Measurement Rsm

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Measurement-1

Measurement

Y520

Strategies for Educational Inquiry

Robert S Michael

Measurement-2

How are variables measured?

First, variables are defined by conceptual definitions(constructs) that explain the concept the variable is

attempting to capture.

Second, variables are defined by operationaldefinitions; that is, definitions of how variables will be

measured.


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Example: Study effort (a)

The variable study effort may be definedconceptually as the amount of effort required to mastera body of material, including reading, looking updefinitions, note-taking, drill, self-quizzing, and soforth.

Each of these components must be operationalized inorder to be measured.

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Example: Study effort (b)

The variable study effort may be said to consist ofreading, looking up definitions, note-taking, drill, and

self-quizzing.

Reading (operational definition): How many hoursper day do you read course related material?

Looking up definitions (operational definition): On

average, how many words per textbook page do

you look up?


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Example: Study effort (c)

The variable study effort may be said to consist ofreading, looking up definitions, note-taking, drill, andself-quizzing.

Note-taking (operational definition): How manypages of notes do you take per textbook page? Doyou consolidate your notes by taking notes on youroriginal notes?

Drill (operational definition): How many hours perday do you drill on new terms and formulas?

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Operational definitions - Constructs

In any research project it is important to involve keyplayers in the formulation of operational definitions

because:

Operational definitions should be consistent withconstructs.

Critiques of poorly constructed operational

definitions can be used for improvement.

Constructs are often inferred from operationaldefinitions.


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What is Measurement?

Measurement is the assignment of numerals to objects

or events according to rules.

Numerals are labels that have no inherentmeaning, for example zip codes, or automobilelicense plates.

Numbers are numerals that have quantitativemeaning and can be analyzed, for example, age.

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What is Measurement?

The rules for assigning labels to properties ofvariables are the most important componentsof measurement, because the result of poorrules is meaningless outcomes.

Concepts often cannot be measured directly,

e.g., intelligence, so what is usuallymeasured are indicators of constructs, such as

speed, logic, verbal skill, etc.


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Levels of Measurement

Four levels of measurement have been identified.

These levels differ in how closely they approach thestructure of the number system we use.

Understanding the level of measurement of variablesused in research is important because the level ofmeasurement determines the types of statisticalanalyses that can be conducted.

The conclusions that can be drawn from researchdepend on the statistical analysis used.

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Levels of Measurement: Nominal

Nominal level measurement uses symbols to classifyobservations into mutually exclusive and exhaustivecategories.

Mutually exclusive means the categories must bedistinct so that no observation falls into more thanone category.

Exhaustive means sufficient categories must existso that all observations fall into some category.


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This is the most basic level of measurement.

At this level we can determine only whethertwo observations are alike or different.

Example: In a survey of teachers, sex wasdetermined by a question. Observations weresorted into two mutually exclusive andexhaustive categories, male and female.

Observations could be labeled with the lettersM and F, or the numerals 0 and 1.

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In the same survey the variable of martialstatus could be measured by two categories,married and unmarried.

But, these categories must each be defined sothat all possible observations will fit into onecategory but no more than one: legally

married, common-law marriage, religiousmarriage, civil marriage, living together, nevermarried, divorced, informally separated, legallyseparated, widowed, annulled, abandoned, etc


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In nominal measurement, all observations inone category are alike on some property anddiffer from the members in the other categoryon that property (e.g., sex, martial status).

On ordering of categories exists. We cannotsay one category is better or worse, or more orless than another.

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Levels of Measurement:

Nominal Numbers used as Names

Basic Empirical Operations

Determination of equality

Permissible Statistics

Number of cases

Mode

Contingency correlation

Examples Numbers on basketball jerseys

Assignment of type or model numbers to classes


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Ordinal Rank order data


Determination of greater or less


Median

Percentiles

Rank order correlation

Examples

Scores on cognitive & affective measures

Hardness of minerals

Quality of performance; objects (wool, meals, etc)

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Level of Measurement: Interval

The interval level of measurement classifiesobservations into mutually exclusive andexhaustive categories that have some explicitrelationship among them, and the relationshipbetween the categories is known and exact.This is the first quantitative application of

numbers.


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In the interval level of measurement, acommon and constant unit of measurement isestablished between the categories. Forexample, measures of temperature areinterval scales.

A temperature of 75 is one degree coolerthan a temperature of 76; likewise, a

temperature of 32 is one degree warmerthan a temperature of 31.

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Numbers may be assigned to observationsbecause the relationship between any twocategories is assumed to be the same as therelationship between numbers in the numbersystem. For example, 76-1=75 and 31+1=32.

Intervals between categories are equal but

they originate from some arbitrary point oforigin. No meaningful zero point exists.


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Interval Equal intervals


Determination of equality of intervals / differences


Mean

Standard deviation

Product-moment correlation

Examples

Standard scores on cognitive & affective scales

Temperature: Fahrenheit & centigrade scales

Calendar dates

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Levels of Measurement: Ratio

The ratio level is the same as the intervallevel with the addition of a meaningful andnon-arbitrary zero point.

Examples: Weight, area, speed, velocity. Ineducation, budgets and number of studentsare measured on ratio scales.


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Levels of Measurement: Ratio

Variables measured at a higher level canalways be converted to a lower level but notvice versa.

Observations of actual age (ratio scale) canbe collapsed to categories of younger andolder (ordinal scale), but age measuredsimply as younger or older cannot be

converted to measures of actual age.

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Ratio Equal intervals & Absolute zero


Determination of equality of ratios


Same as for interval

Coefficient of variation

Logarithmic transformations

Examples Temperature: Kelvin scale

Length, weight, force, etc.

Money


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Review

What level of measurement is each of thefollowing, and what is your reasoning?

Numbers in street addresses.

Order of finish in 100 yard dash.

Social Security Numbers.

Number correct on classroom spelling quiz.

Number correct on SAT.

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Inferences in Measurement

The following slide contains a list of nine

items.

For each item:

Describe how we measure,

Identify the level of measurement,

Describe the inference we make, and

Describe the construct.


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Inferences in Measurement

1. Length of table

2. Weight of person

3. Speed of car

4. Temperature

5. Humidity

6. Wind chill index

7. Discomfort Index (Smog Index / Pollen Index)

8. Intelligence9. Anxiety

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Inventing Constructs

How would you describe the relationship(s) amongthe following:

Operational definitions

Variables

Measurement

Scales of measurement

Inferences from measurements

Constructs

Discuss each for the items on the following slide


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Inventing Constructs

1. Temperature

2. Wind Chill

3. Discomfort Index

4. Intelligence

5. Extroversion

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Example:

Intelligence and its Measurement

Intelligence is one construct that continues togenerate discussion, and divergent opinions.

The Journal of Educational Psychology helda symposium in 1921 entitled Intelligenceand its Measurement.

Definitions of the constructed were offered by

researchers. As you read, how would youoperationalize each definition? What woulditems on a scale look like?


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Definitions:

Intelligence and its Measurement (a)

1. The ability to give responses that are true orfactual. E. L. Thorndike

2. The ability to carry on abstract thinking. L. M. Terman

3. The ability to learn to adjust oneself to theenvironment. S. S. Colvin

4. The ability to adapt oneself to relatively new

situations in life. R. Pinter

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Definitions:

Intelligence and its Measurement (b)

5. The capacity for knowledge and knowledgepossessed. V. A. C. Henmon

6. A biological mechanism by which the effect ofa complexity of stimuli are brought togetherand given a somewhat unified effect in

behavior. J. Peteson


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Definitions:

Intelligence and its Measurement (c)

7. The ability to inhibit an instinctive adjustment,to redefine the inhibited instinctive adjustmentin the light of imaginally experienced trial anderror, and to realize the modified instinctiveadjustment into overt behavior to theadvantage of the individual as a socialanimal. L. L. Thurstone

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Definitions:

Intelligence and its Measurement (d)

8. The ability to acquire abilities. H. Woodrow

9. The ability to learn or profit by experience. W. F. Dearborn

Intelligence is what intelligence tests test. E. G. Boring (1923)


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