measures of scales
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Variables & Measures of Scales
Dr. Shanti TejwaniAsst. Prof. M.B. Khalsa Institute of Education, [email protected]
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An attributes/ characteristics of thing ,objects or events which varies (which can different Values) is known as Variable.
Attandence of Students SexReligionBooks in libraryMode of journeyTime durationAggressionAngerAge
Variables
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Variables
Continuous
Discontinuous
Dichotomy
Polytomy
Types of Variable
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Measures of Scales
Nominal
Ordinal
Interval
Ratio
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Nominal Scale
1
2
3
4
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Categorization of dataClassified into category
Nominal Scale
Numbers forming a nominal scale are no more than labels used solely to identify different categories of responses
Example: RELIGION
Hindu –1 Christian--2 Muslim---3 Buddhism----4
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Central Tendency– Mode The mode is the most frequent category – only statistics applicable to nominal variableNon Parametric Statistics ---- Chi- Square
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ORDINAL SCALE
Secondplace
Firstplace
Thirdplace
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Ordinal-Scaled Responses
An ordinal scale is more powerful than a nominal scale in that the numbers possess the property of rank order
Classification + Order
Examples : To categories people according to level of EducationPunctualityHome work Cleanliness
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Measures of Central Tendency Mode Median Percentile Rank Difference Correlation (ρ)
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INTERVAL SCALE
5, 8, 10, 11
3, 6, 8, 9
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Interval-Scaled Responses
An interval scale has all the properties of an ordinal scale and the differences between the scale values can be meaningfully interpreted
EXAMPLE
Achievement of the students
Creativity of Students
All Psychological Variable
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Impact of Arbitrariness of an Interval Scale’s Starting Point
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Mode Median Arithmetic Mean Rank Difference correlation Product Moment Correlation Variance
Measures of Central Tendency and Variability
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Ratio Scale Kilogram
Gram
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Copyright © Houghton Mifflin Company. All rights reserved. 9 |
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Ratio-Scaled Responses Ratio scales possess all the properties of an
interval scale and the ratios of numbers on these scales have meaningful interpretations
Examples
Length of the Rod
Weight of School Bag
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Mode Median Arithmetic Mean Rank Difference correlation Product Moment Correlation Variance
Measures of Central Tendency and Variability
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Characteristics of Different Levels of Scale Measurement
Type of Scale
Data Characteristics
Numerical Operation
Descriptive Statistics
Examples
Nominal Classification but no order, distance, or origin
Counting Frequency in each categoryPercent in each categoryMode
Gender (1=Male, 2=Female)
Ordinal Classification and order but no distance or unique origin
Rank ordering MedianRangePercentile ranking
Academic status (1=Professor 2= Associate Professor 3= Assistant Professor)
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Characteristics of Different Levels of Scale Measurement
Type of Scale
Data Characteristics
Numerical Operation
Descriptive Statistics
Examples
Interval Classification, order, and distance but no unique origin
Arithmetic operations that preserve order and magnitude
MeanStandard deviationVariance
Temperature in degrees
Ratio Classification, order, distance and unique origin
Arithmetic operations on actual quantities
Geometric meanCoefficient of variation
Age in yearsIncome
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Summarisation
Four levels of Measurements Nominal
◦ Measures categories Ordinal
◦ Categories + rank and order Interval
◦ Equal distance between any two consecutive measures
Ratio◦ Intervals + meaningful zeros
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