scales and levels in measurement 1. measurement the process of assigning numbers to objects in such...

Scales and Levels in Measurement

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MeasurementMeasurement

• The process of assigning numbers to objects in such a way that specific properties of the objects are faithfully represented by specific properties of the numbers.

• Such ways of assigning numbers do not attempt to measure the total phenomenon, but only a specific set of attributes.

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Measurement (cont.)Measurement (cont.)

•Measurement is used to capture some “construct”- For example, if research is needed on the construct of “depression”, it is likely that some systematic measurement tool will be needed to assess depression.

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MeasurementMeasurement

MeasurementMeasurement--defined as application of --defined as application of rules to assign numbers to objects (or rules to assign numbers to objects (or attributes).attributes).

Measurement rulesMeasurement rules--the procedures used --the procedures used to transform the qualities of attributes into to transform the qualities of attributes into numbers (e.g., type of scale used).numbers (e.g., type of scale used).

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Why bother assigning numbers?Why bother assigning numbers?

quantifying something that is expected to quantifying something that is expected to vary.vary.

individual differencesindividual differences -- premise that -- premise that people will vary (get different scores) on people will vary (get different scores) on the attributethe attribute

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Scales of measurementScales of measurement Three important properties:Three important properties:

Magnitude--property of “moreness”. Higher Magnitude--property of “moreness”. Higher score refers to more of something.score refers to more of something.

Equal intervals--is the difference between any Equal intervals--is the difference between any two adjacent numbers referring to the same two adjacent numbers referring to the same amount of difference on the attribute?amount of difference on the attribute?

Absolute zero--does the scale have a zero point Absolute zero--does the scale have a zero point that refers to having none of that attribute?that refers to having none of that attribute?

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Levels of Measurement

1. Nominal

2. Ordinal

3. Interval

4. Ratio

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Nominal Scales - there must be distinct classes but these classes have no quantitative properties. Therefore, no comparison can be made in terms of one category being higher than the other.

For example - there are two classes for the variable gender -- males and females. There are no quantitative properties for this variable or these classes and, therefore, gender is a nominal variable.

Other Examples:country of originbiological sex (male or female)animal or non-animalmarried vs. single

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Nominal ScaleNominal Scale Sometimes numbers are used to designate Sometimes numbers are used to designate

category membershipcategory membership

Example: Example: Country of OriginCountry of Origin1 = United States1 = United States 3 = Canada3 = Canada

2 = Mexico2 = Mexico 4 = Other4 = Other

However, in this case, it is important to keep in mind However, in this case, it is important to keep in mind that the numbers do not have intrinsic meaningthat the numbers do not have intrinsic meaning

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Ordinal Scales - there are distinct classes but these classes have a natural ordering or ranking. The differences can be ordered on the basis of magnitude.

For example - final position of horses in a thoroughbred race is an ordinal variable. The horses finish first, second, third, fourth, and so on. The difference between first and second is not necessarily equivalent to the difference between second and third, or between third and fourth.

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Ordinal ScalesOrdinal Scales

Does not assume that the intervals between numbers Does not assume that the intervals between numbers are equalare equal

ExampleExample::

finishing place in a race (first place, second place)finishing place in a race (first place, second place)

1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours

1st place 2nd place 3rd place 4th place

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Levels of Measurement (cont.)

Interval Scales - it is possible to compare differences in magnitude, but importantly the zero point does not have a natural meaning. It captures the properties of nominal and ordinal scales -- used by most psychological tests.

Designates an equal-interval ordering - The distance between, for example, a 1 and a 2 is the same as the distance between a 4 and a 5

Example - Celsius temperature is an interval variable. It is meaningful to say that 25 degrees Celsius is 3 degrees hotter than 22 degrees Celsius, and that 17 degrees Celsius is the same amount hotter (3 degrees) than 14 degrees Celsius. Notice, however, that 0 degrees Celsius does not have a natural meaning. That is, 0 degrees Celsius does not mean the absence of heat!

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Levels of Measurement (cont.)

Ratio Scales - captures the properties of the other types of scales, but also contains a true zero, which represents the absence of the quality being measured.

For example - heart beats per minute has a very natural zero point. Zero means no heart beats. Weight (in grams) is also a ratio variable. Again, the zero value is meaningful, zero grams means the absence of weight.

Example: the number of intimate relationships a person has had

0 quite literally means nonea person who has had 4 relationships has had twice as many as someone who has had 2 1313

Levels of Measurement Scales (cont.)

• Each of these scales have different properties (i.e., difference, magnitude, equal intervals, or a true zero point) and allows for different interpretations.

• The scales are listed in hierarchical order. Nominal scales have the fewest measurement properties and ratio having the most properties including the properties of all the scales beneath it on the hierarchy.

• The goal is to be able to identify the type of measurement scale, and to understand proper use and interpretation of the scale.

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Types of scalesTypes of scales

Nominal scales--qualitative, not quantitative Nominal scales--qualitative, not quantitative distinction (no absolute zero, not equal distinction (no absolute zero, not equal intervals, not magnitude)intervals, not magnitude)

Ordinal scales--ranking individuals (magnitude, Ordinal scales--ranking individuals (magnitude, but not equal intervals or absolute zero)but not equal intervals or absolute zero)

Interval scales--scales that have magnitude Interval scales--scales that have magnitude and equal intervals but not absolute zeroand equal intervals but not absolute zero

Ratio scales--have magnitude, equal intervals, Ratio scales--have magnitude, equal intervals, and absolute zero (so can compute ratios)and absolute zero (so can compute ratios)

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Type of Scale Numerical Operation Descriptive Statistics

Nominal Counting Frequency in each category, percentage in each category, mode

Ordinal Rank Ordering Median, range, percentile ranking

Interval Arithmetic Operations on Intervals between numbers

Mean, standard deviation, variance

Ratio Arithmetic Operations on actual quantities

Geometric mean, coefficient of variation

Rating Scales for Rating Scales for MeasurementMeasurement

A A scale represents a composite scale represents a composite measure measure of a variable; of a variable;

it is based on more than one item. it is based on more than one item. Scales are generally used with Scales are generally used with

complex variables that do not easily complex variables that do not easily lend themselves to single-item or lend themselves to single-item or single-indicator measurements.single-indicator measurements.

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Rating Techniques for Rating Techniques for MeasurementMeasurement

Some items, such as age, newspaper Some items, such as age, newspaper circulation, or number of radios in the circulation, or number of radios in the house, can be adequately measured house, can be adequately measured without scaling techniques. without scaling techniques.

Measurement of other variables, such Measurement of other variables, such as attitude toward TV news or as attitude toward TV news or gratification received from going to a gratification received from going to a movie theater, generally requires the movie theater, generally requires the use of scales.use of scales.

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Simple Rating ScalesSimple Rating Scales

Rating scales are common in mass Rating scales are common in mass media media research. research.

Researchers frequently ask respondents Researchers frequently ask respondents to rate a list of items such as a list of to rate a list of items such as a list of programming elements that can be programming elements that can be included in a radio station’s weekday included in a radio station’s weekday morning show,morning show,

or to rate how much respondents like or to rate how much respondents like radio or TV on-air personalities.radio or TV on-air personalities.

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Simple Rating ScalesSimple Rating Scales

The researcher’s decision is to decide The researcher’s decision is to decide which type of scale to use: 1 to 3? 1 to 5? which type of scale to use: 1 to 3? 1 to 5? 1 to 7?1 to 7?

1 to 10? 1 to 100? Or even a 0 to 9 scale, 1 to 10? 1 to 100? Or even a 0 to 9 scale, which is commonly used by researchers which is commonly used by researchers who don’t have computer software to who don’t have computer software to accept double-digit numbers (like 10).accept double-digit numbers (like 10).

Selecting a type of scale is largely a Selecting a type of scale is largely a matter of personal preference,matter of personal preference,

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SPECIALIZED RATING SPECIALIZED RATING SCALESSCALES

Thurstone ScalesThurstone Scales Thurstone scales are also called Thurstone scales are also called

equal appearing interval scales equal appearing interval scales because of the technique because of the technique used to used to develop them and are typically used develop them and are typically used to measure the attitude toward a to measure the attitude toward a given concept or construct.given concept or construct.

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Reserahcer first collects a large number Reserahcer first collects a large number of statements (Thurstone recommends of statements (Thurstone recommends at least 100) that relate to the concept at least 100) that relate to the concept or construct to be measured.or construct to be measured.

Next, judges rate these statements Next, judges rate these statements along an 11-category scale in which along an 11-category scale in which each category expresses a different each category expresses a different degree of favorableness toward the degree of favorableness toward the concept.concept.

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Reserahcer first collects a large number Reserahcer first collects a large number of statements (Thurstone recommends of statements (Thurstone recommends at least 100) that relate to the concept at least 100) that relate to the concept or construct to be measured.or construct to be measured.

Next, judges rate these statements Next, judges rate these statements along an 11-category scale in which along an 11-category scale in which each category expresses a different each category expresses a different degree of favorableness toward the degree of favorableness toward the concept.concept.

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The items are then ranked according to The items are then ranked according to the mean or median ratings assigned by the mean or median ratings assigned by the judges and are used to construct a the judges and are used to construct a questionnaire of 20 to 30 items that are questionnaire of 20 to 30 items that are chosen more or less evenly from across chosen more or less evenly from across the range of ratings. the range of ratings.

The statements are worded so that a The statements are worded so that a person can agree or disagree with them. person can agree or disagree with them.

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The scale is then administered to a sample The scale is then administered to a sample of respondents whose scores are of respondents whose scores are determined by computing the mean or determined by computing the mean or median value of the items agreed with. median value of the items agreed with.

A person who disagrees with all the items A person who disagrees with all the items has a score of zero.has a score of zero.

Thurstone scales are not often used in Thurstone scales are not often used in mass media research, but they are mass media research, but they are common in psychology and education common in psychology and education research.research.

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Guttman ScalingGuttman Scaling Guttman scaling, also called Guttman scaling, also called scalogram scalogram

analysis, is based on the idea that analysis, is based on the idea that items can be arranged along a items can be arranged along a continuum in such a way that a person continuum in such a way that a person who agrees with an item or finds an who agrees with an item or finds an item acceptable will also agree with or item acceptable will also agree with or find acceptable all other items find acceptable all other items expressing a less extreme position.expressing a less extreme position.

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a hypothetical four-item Guttman scale:a hypothetical four-item Guttman scale:

1. Indecent programming on TV is 1. Indecent programming on TV is harmful harmful to society.to society.

2. Children should not be allowed to 2. Children should not be allowed to watch indecent TV shows.watch indecent TV shows.

3. Television station managers should 3. Television station managers should not not allow indecent programs on their stations.allow indecent programs on their stations.

4. The government should ban indecent 4. The government should ban indecent programming from TV.programming from TV.

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A Guttman scale requires a great deal A Guttman scale requires a great deal of time and energy to develop. of time and energy to develop.

Although they do not appear often in Although they do not appear often in mass media research,mass media research,

Guttman scales are common in Guttman scales are common in political science, sociology, public political science, sociology, public opinion research, and anthropology.opinion research, and anthropology.

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Likert ScalesLikert Scales Perhaps the most commonly used scale inPerhaps the most commonly used scale in mass media research is the Likert scale, mass media research is the Likert scale,

also called the also called the summated rating approach.summated rating approach. A A number of statements are developed with number of statements are developed with

respect to a topic, and respondents can respect to a topic, and respondents can strongly agree, agree, be neutral, disagree, strongly agree, agree, be neutral, disagree, or strongly disagree with the statementsor strongly disagree with the statements

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SPECIALIZED RATING SPECIALIZED RATING SCALESSCALES Each response option is weighted, and each Each response option is weighted, and each

subject’s responses are added to produce a subject’s responses are added to produce a single score on the topic.single score on the topic.

1. Only U.S. citizens should be allowed to 1. Only U.S. citizens should be allowed to own broadcasting stations.own broadcasting stations.

Strongly agree 5Strongly agree 5 Agree 4Agree 4 Neutral 3Neutral 3 Disagree 2Disagree 2 Strongly disagree 1Strongly disagree 1

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2. Prohibiting foreign ownership of 2. Prohibiting foreign ownership of broadcasting stations is bad for broadcasting stations is bad for business.business.

Strongly agree 1Strongly agree 1 Agree 2Agree 2 Neutral 3Neutral 3 Disagree 4Disagree 4 Strongly disagree 5Strongly disagree 5

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Semantic Differential ScalesSemantic Differential Scales Another commonly used scaling Another commonly used scaling

procedureprocedure is the is the semantic differential semantic differential

technique. technique. As As originally conceived by Osgood, originally conceived by Osgood,

Suci, and Tannenbaum (1957), this Suci, and Tannenbaum (1957), this technique is used to measure the technique is used to measure the meaning an item has for an individual.meaning an item has for an individual.

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SPECIALIZED RATING SPECIALIZED RATING SCALESSCALES To use the technique, a name or a conceptTo use the technique, a name or a concept

is placed at the top of a series of seven-point is placed at the top of a series of seven-point scales anchored by bipolar attitudes.scales anchored by bipolar attitudes.

The bipolar adjectives that typically “anchor” The bipolar adjectives that typically “anchor” such evaluative scales are such evaluative scales are pleasant/ pleasant/ unpleasant, valuable/worthless, honest/ unpleasant, valuable/worthless, honest/ dishonest, nice/awful, clean/dirty, fair/unfair, dishonest, nice/awful, clean/dirty, fair/unfair, and and good/bad. good/bad.

Unique set of anchoring adjectives be Unique set of anchoring adjectives be developed for each particular measurement developed for each particular measurement situation.situation.

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Time MagazineTime Magazine Biased : : : : : : UnbiasedBiased : : : : : : Unbiased Trustworthy : : : : : : UntrustworthyTrustworthy : : : : : : Untrustworthy Valuable : : : : : : WorthlessValuable : : : : : : Worthless Unfair : : : : : : FairUnfair : : : : : : Fair

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scales and levels in measurement 1. measurement the process of assigning numbers to objects in such...

Documents

adjacent numbers

levels of measurement

nominal scalesometimes

process of assigning

ways of assigning numbers

measurement rules

specific properties

properties of nominal