Measures of scales

Variables & Measures of Scales

Dr. Shanti TejwaniAsst. Prof. M.B. Khalsa Institute of Education, Indoreshanti_tejwani@yahoo.com

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

Variables

Continuous

Discontinuous

Dichotomy

Polytomy

Types of Variable

Measures of Scales

Nominal

Ordinal

Interval

Ratio

Nominal Scale

1

2

3

4

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

Central Tendency– Mode The mode is the most frequent category – only statistics applicable to nominal variableNon Parametric Statistics ---- Chi- Square

ORDINAL SCALE

Secondplace

Firstplace

Thirdplace

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

Measures of Central Tendency Mode Median Percentile Rank Difference Correlation (ρ)

INTERVAL SCALE

5, 8, 10, 11

3, 6, 8, 9

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

9 | 13

Impact of Arbitrariness of an Interval Scale’s Starting Point

Mode Median Arithmetic Mean Rank Difference correlation Product Moment Correlation Variance

Measures of Central Tendency and Variability

Ratio Scale Kilogram

Gram

Copyright © Houghton Mifflin Company. All rights reserved. 9 |

16

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

Mode Median Arithmetic Mean Rank Difference correlation Product Moment Correlation Variance

Measures of Central Tendency and Variability

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)

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

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

THANKS