2 Variables: Operational Definitions A statement which defines a variable by specifying the operations used to measure and manipulate it.Vs. Conceptual definitions (more dictionary like)Variable in research Problem: Computer usage by end usersLabeling the variable: Attitudes towards computer usageOperational Definition: An individual’s score on the attitudes towards computer usage instrument
3 Measurement of Variables Measurement: Assigning numbers to objects or events according to rulesMeasurement is used in every research projectDetermine the level of measurement for each variableDecide if the level of measurement could be changed to a higher level, and if this would improve the researchReview validity and reliability in order to critique the literature and for later use at the instrumentation stage
4 Measurement By definition, measurement implies a three-part process: Selecting observable empirical eventsDeveloping a mapping rule: a scheme for assigning numbers or symbols to represent aspects of the events being measuredApplying the mapping rule(s) to connect the observation to the symbol
5 One ExampleAssume you are studying people who attend a computer show where all of the year’s new products are on display. You are interested in learning the male-to-female ratio among attendees. You observe those who enter the show area. If a person is female, you record an F; if male, an M. Any other symbols such as 0 and 1 or % and # also may be used if you know what group the symbol identifies.
6 What is Measured?Variables being studied may be classified as objects or properties.Objects include:Things of ordinary experience (e.g., people, tables, books, computer systems, etc.)Some things not concrete (e.g., attitudes, genes, neutrons, etc.)Properties are:Characteristics of objectsPhysical properties (e.g., weight, height, etc.)Psychological properties (e.g., attitudes, perceptions, etc.)Social properties (e.g., leadership ability, status, etc.)
7 Characteristics of Data Mapping rules for data have four characteristics:ClassificationNumbers are used to group or sort responses. No order exists.OrderNumbers are ordered. One number is greater than, less than, or equal to another number.Distance (interval between numbers)Differences between numbers are ordered. The difference between any pair of numbers is greater than, less than, or equal to any other pair of numbers.Origin of number seriesThe number series has a unique origin indicated by the number zero.
8 Levels of Measurement Order Interval Origin Nominal none none none Ordinal yes unequal none(e.g., Doneness of meat: well, medium well, medium rare, rare)Interval yes equal or noneunequal(e.g., Temperature in degrees)Ratio yes equal zero(e.g., Age in years)NOTE: Nominal is the lowest and Ratio is the highest level of measurement.With higher levels of measurement, more precise statistical tests can be used.
9 THE FOUR LEVELS OF MEASUREMENT: NOMINAL Nominal Level of MeasurementLowest level of measurement because numbers are assigned to variables only to classify or categorize them.Categories are mutually exclusiveTypical statistics used: chi-square or other nonparametric statisticsExample: Nature of investment (Stocks = 1 or Bonds = 2)
10 THE FOUR LEVELS OF MEASUREMENT: ORDINAL Ordinal Level of MeasurementNumbers are used to: Classify or RankExample of assigning numbers: Rank of TV Stations: ABC=1, CBS=2, Fox=3)Numbers Indicate:DifferenceGreater than or less thanThe number assigned must maintain order in the numbering systemTypical statistics used: Mean, sign test or other nonparametric statistics
11 THE FOUR LEVELS OF MEASUREMENT: INTERVAL Interval Level of MeasurementNumbers are used to classify, rank, indicate equal units, indicate an arbitrary zero point.Numbers Indicate: Difference, Greater than or less than, equal distance between numbers, zero does not indicate absence of variable.Permissible arithmetic operations: Counting, ranking, addition, subtractionTypical statistics used: Mean, t-test or other parametric test
12 Interval Level of Measurement In social science research, researchers assume interval level of measurement for variables which are probably more accurately measured at on ordinal level.Scales that use responses with labels such as “very important” (coded as 3), “somewhat important” (coded as 2), and “not very important” (coded as 1) are used in social science research so that statistical calculations and tests appropriate for interval data can be usedThe assumption that the distance between the scale numbers such as “very important” and “somewhat important” is equal to that between “somewhat important” and “not very important” is questionable and should be analyzed as ordinal data.
13 THE FOUR LEVELS OF MEASUREMENT: RATIO Nominal Level of MeasurementNumbers are used to classify, rank, indicate equal units, indicate absolute zero.Example of assigning numbers: Income or Age.Numbers Indicate: Difference, Greater than or less than, Equal distance between numbers, Zero indicates absence of the variable.Permissible arithmetic operations: Counting, Ranking, Addition, Subtraction, Multiplication, Division.Typical statistics used: Geometric mean, t-tests or other parametric statistics
14 RATIO AND ORDINAL LEVELS Example of Ratio level questionsNOTE: This is the only measure that can be used to make proportional statements like something is twice something else.What was your income last year?Example pf changing ratio level to ordinal levelIn which category was your income last year?1. Above $50,0002. $30,000 to $50,0003. Below $30,000
15 Summated Rating Scales (Likert-Type ) In MIS and other social science research, Likert-type interval scales (ratings) are used to assess subjects attitudes, opinions, etc. toward an object by summing, and sometimes averaging, over all items.This assumes that each item in a measurement is of “equal value” to each respondentThe response categories, usually degrees of disagreement and agreement, must be the same for all itemsThe measurement for the construct “PERCEIVED USEFULNESS OF MIS” utilizes 12 items that respondents rate on a Likert-type interval scale ranging from “Not at all” to “Very much.”E.g., To what extent do you actually use this system compared to your original expectations?
16 Semantic-Differential Scales Measure the meaning of concepts by selecting a concept and then choosing a series of bipolar adjectives to which subjects respond on a 7 point rating scale.E.g., user information satisfaction construct uses a 39 item semantic differential scale.Analyses can take many forms: comparing concepts, groups of Ss or even factors. Sometimes scores are summed for adjectives measuring the same factor. Graphical analysis is a common tool used for this type of scale.
17 Where you are now Determined the level of measurement of each variable Decided if the level of measurement could and should be changed to a higher level,and recognized thatThe level of measurement determines the statistical techniques