measurenent scales

Measurement Scales

Definition

• Measurement is to discover the extent, dimension, quantity or capacity of something, especially by comparison with a standard.

• Measurement in research consists of assigning numbers to empirical events in compliance with the set of rules.

Three parts of measurement

• Selecting a observable empirical events

• Developing a set of mapping rules: a scheme for assigning numbers or symbols to represent aspects of the event being measured.

• Applying the mapping rule(s) to each observation of that event.

Goal of measurement

• To provide the highest quality, lowest error data for testing hypotheses.

Must know…..

• Concept• Construct• Constitutive Concept• Operational Concept

• Unidimensionality • Linearity• Validity • Reliability• Accuracy and precision • Simplicity • Practicability

Characteristics of a Good measurement

Investigative Que

What do I plan to do with the data

Description?

Exploration?

Discovering of difference?

Finding of relationships?

Type of data?

Nominal

Ordinal

Interval

Ratio

Is dn expected to be normal?

What is my expected

sample size?

How many groups will be

compared?

Are groups related or

independent?

What Measurement Scale should I use?

Measurement Que

Moving from Investigative

Que to Measurement

Que.

Measurement Scales

• Nominal scale• Ordinal Scale• Interval Scale• Ratio Scale

Nominal Scale

• Most elementary method of measurement.

• Categorical data and numbers that are simply used as identifiers or names.

• Mutually exclusive and collectively exhaustive.

Nominal Scale Cont…

• Numbers doesn't have any quantitative value.

• Arithmetic opn. – Counting

• Mode is the only measure of central tendency.

Nominal Scale Cont…

Examples:Numbers on Cricket players' jerseys that are used to identify each player.

Classifying data, e.g. m/f

No ordering, e.g. it makes no sense to state that M > F

Arbitrary labels, e.g., m/f, 0/1, etc

Ordinal Scale

• Numbers, letters or numerals are used to rank objects.

• Relative position of two or more objects on some characteristic.

• Used in Customer-oriented research.

Ordinal Scale Cont…

• Doesn’t provide how much less or more the attribute is.

• size of the interval between any two numerals is unknown.

• Operations: Mode, Median, Non parametric tests.

Ordinal Scale Cont…

Examples:

Grades scored by students at IBS.Rank preferences for several brands, flavors.Restaurants ranked from most like to least liked.Movie Ratings.

Interval Scale

• Also uses numerals to rank objects.

• Numerically equal distances on the scale represent equal distances in the property being measured.

• Arbitrary zero i.e. no natural zero.

Interval Scale Cont…

• Descriptive measures: mean, median, mode, range and standard deviation.

• Bi-variate correlation analysis, t-test, analysis of variance tests.

Interval Scale Cont…

Examples:Centigrade and Fahrenheit temperature scales.Measurement of Sea Level.Personality measures.

Differences make sense, but ratios do not (e.g., 30°-20°=20°-10°, but 20°/10° is not twice as hot!)

Ratio Scale

• All properties of Interval.• True, Natural or Absolute Zero.• Value of zero on a ratio scale

indicates the complete absence of the characteristic of interest.

• All Descriptive measures and inferential techniques are applicable to ratio-measured data.

Ratio Scale Cont…

Examples:Length, time, force, volume and area. A negative length is not possible.Temperature in Kelvin.Quantitative data such as interval or ratio data can be converted to categories on a qualitative scale but not Vice Versa.

Indicates Difference

Indicates direction of Difference

Indicate amount ofDifference

AbsoluteZero

Nominal

Ordinal

Interval

Ratio

Fundamental Difference

Permissible Arithmetic Operations

Nominal Ordinal Interval Ratio

Counting Greater than or Smaller

than

Addition or Subtraction

of scale values

Multiplication or Division of scale values

Examples of Appropriate Statistics

Nominal Ordinal Interval Ratio

Chi Square

Runs test

Median,Interquartile

range, Spearman's

rank correlation, Kolmogorov-smirnov test,

Mann-Whitney U

Mean, SD,

t –test, ANOVA,

Regression

Coefficient of Variation

Reliability

• Meaning:• The extent to which the instrument yields

the same results on repeated trials.• Consistency• Free from error

Reliability Cont…

• Examples:• ordinal measures are reliable if they

consistently rank order items in the same manner

• reliable interval measures consistently rank order and maintain the same distance between items.

Concept of Reliability

• Two Dimensions• Repeatability• Internal Consistency

Tests of Reliability

• Retest Method

• Same test is given to the same people after a period of time.

• Examination of consistency • Eg. Measuring Satisfaction level

Tests of Reliability Cont…

• Problems:• Time delays between measurement• Insufficient time between measurements• Respondent’s discernment of a disguised

purpose• Topic sensitivity• Introduction of extraneous moderating

variables between measurements

Equivalent Form Method

• Two measurement scales of a similar nature are developed

• Measure the correlation of scores generated by two instruments.

Equivalent form Method Contd..

• Problem• Framing two totally equivalent

questionnaires

Internal Consistency method

• Testing whether the data give same results even after some manipulations.

• Example

Internal Consistency method Contd..

• Problem: • Dependent on data manipulation or

divisions

Cronbach’s Alpha

WhereN = Number of items = Sum of item variance = Variance of the total composite

Kuder Richardson Formula-20

• In case of difficulty in obtaining the data at equal interval of time

ValidityValidity

• Ability of a scale or a measuring Ability of a scale or a measuring

instrument to measure what it is instrument to measure what it is

intended to measureintended to measure

• Does the instrument really measure Does the instrument really measure

what its designer claims it does?what its designer claims it does?

ExampleExample

• Validity of an examValidity of an exam

• Measure of the morale of employees Measure of the morale of employees

based on their absenteeism alonebased on their absenteeism alone

Classification of ValidityClassification of Validity

• Face ValidityFace Validity

• Collective agreement of experts and Collective agreement of experts and

researchers on the validity of the researchers on the validity of the

measurement scalemeasurement scale

• Experts determine if the scale is measuring Experts determine if the scale is measuring

what it is expected to measurewhat it is expected to measure

Classification of validityClassification of validity

• Content ValidityContent Validity• Adequacy in the selection of relevant Adequacy in the selection of relevant

variables for measurementvariables for measurement• Measurement contains a Measurement contains a

representative sample of the universe representative sample of the universe of subject matter of interest : Content of subject matter of interest : Content Validity is goodValidity is good

Classification of validityClassification of validity

• Determination of content validityDetermination of content validity• Intuitive logical process by research Intuitive logical process by research

designerdesigner• Use a panel of persons to judge how Use a panel of persons to judge how

well the instrument meets the well the instrument meets the standardsstandards

Classification of validityClassification of validity

“ “ Content Validity is primarily Content Validity is primarily

concerned with inferences about concerned with inferences about

test test constructionconstruction rather than the rather than the

inferences about the test inferences about the test scoresscores ” ”

Classification of validityClassification of validity

• Criterion Related ValidityCriterion Related Validity

• Degree to which a measurement Degree to which a measurement

instrument can analyze a variableinstrument can analyze a variable

• If a new measure is developed, it must If a new measure is developed, it must

correlate with other measures of the correlate with other measures of the

same constructsame construct

Classification of validity Classification of validity

• Criterion related validity can be Criterion related validity can be

categorized as :categorized as :

• Predictive ValidityPredictive Validity

• Concurrent Validity Concurrent Validity

Classification of validityClassification of validity

• Predictive validityPredictive validity

• The extent to which a future level of a The extent to which a future level of a

criterion variable can be predicted by criterion variable can be predicted by

a current measurement on a scalea current measurement on a scale

Classification of validityClassification of validity

• Concurrent validityConcurrent validity

• Related with the relationship Related with the relationship

between predictor variable and between predictor variable and

criterion variable ; evaluated at the criterion variable ; evaluated at the

same point of time same point of time

Classification of validityClassification of validity

• Construct ValidityConstruct Validity• Degree to which a measurement Degree to which a measurement

instrument represents and logically instrument represents and logically

connects through the underlying connects through the underlying

theory theory

Classification of validityClassification of validity

• ExampleExample

• A particular product purchased by a A particular product purchased by a

consumer or not, is not the question ; consumer or not, is not the question ;

why he has or has not purchased the why he has or has not purchased the

product is taken into account to judge product is taken into account to judge

construct validity construct validity

• Construct Validity is classified asConstruct Validity is classified as

• Convergent validityConvergent validity

• Discriminant validityDiscriminant validity

Classification of validityClassification of validity

Classification of validityClassification of validity

• Convergent ValidityConvergent Validity• Extent of correlation among different Extent of correlation among different

measures that are intended to measure the measures that are intended to measure the same conceptsame concept

• Discriminant ValidityDiscriminant Validity• Denotes the lack of or low correlation Denotes the lack of or low correlation

among the constructs that are supposed to among the constructs that are supposed to be differentbe different

• SensitivitySensitivity• Ability to accurately measure variability in Ability to accurately measure variability in

responses responses • GeneralizationGeneralization

• Amount of flexibility in interpreting the data in Amount of flexibility in interpreting the data in

different research designs.different research designs.• RelevanceRelevance

• Appropriateness of using a particular scale for Appropriateness of using a particular scale for measuring variablemeasuring variable..

Classification of validityClassification of validity

Understanding Reliability and ValidityUnderstanding Reliability and Validity

Sources of measurement problemsSources of measurement problems

RESPONDENT ASSOCIATED ERRORS:RESPONDENT ASSOCIATED ERRORS:

Non-Response ErrorsNon-Response Errors It includes,It includes,• Failure to respond completely Failure to respond completely • Failure to respond to one or more questions of the Failure to respond to one or more questions of the

surveyorsurveyor• Unit non-response, Item non-response Unit non-response, Item non-response

Response bias Response bias

Sources of measurement problemsSources of measurement problems

• INSTRUMENT ASSOCIATED ERRORINSTRUMENT ASSOCIATED ERROR

• Poor questionnaire designPoor questionnaire design

• Improper selection of samplesImproper selection of samples

• Complex questionnaireComplex questionnaire

Sources of measurement problemsSources of measurement problems

• SITUATIONAL ERRORSSITUATIONAL ERRORS• Example: Location of the interviewExample: Location of the interview

• MEASURER AS ERROR SOURCEMEASURER AS ERROR SOURCE• Body language and gestures Body language and gestures • Failure to record the full responseFailure to record the full response• Using irrelevant statistical toolsUsing irrelevant statistical tools