measurenent scales
TRANSCRIPT
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Measurement Scales
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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.
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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.
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Goal of measurement
• To provide the highest quality, lowest error data for testing hypotheses.
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Must know…..
• Concept• Construct• Constitutive Concept• Operational Concept
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• Unidimensionality • Linearity• Validity • Reliability• Accuracy and precision • Simplicity • Practicability
Characteristics of a Good measurement
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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.
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Measurement Scales
• Nominal scale• Ordinal Scale• Interval Scale• Ratio Scale
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Nominal Scale
• Most elementary method of measurement.
• Categorical data and numbers that are simply used as identifiers or names.
• Mutually exclusive and collectively exhaustive.
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Nominal Scale Cont…
• Numbers doesn't have any quantitative value.
• Arithmetic opn. – Counting
• Mode is the only measure of central tendency.
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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
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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.
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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.
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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.
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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.
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Interval Scale Cont…
• Descriptive measures: mean, median, mode, range and standard deviation.
• Bi-variate correlation analysis, t-test, analysis of variance tests.
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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!)
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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.
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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.
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Indicates Difference
Indicates direction of Difference
Indicate amount ofDifference
AbsoluteZero
Nominal
Ordinal
Interval
Ratio
Fundamental Difference
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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
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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
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Reliability
• Meaning:• The extent to which the instrument yields
the same results on repeated trials.• Consistency• Free from error
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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.
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Concept of Reliability
• Two Dimensions• Repeatability• Internal Consistency
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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
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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
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Equivalent Form Method
• Two measurement scales of a similar nature are developed
• Measure the correlation of scores generated by two instruments.
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Equivalent form Method Contd..
• Problem• Framing two totally equivalent
questionnaires
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Internal Consistency method
• Testing whether the data give same results even after some manipulations.
• Example
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Internal Consistency method Contd..
• Problem: • Dependent on data manipulation or
divisions
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Cronbach’s Alpha
WhereN = Number of items = Sum of item variance = Variance of the total composite
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Kuder Richardson Formula-20
• In case of difficulty in obtaining the data at equal interval of time
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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?
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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
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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
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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
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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
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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 ” ”
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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
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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
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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
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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
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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
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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
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• Construct Validity is classified asConstruct Validity is classified as
• Convergent validityConvergent validity
• Discriminant validityDiscriminant validity
Classification of validityClassification of validity
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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
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• 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
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Understanding Reliability and ValidityUnderstanding Reliability and Validity
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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
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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
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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