1 LEVELS/SCALES OF MEASUREMENT. Developing Research Hypotheses Intriguing Observation/Experience, Intellectual Curiosity Defining Research Problem & Objectives.

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LEVELS/SCALES OF LEVELS/SCALES OF MEASUREMENTMEASUREMENT

Developing ResearchHypotheses

IntriguingObservation/Experience,

Intellectual Curiosity

Defining ResearchProblem & Objectives

Testing Hypo.:Data Analysis &Interpretation

Sampling Design

Refinement of theory

Data Coding,And

Editing

Operational Definition& Measurement ofResearch Variables

Building the Theoretical Framework and the

Research Model

Data Collection

More Careful Studyingof the Phenomenon

THE PROCESS OF

EMPIRICAL RESEARCH

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LEVELS/SCALES OFLEVELS/SCALES OF MEASUREMENT MEASUREMENT

– Only when we begin to assign numbers to describe Only when we begin to assign numbers to describe an object do we begin to learn about that object. an object do we begin to learn about that object.

““I often say that when you can measure what you are I often say that when you can measure what you are speaking about and express it in numbers you know speaking about and express it in numbers you know something about it. something about it. But, when you cannot measure it, But, when you cannot measure it, when you cannot express it in numbers, your knowledge is when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kindof a meager and unsatisfactory kind; it may be the ; it may be the beginning of knowledge, beginning of knowledge, but you have scarcely, in your but you have scarcely, in your thoughts, advanced to the stage ofthoughts, advanced to the stage of science science, whatever the , whatever the matter may bematter may be.”.”

Lord Kelvin (19th century Lord Kelvin (19th century physicist)physicist)

MEASUREMENT: One of the pillars of science

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LEVELS/SCALES OFLEVELS/SCALES OF MEASUREMENT MEASUREMENT

– Careful and deliberate observationCareful and deliberate observation of a phenomenon for the of a phenomenon for the purpose of purpose of describing study subjects describing study subjects (e.g., people, objects, (e.g., people, objects, organizations, events) organizations, events) in terms of their attributes and in terms of their attributes and properties.properties.

– Assigning numbersAssigning numbers to to attributes/characteristicsattributes/characteristics of study subjects of study subjects (e.g., people, objects, events, etc.) (e.g., people, objects, events, etc.) according to a set of rulesaccording to a set of rules..

– Measurement represents:Measurement represents:“Rules for “Rules for assigning symbols to objectsassigning symbols to objects so as to so as to

1.1. represent quantities of attributes numerically (i.e., scaling) orrepresent quantities of attributes numerically (i.e., scaling) or2.2. define whether the objects fall in the same or different define whether the objects fall in the same or different

categories with respect to a given attribute (i.e., classification)”categories with respect to a given attribute (i.e., classification)”(Nunnally & Bernstein, 1994)(Nunnally & Bernstein, 1994)

Definition?

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LEVELS OF MEASUREMENTLEVELS 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!

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QUESTION:QUESTION: What are some of the ways you What are some of the ways you would measure/characterize/describe and, would measure/characterize/describe and, thus, compare thus, compare people’s heightspeople’s heights? ? WeatherWeather??

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

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LEVEL/SCALES OF MEASUREMENTLEVEL/SCALES OF MEASUREMENT

What is the Significance of Level of Measurement?

The choice of level of measurement The choice of level of measurement (i.e., precision/crudeness of (i.e., precision/crudeness of measurement procedure) greatly measurement procedure) greatly determines what can/cannot be determines what can/cannot be done with the resulting datadone with the resulting data when when attempting to analyze them—i.e., attempting to analyze them—i.e., determines determines what what statistical statistical methodsmethods can/cannot be utilized can/cannot be utilized..

Let’s examine various levels of Let’s examine various levels of measurement!measurement!

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LEVEL OF MEASUREMENTLEVEL OF MEASUREMENT

INDEPENDENT Var.INDEPENDENT Var. NOMINAL/CATEGORICALNOMINAL/CATEGORICAL METRIC (ORDERED METRIC or METRIC (ORDERED METRIC or

HIGHER) HIGHER)

* Chi-Square* Chi-Square * Discriminant Analysis * Discriminant Analysis

* Fisher’s Exact Prob.* Fisher’s Exact Prob. * Logit Regression * Logit Regression

* T-Test* T-Test * Correlation Analysis * Correlation Analysis

* Analysis of Variance* Analysis of Variance * Regression Analysis * Regression Analysis

Statistical Techniques and Levels of Measurement:

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We will come back to this later!

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LEVELS/SCALES OF LEVELS/SCALES OF MEASUREMENTMEASUREMENT

– Lowest level/Lowest level/crudest formcrudest form– Typically Typically for classificationfor classification of people, objects, of people, objects,

ideas, events, etc. into ideas, events, etc. into discrete categoriesdiscrete categories– Typically involves a choice from a set of Typically involves a choice from a set of mutually mutually

exclusiveexclusive categories (e.g., male vs. female) categories (e.g., male vs. female)– Ideally, the list of categories Ideally, the list of categories is exhaustiveis exhaustive

IMPORTANT FEATURES:IMPORTANT FEATURES:– Numbers used to designate categories are of Numbers used to designate categories are of no no

quantitativequantitative or relative value-- or relative value--only labelsonly labels – All subjects in a group considered equal All subjects in a group considered equal

NOMINALNOMINAL (CATEGORICAL/DISCRETE): (CATEGORICAL/DISCRETE):

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LEVELS OF MEASUREMENT—LEVELS OF MEASUREMENT—

– CountingCounting--the only arithmetic operation permitted, and--the only arithmetic operation permitted, and– Comparison Comparison of group frequencies/percentages--the only of group frequencies/percentages--the only

empirical operation applicableempirical operation applicable

NOMINAL (Cont.)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

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These scales typically These scales typically involve forced rankinginvolve forced ranking of a set of of a set of available options.available options.Subjects are askedSubjects are asked to to rank (rank order)rank (rank order) entities/ objects in entities/ objects in terms of the degree to which they possess the characteristic terms of the degree to which they possess the characteristic being measured (e.g., brand preference), being measured (e.g., brand preference), while while NOT allowing NOT allowing assignments of equal ranks to multiple items.assignments of equal ranks to multiple items.

– Relative magnitudesRelative magnitudes/quantitative values of numbers become /quantitative values of numbers become relevant--numbers not just labels anymorerelevant--numbers not just labels anymore

– They indicate some subjects are They indicate some subjects are lower or higherlower or higher than others on the than others on the characteristic being measured, but not by how much (e.g., characteristic being measured, but not by how much (e.g., preference). preference).

IMPORTANT FEATURE: IMPORTANT FEATURE: – IntervalsIntervals between consecutive ranks do not represent equal amounts between consecutive ranks do not represent equal amounts

of the attribute being measured (e.g., first, second, or third most of the attribute being measured (e.g., first, second, or third most preferred brand)preferred brand)

– They are more precise than nominal scales, but They are more precise than nominal scales, but not yet very precisenot yet very precise, , still crudestill crude

ORDINALORDINAL::

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LEVELS OF MEASUREMENTLEVELS OF MEASUREMENTORDINAL (Con.):ORDINAL (Con.):

– Central tendency--Central tendency--modemode and and medianmedian ModeMode: For most subjects brand X was the 2: For most subjects brand X was the 2ndnd choice choice MedianMedian: For 50% (or more) of the subjects, Brand X was among : For 50% (or more) of the subjects, Brand X was among

the top 3 choices the top 3 choices

– spread/variability--spread/variability--range range (minimum and (minimum and maximum)maximum)

Inferential statistics:Inferential statistics:– nonparametricnonparametric tests 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?

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– Provides continuous/Provides continuous/metricmetric measures measuresImportant Features:Important Features:– Very preciseVery precise measures measures– UnitsUnits along the scale along the scale are of equal sizeare of equal size– That is, That is, intervals between consecutive pointsintervals between consecutive points on the scale on the scale

represent equal amountsrepresent equal amounts of the attribute being measures. of the attribute being measures. Thus, score intervals can be compared (e.g., temperature)Thus, score intervals can be compared (e.g., temperature)

80 degrees – 60 degrees = 2080 degrees – 60 degrees = 2090 degrees – 70 degrees = 2090 degrees – 70 degrees = 20

20 = 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 Can you say the same for differences in test scorestest scores??

– But, the But, the zerozero on the scale is on the scale is arbitrary;arbitrary; The scale does The scale does NOTNOT have an have an absolute/true zero.absolute/true zero.

INTERVAL:INTERVAL:

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LEVELS OF MEASUREMENTLEVELS OF MEASUREMENTINTERVAL (Con.)INTERVAL (Con.)

– So, So, ratios of scores will be misleadingratios of scores will be misleading E.g., comparisons such as “Object A is 3-times hotter E.g., comparisons such as “Object A is 3-times hotter

than object B,” is typically wrong.than object B,” is typically wrong.NOTE: There are very few technically true/pure interval scales NOTE: There are very few technically true/pure interval scales

(i.e., (i.e., exact but with an arbitrary zeroexact but with an arbitrary zero, notable among , notable among them Fahrenheit and Celsius temperature scales). them Fahrenheit and Celsius temperature scales).

Descriptive statistics?Descriptive statistics?– Central tendency--mean, mode, median– Spread/variability--standard deviation or variance, range, minimum and maximum

• Inferential statistics?–parametric tests–nonparametric tests

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– Highest/Highest/most precisemost precise level of measurement level of measurement

Important Features:Important Features:– Precise/exact like interval scales, but with a Precise/exact like interval scales, but with a

true/absolutetrue/absolute/meaningful /meaningful zerozero– Meaningful ratiosMeaningful ratios of scores can be derived of scores can be derived

““A is twice as long as B” would be a correct comparison (e.g., income, age)A is twice as long as B” would be a correct comparison (e.g., income, age)

Descriptive statistics?Descriptive statistics?

RATIORATIO::

–Central tendency--mean, median, mode–Spread/variability--standard deviation or variance, range, minimum and maximum

• Inferential statistics?–parametric tests–nonparametric tests

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– Technically/strictly speakingTechnically/strictly speaking NOT really interval (not as precise), NOT really interval (not as precise), but are superior to purely ordinal (forced ranking) scales. but are superior to purely ordinal (forced ranking) scales.

EXAMPLES?EXAMPLES? IQIQ scores, score on an scores, score on an examexam, and many , and many rating scalesrating scales used in survey used in survey

research (e.g., research (e.g., Likert scales, comparative scalesLikert scales, comparative scales, etc.), etc.)

– In practiceIn practice, can be treated as if they were , can be treated as if they were intervalinterval (They provide (They provide continuous/metriccontinuous/metric measures/ratings) measures/ratings)

– Permit virtually all same operations and analyses that are Permit virtually all same operations and analyses that are applicable to interval scalesapplicable to interval scales

– NOTE:NOTE: Measures that are Measures that are ordered metric or higherordered metric or higher(i.e., ordered metric, interval, or ratio) we(i.e., ordered metric, interval, or ratio) wewill refer to as will refer to as “METRIC or CONTINUOUS ”“METRIC or CONTINUOUS ”

ORDERED METRICORDERED METRIC::

When response options follow an ordered sequence; larger number represent more /less of what is being measured.

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EXAMPLE:

Height--Operationalization Level of Measurement


IMPORTANT NOTE:IMPORTANT NOTE: Level of measurementLevel of measurementis a function of how you choose to measureis a function of how you choose to measurea variables, and a variables, and often NOT an inherent often NOT an inherent characteristiccharacteristic of the concept being measured. 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

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– When you have a choice, When you have a choice, measure your measure your variables at the highest levels of variables at the highest levels of measurement possiblemeasurement possible, unless there is , unless there is a compelling/practical reason for not a compelling/practical reason for not doing so. doing so.

NOTE: NOTE: Higher-level measures can be converted Higher-level measures can be converted to lower-levels and, thus, treated as such. to lower-levels and, thus, treated as such. But the opposite cannot be done. But the opposite cannot be done.

CONCLUSION:CONCLUSION:

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LEVEL OF MEASUREMENTLEVEL OF MEASUREMENT

INDEPENDENT Var.INDEPENDENT Var. NOMINAL/CATEGORICALNOMINAL/CATEGORICAL METRIC (ORDERED METRIC or METRIC (ORDERED METRIC or

HIGHER) HIGHER)

* Chi-Square* Chi-Square * Discriminant Analysis * Discriminant Analysis

* Fisher’s Exact Prob.* Fisher’s Exact Prob. * Logit Regression * Logit Regression

* T-Test* T-Test * Correlation Analysis * Correlation Analysis

* Analysis of Variance* Analysis of Variance * Regression Analysis * Regression Analysis

Remember: Level of measurement determines choice of statistical method.

Statistical Techniques and Levels of Measurement:

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2020

LEVELS OF LEVELS OF MEASUREMENTMEASUREMENT

QUESTIONSQUESTIONSOROR

COMMENTS COMMENTS

1 LEVELS/SCALES OF MEASUREMENT. Developing Research Hypotheses Intriguing Observation/Experience, Intellectual Curiosity Defining Research Problem & Objectives.

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