” factor. *

In educational measurement, we shall be concerned with indicators, variables and factors of interest in the field of education.