Measurement Scales

Measurement: A systematic way of assigning numbers or names to objects and their attributes.

The most important aspect of measurement scale is the implications that the scale of measurement has on the statistical test used to evaluate the null hypothesis.   The type of statistic selected to evaluate the null hypothesis depends only on the scale of measurement for the variables.  The type of statistical test used has nothing to do with the type of design used to conduct the research (i.e., descriptive, relational or experimental).

To determine the appropriate statistic, use the table below:

		Type of Independent Variable^1
		Continuous (Interval or Ratio)	Categorical (Nominal)
Type of Dependent Variable^2	Continuous (Interval or Ratio)	Pearson r correlation coefficient	z-test, t-test, or F-test
	Categorical (Nominal)	Logistic Regression^3	Chi-Square (X^2)

¹ Independent variables are only present in experiments. Relational designs and Quasi-experiments use non-manipulated variables called subject variables or predictors.

² Dependent variables are only present in experiments. Relational designs use criterion variables.

 ³ We will not learn to compute Logistic Regression in this class.

fundamental Properties of Measurement Scales

Difference

Tells only that one object differs from another

Magnitude

Tells not only that one object is different from another, but also what objects contain more of the underlying construct than others. The intervals between adjacent units on the scale might not be equivalent.

Equal intervals

Tells exactly how much more or less of the underlying construct the objects possess. The intervals between adjacent units on the scale are equivalent.

True zero point

Tells how much (in the absolute sense) of the underlying construct an object possesses.

types of measurement scales

Nominal Scale

Measures the property of difference, no more. It's a scale of measurement with two or more categories that have no numerical (less than, greater than) properties. Objects are measured by determining the category to which they belong. The only operation that can be performed on a nominal scale is that of counting. There are no numeric properties to nominal scales. The information obtained from a nominal scale is qualitative, meaning object are classified by name only.

Ordinal Scales

Measures differences in magnitude (i.e., rank order). It's a scale of measurement in which the measurement categories form a rank order along a continuum. If A < B and B < C, then A < C. There are only crude numeric properties to ordinal scales, numbers assigned cannot be meaningfully added or subtracted. However, the extent to which A is less than B may not be the same as the extent to which B is less than C. You can rank-order the objects according to whether they possess more, less of the same amount of the variable being measured. Thus, you can determine whether A > B, A = B, or A < B. The information obtained from an ordinal scale is rank order. The differences among objects are valid only relative to the other objects measured.

Interval Scales

Measures differences in magnitude, but also possesses the property equal intervals. It's a scale of measurement in which the intervals between numbers on the scale are all equal in size. There are numeric properties to interval scales, and the numbers assigned can be meaningfully added or subjected, but not multiplied or divided. You can determine if A - B = B - C. The information obtained from an interval scale is the exact amount of the underlying construct that one object differs from another.

Ratio Scales

Possess all properties of interval scales plus an absolute zero point. It's a scale of measurement in which there is an absolute zero point, indicating an absence of the variable being measured. An implication is that ratios of numbers on the scale can be formed (generally, these are physical measures such as weight or timed measures such as duration or reaction time). There are numeric properties to interval scales, and the numbers assigned can not only be meaningfully added or subjected, but also multiplied and divided. The information obtained from a ratio scale is an absolute indication of how much of the underlying construct being measured an object has.

Property
Scale:	Difference	Magnitude	Equal Intervals	True Zero	Example
Nominal	i				Race or religion
Ordinal	i	i			Athletic Seeding
Interval	i	i	i		Celsius temperature
Ratio	i	i	i	i	Time, Kelvin temperature