1 LEVELS/SCALES OF MEASUREMENT

Developing Research Hypotheses Intriguing Observation/Experience, Intellectual Curiosity Defining Research Problem & Objectives Testing Hypo.: Data Analysis & Interpretation Sampling Design Refinement of theory Data Coding, And Editing Operational Definition & Measurement of Research Variables Building the Theoretical Framework and the Research Model Data Collection More Careful Studying of the Phenomenon THE PROCESS OF EMPIRICAL RESEARCH

3 LEVELS/SCALES OF MEASUREMENT –Only when we begin to assign numbers to describe an object do we begin to learn about that object. “I often say that when you can measure what you are speaking about and express it in numbers you know something about it. But, when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.” Lord Kelvin (19th century physicist) Lord Kelvin (19th century physicist) MEASUREMENT: One of the pillars of science

4 LEVELS/SCALES OF MEASUREMENT –Careful and deliberate observation of a phenomenon for the purpose of describing study subjects (e.g., people, objects, organizations, events) in terms of their attributes and properties. –Assigning numbers to attributes/characteristics of study subjects (e.g., people, objects, events, etc.) according to a set of rules. –Measurement represents: “Rules for assigning symbols to objects so as to 1.represent quantities of attributes numerically (i.e., scaling) or 2.define whether the objects fall in the same or different categories with respect to a given attribute (i.e., classification)” (Nunnally & Bernstein, 1994) Definition?

5 LEVELS OF MEASUREMENT A fundamental consideration in measurement that influences our choice of alternative measurement procedures is: Levels/Scales of Measurement Let’s first see what this means!

6 LEVELS OF MEASUREMENT QUESTION: What are some of the ways you would measure/characterize/describe and, thus, compare people’s heights? Weather? 1. X feet and Y inches 2. Very Tall, Tall, Neither tall or short, Short, Very short 3. Taller than average, Average, Shorter than average 4. Tall vs Short 1. X Degrees Fahrenheit 2. Unseasonably hot, Hot, Mild, Cold, Unseasonably cold 3. Hotter than last year, Same as last year, Colder than last year 4. Hot vs. Cold Height?Weather? These represent different levels of precision/crudeness—Levels of Measurement

7 LEVEL/SCALES OF MEASUREMENT What is the Significance of Level of Measurement?  The choice of level of measurement (i.e., precision/crudeness of measurement procedure) greatly determines what can/cannot be done with the resulting data when attempting to analyze them—i.e., determines what statistical methods can/cannot be utilized.  Let’s examine various levels of measurement!

8 LEVEL OF MEASUREMENT INDEPENDENT Var. INDEPENDENT Var. NOMINAL/CATEGORICAL METRIC (ORDERED METRIC or HIGHER) NOMINAL/CATEGORICAL METRIC (ORDERED METRIC or HIGHER) * Chi-Square * Discriminant Analysis * Chi-Square * Discriminant Analysis * Fisher’s Exact Prob. * Logit Regression * Fisher’s Exact Prob. * Logit Regression * T-Test * Correlation Analysis * T-Test * Correlation Analysis * Analysis of Variance * Regression Analysis * Analysis of Variance * Regression Analysis Statistical Techniques and Levels of Measurement: DEPENDENT Var. NOMINALNOMINALNOMINALNOMINAL METRICMETRICMETRICMETRIC We will come back to this later!

9 LEVELS/SCALES OF MEASUREMENT –Lowest level/crudest form –Typically for classification of people, objects, ideas, events, etc. into discrete categories –Typically involves a choice from a set of mutually exclusive categories (e.g., male vs. female) –Ideally, the list of categories is exhaustive IMPORTANT FEATURES: –Numbers used to designate categories are of no quantitative or relative value--only labels –All subjects in a group considered equal NOMINAL (CATEGORICAL/DISCRETE):

10 LEVELS OF MEASUREMENT— –Counting--the only arithmetic operation permitted, and –Comparison of group frequencies/percentages-- the only empirical operation applicable NOMINAL (Cont.) Permissible operations? Applicable descriptive statistics (Numbers that help describe characteristics of a group/data set in summary form)? –Central tendency--mode –Spread/variability--none Inferential statistics: Nonparametric test

11 LEVELS OF MEASUREMENT These scales typically involve forced ranking of a set of available options. Subjects are asked to rank (rank order) entities/ objects in terms of the degree to which they possess the characteristic being measured (e.g., brand preference), while NOT allowing assignments of equal ranks to multiple items. –Relative magnitudes/quantitative values of numbers become relevant--numbers not just labels anymore –They indicate some subjects are lower or higher than others on the characteristic being measured, but not by how much (e.g., preference). IMPORTANT FEATURE: –Intervals between consecutive ranks do not represent equal amounts of the attribute being measured (e.g., first, second, or third most preferred brand) –They are more precise than nominal scales, but not yet very precise, still crude ORDINAL:

12 LEVELS OF MEASUREMENT ORDINAL (Con.): LEVELS OF MEASUREMENT ORDINAL (Con.): –Central tendency--mode and median  Mode: For most subjects brand X was the 2 nd choice  Median: For 50% (or more) of the subjects, Brand X was among the top 3 choices –spread/variability--range (minimum and maximum)  Inferential statistics: –nonparametric tests Additional empirical operations are applicable: – Determination of greater or lesser, higher or lower, larger or smaller, darker or lighter, etc. – Transitivity postulate acceptable--i.e., comparison of ranks/positions is allowed (e.g., if a>b and b>c, then a>c) Descriptive statistics?

13 LEVELS OF MEASUREMENT –Provides continuous/metric measures Important Features: –Very precise measures –Units along the scale are of equal size –That is, intervals between consecutive points on the scale represent equal amounts of the attribute being measures.  Thus, score intervals can be compared (e.g., temperature) 80 degrees – 60 degrees = degrees – 60 degrees = degrees – 70 degrees = = 20 (both represent equal levels of heat differential) 20 = 20 (both represent equal levels of heat differential) Can you say the same for differences in test scores? –But, the zero on the scale is arbitrary;  The scale does NOT have an absolute/true zero. INTERVAL:

14 LEVELS OF MEASUREMENT INTERVAL (Con.) –So, ratios of scores will be misleading  E.g., comparisons such as “Object A is 3-times hotter than object B,” is typically wrong. NOTE: There are very few technically true/pure interval scales (i.e., exact but with an arbitrary zero, notable among them Fahrenheit and Celsius temperature scales).  Descriptive statistics? – Central tendency--mean, mode, median – Spread/variability--standard deviation or variance, range, minimum and maximum Inferential statistics? –parametric tests –nonparametric tests

15 LEVELS OF MEASUREMENT –Highest/most precise level of measurement Important Features: –Precise/exact like interval scales, but with a true/absolute/meaningful zero –Meaningful ratios of scores can be derived  “A is twice as long as B” would be a correct comparison (e.g., income, age)  Descriptive statistics? RATIO: –Central tendency--mean, median, mode –Spread/variability--standard deviation or variance, range, minimum and maximum Inferential statistics? –parametric tests –nonparametric tests

16 LEVELS OF MEASUREMENT –Technically/strictly speaking NOT really interval (not as precise), but are superior to purely ordinal (forced ranking) scales. EXAMPLES? EXAMPLES?  IQ scores, score on an exam, and many rating scales used in survey research (e.g., Likert scales, comparative scales, etc.) –In practice, can be treated as if they were interval  (They provide continuous/metric measures/ratings) –Permit virtually all same operations and analyses that are applicable to interval scales –NOTE: Measures that are ordered metric or higher (i.e., ordered metric, interval, or ratio) we will refer to as “METRIC or CONTINUOUS ” ORDERED METRIC: When response options follow an ordered sequence; larger number represent more /less of what is being measured.

17 EXAMPLE: Height--OperationalizationLevel of Measurement LEVELS OF MEASUREMENT IMPORTANT NOTE: Level of measurement is a function of how you choose to measure a variables, and often NOT an inherent characteristic of the concept being measured. Number of feet/inches ? 1=Very Short, 2=Short, 3=Average, 4=Tall, 5=Very Tall ? 1=Short, 2=Tall ? 1=Freshman, 2=Sophomore, 3=Junior, 4=Senior, 5=Graduate ? Ratio Ordered Metric Nominal Ordered Metric

18 LEVELS OF MEASUREMENT –When you have a choice, measure your variables at the highest levels of measurement possible, unless there is a compelling/practical reason for not doing so. NOTE: Higher-level measures can be converted to lower-levels and, thus, treated as such. But the opposite cannot be done. CONCLUSION:

19 LEVEL OF MEASUREMENT INDEPENDENT Var. NOMINAL/CATEGORICAL METRIC (ORDERED METRIC or HIGHER) NOMINAL/CATEGORICAL METRIC (ORDERED METRIC or HIGHER) * Chi-Square * Discriminant Analysis * Chi-Square * Discriminant Analysis * Fisher’s Exact Prob. * Logit Regression * Fisher’s Exact Prob. * Logit Regression * T-Test * Correlation Analysis * T-Test * Correlation Analysis * Analysis of Variance * Regression Analysis * Analysis of Variance * Regression Analysis Remember: Level of measurement determines choice of statistical method. Statistical Techniques and Levels of Measurement: DEPENDENT VAR. NOMINALNOMINALNOMINALNOMINAL METRICMETRICMETRICMETRIC

20 LEVELS OF MEASUREMENT QUESTIONSOR COMMENTS COMMENTS