Scales and Levels in Measurement

Measurement • 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.

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.

Measurement Measurement--defined as application of rules to assign numbers to objects (or attributes). Measurement rules--the procedures used to transform the qualities of attributes into numbers (e.g., type of scale used).

Why bother assigning numbers? quantifying something that is expected to vary. individual differences -- premise that people will vary (get different scores) on the attribute

Scales of measurement Three important properties: Magnitude--property of “moreness”. Higher score refers to more of something. Equal intervals--is the difference between any two adjacent numbers referring to the same amount of difference on the attribute? Absolute zero--does the scale have a zero point that refers to having none of that attribute?

Levels of Measurement 1. Nominal 2. Ordinal 3. Interval 4. Ratio

Levels of Measurement 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 origin biological sex (male or female) animal or non-animal married vs. single

Nominal Scale Sometimes numbers are used to designate category membership Example: Country of Origin 1 = United States 3 = Canada 2 = Mexico 4 = Other However, in this case, it is important to keep in mind that the numbers do not have intrinsic meaning

Levels of Measurement 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.

Ordinal Scales Does not assume that the intervals between numbers are equal Example: finishing place in a race (first place, second place) 1st place 2nd place 3rd place 4th place 1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours

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!

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 none a person who has had 4 relationships has had twice as many as someone who has had 2

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.

Types of scales Nominal scales--qualitative, not quantitative distinction (no absolute zero, not equal intervals, not magnitude) Ordinal scales--ranking individuals (magnitude, but not equal intervals or absolute zero) Interval scales--scales that have magnitude and equal intervals but not absolute zero Ratio scales--have magnitude, equal intervals, and absolute zero (so can compute ratios)

Descriptive Statistics 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 Measurement A scale represents a composite measure of a variable; it is based on more than one item. Scales are generally used with complex variables that do not easily lend themselves to single-item or single-indicator measurements.

Rating Techniques for Measurement Some items, such as age, newspaper circulation, or number of radios in the house, can be adequately measured without scaling techniques. Measurement of other variables, such as attitude toward TV news or gratification received from going to a movie theater, generally requires the use of scales.

Simple Rating Scales Rating scales are common in mass media research. Researchers frequently ask respondents to rate a list of items such as a list of programming elements that can be included in a radio station’s weekday morning show, or to rate how much respondents like radio or TV on-air personalities.

Simple Rating Scales The researcher’s decision is to decide which type of scale to use: 1 to 3? 1 to 5? 1 to 7? 1 to 10? 1 to 100? Or even a 0 to 9 scale, which is commonly used by researchers who don’t have computer software to accept double-digit numbers (like 10). Selecting a type of scale is largely a matter of personal preference,

SPECIALIZED RATING SCALES Thurstone Scales Thurstone scales are also called equal appearing interval scales because of the technique used to develop them and are typically used to measure the attitude toward a given concept or construct.

SPECIALIZED RATING SCALES Reserahcer first collects a large number of statements (Thurstone recommends at least 100) that relate to the concept or construct to be measured. Next, judges rate these statements along an 11-category scale in which each category expresses a different degree of favorableness toward the concept.

SPECIALIZED RATING SCALES Reserahcer first collects a large number of statements (Thurstone recommends at least 100) that relate to the concept or construct to be measured. Next, judges rate these statements along an 11-category scale in which each category expresses a different degree of favorableness toward the concept.

SPECIALIZED RATING SCALES The items are then ranked according to the mean or median ratings assigned by the judges and are used to construct a questionnaire of 20 to 30 items that are chosen more or less evenly from across the range of ratings. The statements are worded so that a person can agree or disagree with them.

SPECIALIZED RATING SCALES The scale is then administered to a sample of respondents whose scores are determined by computing the mean or median value of the items agreed with. A person who disagrees with all the items has a score of zero. Thurstone scales are not often used in mass media research, but they are common in psychology and education research.

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

SPECIALIZED RATING SCALES a hypothetical four-item Guttman scale: 1. Indecent programming on TV is harmful to society. 2. Children should not be allowed to watch indecent TV shows. 3. Television station managers should not allow indecent programs on their stations. 4. The government should ban indecent programming from TV.

SPECIALIZED RATING SCALES A Guttman scale requires a great deal of time and energy to develop. Although they do not appear often in mass media research, Guttman scales are common in political science, sociology, public opinion research, and anthropology.

SPECIALIZED RATING SCALES Likert Scales Perhaps the most commonly used scale in mass media research is the Likert scale, also called the summated rating approach. A number of statements are developed with respect to a topic, and respondents can strongly agree, agree, be neutral, disagree, or strongly disagree with the statements

SPECIALIZED RATING SCALES Each response option is weighted, and each subject’s responses are added to produce a single score on the topic. 1. Only U.S. citizens should be allowed to own broadcasting stations. Strongly agree 5 Agree 4 Neutral 3 Disagree 2 Strongly disagree 1

SPECIALIZED RATING SCALES 2. Prohibiting foreign ownership of broadcasting stations is bad for business. Strongly agree 1 Agree 2 Neutral 3 Disagree 4 Strongly disagree 5

SPECIALIZED RATING SCALES Semantic Differential Scales Another commonly used scaling procedure is the semantic differential technique. As originally conceived by Osgood, Suci, and Tannenbaum (1957), this technique is used to measure the meaning an item has for an individual.

SPECIALIZED RATING SCALES To use the technique, a name or a concept is placed at the top of a series of seven-point scales anchored by bipolar attitudes. The bipolar adjectives that typically “anchor” such evaluative scales are pleasant/ unpleasant, valuable/worthless, honest/ dishonest, nice/awful, clean/dirty, fair/unfair, and good/bad. Unique set of anchoring adjectives be developed for each particular measurement situation.

SPECIALIZED RATING SCALES Time Magazine Biased : : : : : : Unbiased Trustworthy : : : : : : Untrustworthy Valuable : : : : : : Worthless Unfair : : : : : : Fair