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Measurements & Scaling
The Learners
Serial Name Roll
01 Atiullah Akond 21-070
02 Ripon Miya 21-077
03 Umar Khaled 21-098
04 Md. Sakil Ahmed 21-106
05 Al Mamun 21-127
06 Md. Abdur Rahim 21-202
Measurements & Scaling
Measurement
 Measurement refers to assigning numbers and symbols to the
characteristics of the object as per the specified rules.
 It’s actually the use of a yardstick to determine or judge some
features of a physical or abstract objects or concepts (eg.
weight, height , motivation, love etc.).
Measurements & Scaling (cont.)
Scaling
 the procedure of measuring and assigning the objects to the numbers
according to the specified rules.
 Locating the measured objects on the continuum.
Measurements & Scaling (cont.)
Example
Consider a scale from 1 to 10 for locating consumer characteristics
(preference for the product). Each respondent is assigned a number from 1
to 10 denoting the degree of unfavourableness for the product, with ‘1’
indicating extremely unfavorable and ’10’ indicating extremely favorable.
Here, the Measurement is...
the process of assigning the actual number from 1 to 10 to each respondent.
And the Scaling is…
placing respondents on a continuum with respect to their preference for the
product.
Concepts
 To understand and communicate information about objects and events,
there must be a common ground on which to do it. Concepts serve this
purpose.
 A concept is a generally accepted collection of meanings or
characteristics associated with certain events, objects, conditions,
situations, and behaviors.
 For example, we see a man passing and identify that he is running,
walking, skipping, crawling, or hopping. These movements all
represent concepts.
Constructs
 Constructs are mental abstractions that we used to express the ideas,
people, organizations, events and/objects/things.
 Examples: morality, depression, air pollution, height, secularism etc.
 constructs are mental abstractions because seldom are
constructs directly observable (e.g., we cannot directly
observe depression, even though we may associate depression with signs
such as a person that often cries, engages in self-harm, has mood swings,
and so forth).
Variables
When we operationalized a concept, we are creating
variables.
Variables can be defined as any characteristics that varies
(meaning it must have at least two variables)
Examples:
 Height ( participant or subject variable)
Stress ( response variable)
Age ( participant or subject variable)
Levels of Measurement Scale
Four Types
Nominal scale
Ordinal scale
Interval scale
Ratio scale
Measurement means-
The process of applying numbers to objects
according to a set of rules.
WHY SCALING-
Measurement scales are used to categorize
and/or quantify variables.
NOMINAL SCALE
Assign numbers to objects where different number
indicates different objects.
 No real meanings
 Just differentiate between objects
Example-
-Football players uniform number
The number provides no insights into the players
position.
Generally shown in pie chart.
ORDINAL SCALE
Assign numbers to objects like nominal but
the numbers also have meaningful order.
Numbers indicate placement and order.
Example-
In a race - 1st, 2nd, 3rd and so on.
Generally shown in Bar diagram.
INTERVAL SCALE
Numbers have order like ordinal but there are
also equal intervals between adjacent
categories.
Example-
-Temperature in degrees Fahrenheit –
The difference between 78 degrees and 79
degrees is the same as 45 degrees and 46
degrees.
Generally shown in Histogram.
RATIO SCALE
Ratio is meaningful like interval.
There is a true zero point.(Absence)
Regression analysis in thousands , in
millions.
DIFFERENCE BETWEEN
 INTERVAL VS ORDINAL
 INTERVAL VS RATIO
 NOMINAL VS INTERVAL, ORDINAL,
RATIO.
Mathematical and Statistical Analysis of Scales
1. Discrete Measures
2. Continuous Measures
Discrete Measures
-Measures that take only one of a finite number of values.
-Include any yes-or-no response, matching, color choice etc.
-Do not represent intensity of measures, only membership.
-Nominal and Ordinal Scales are discrete measures.
Example:
Student politics should be banned from Dhaka University Campus-
 Disagree
 Neutral
 Agree
Continuous Measures
- measures that reflect the intensity of a concept by assigning values that take
on any value along some scale range.
- ratio measures are continuous measures.
Example
Strongly
Disagre
e
Disagree Neutral Agree Strongly
Agree
Political turmoil is the main
hindrance for launching a
business in Bangladesh.
1 2 3 4 5
Index Measures
- Indexes
- Composites
Index Measure
-assigns a value based on how much of the concept being measured is
associated with an observation.
-are often formed by putting several variables together.
Example
A researcher is interested in measuring job satisfaction and one of the key
variables is job-related depression.
Questions:
 When I think about myself and my job, I feel downhearted and blue.
 When I’m at work, I often get tired for no reason.
 When I’m at work, I often find myself restless and can’t keep still.
 When at work, I am more irritable than usual.
Composite Measure
- assigns a value based on a mathematical derivation of multiple variables.
Questions Strongly
Disagree
Disagree Neutral Agree Strongly
Agree
When I think about myself and my
job, I feel downhearted and blue.
1 2 3 4 5
When I’m at work, I often get tired
for no reason.
1 2 3 4 5
When I’m at work, I often find
myself restless and can’t keep still.
1 2 3 4 5
When at work, I am more irritable
than usual.
1 2 3 4 5
Comparative Scale
A type of scale where one object is compared with another
and relative measure of performance is obtained.
Types of Comparative Scaling
i. Rank Order Scaling
ii. Paired Comparison Scaling
iii. Constant Sum Scaling
iv. Sorting
Rank Order Scaling
A rank order scale gives the respondent a set of items and ask
them to put the items in some form of order.
Example: Brand Rank
Pepsodent 1
Colgate 2
Whiteplus 3
Paired Comparison Scaling
The paired comparison scaling is a comparative scaling
technique wherein the respondent is shown two objects at the
same time and is asked to select one according to the defined
criteria.
Example of Paired Comparison
10 pairs of soft drink brand out of 5 brands and respondents are asked to indicate the one they
prefer:
Brand Coke Sprite Pepsi Mojo Dew No. of
time
preferre
d
Coke 0 0 1 0 3
Sprite 1 0 1 0 2
Pepsi 1 1 1 1 0
Mojo 0 0 0 0 4
Dew 1 1 0 1 1
No. of
time
preferred
3 2 0 4 1
1=column brand is
preferred to the row
brand
0= row brand is
preferred to the
column brand
Constant Sum Scaling
Respondents are presented with a list of object and asked
to allocate a constant sum of points with respect to some
criterion.
Example: Allocating 100 points among 4 attributes of
Attributes Point
Hassle free ride 20
Saving time 30
Reasonable fare 40
Availability 10
Total 100
Sorting
Respondents are required to indicate their attitudes by sorting object with
respect to some criterion.
Example:
suppose the respondents are given 100 motivational statements on
individual cards and are asked to place these in 11 piles, ranging from the
“most agreed with” to the “least agreed with”. Generally, the most agreed
statement is placed on the top while the least agreed statement at the
bottom.
Non-comparative Scales
1) Continuous Rating Scale
2) Itemized Rating Scale
Likert
Semantic
Differential Stapel
Continuous Rating Scale
 It’s a scale where respondents rate the objects by
placing a mark at the appropriate position on a line
that runs from one extreme to another.
For example: How would you rate ‘’Bata’’ as a brand?
1) Extremely Favoured ---------------------------------------------------------- Extremely Unfavoured.
2) Extremely Favoured ---------------------------------------------------------- Extremely Unfavoured.
0 10 20 30 40 50 60 70 80 90 100
Likert Scale
 It requires the respondents to indicate a degree of agreement or
disagreement about a series of statements related to particular object.
Strongly agree Strongly Disagree
Example:
statements Strongly
Disagree
Disagree Neither
disagree
nor agree
Agree Strongly
Agree
Advertisements
create a sense of
deprivation
1 2 3 4 5
Advertisements
augment sales
revenue
1 2 3 4 5
Advertisements
aid to increase
market share
1 2 3 4 5
Advertisements
create positive
perception .
1 2 3 4 5
Semantic Differential
 It is a seven point rating scale with end points associated with bipolar
labels that have semantic meanings. Here, respondents are asked to rate
a products, service or organizations with multi-point questions with
bipolar adjectives.
Example: If you want to rate Walton BD Ltd. , you may use multi-point questions.
1) Low cost products
Unlikely ---:---:---:---:---:---:---:--- Likely
2) How is its service?
Unattractive ---:---:---:---:---:---:--- Attractive
3) Customer perception
Bad ---:---:---:---:---:---:--- Good
Stapel Scale
 It’s a unipolar scale with 10 categories from -5 to +5 without any neutral point.
Respondents are asked to indicate how accurately the term (pole) describes the objects.
The higher the positive number, the more accurately the term describes the objects. The
lower the negative values, the more inaccurately the term describes the object.
Example: Rating a bank.
+5 +5
+4 +4
+3 +3
+2 +2
+1 +1
Friendly Personnel Lower interest
-1 -1
-2 -2
-3 -3
-4 -4
-5 -5
For well constructing itemized scale six
decisions must be made:
1.Number of a scale categories to use:
-The greater the number of classes, the more the discrimination among stimulus
object is possible.
-The more the number of classes, the greater is the problem for respondents to
handle.
- The appropriate number of classes: 5 -10.
Example:
1.Strongly agree
2.Somewhat agree
3.Neither
4.Somewhat disagree
5.Strongly disagree
2. Balanced versus unbalanced
scale:
Balanced scale means: Number of favorable categories =Number of unfavorable categories.
Unbalanced scale means: Number of favorable categories ≠ Number of unfavorable
categories.
Balanced scale Unbalanced scale
Extremely good Extremely Good
Very good Very Good
Good Good
Bad Somewhat Good
Very bad Bad
Extremely bad Very bad
3. Odd or even number of categories:
 In an odd number there is a neutral point in the middle
-If there are a lot of possible neutral answers then it should be provided.
4. Forced versus non forced scale:
 The question is whether there should be any option for no opinion response
category.
-Depends on the possibility of whether there could be some or more respondents
with no opinion.
5. Nature and degree of category label:
 The scales may have verbal labels, numerical labels or may be unlabeled.
Example: verbal label
Strongly disagree
Disagree
Neither
Agree
Strongly agree
Example: numerical labels
Strongly disagree 1 2 3 4 5 Strongly agree
Example: Unlabeled
Strongly disagree............. Strongly agree
6. Physical form or configuration:
 There could be a number of options with respect to form of configuration of
a scale.
-A scale may be presented vertically or horizontally.
-Response may be positive negative or both.
-There can be number or without number is category may be specified.
-There may be box or without box.

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Measure & scaling

  • 2. The Learners Serial Name Roll 01 Atiullah Akond 21-070 02 Ripon Miya 21-077 03 Umar Khaled 21-098 04 Md. Sakil Ahmed 21-106 05 Al Mamun 21-127 06 Md. Abdur Rahim 21-202
  • 3. Measurements & Scaling Measurement  Measurement refers to assigning numbers and symbols to the characteristics of the object as per the specified rules.  It’s actually the use of a yardstick to determine or judge some features of a physical or abstract objects or concepts (eg. weight, height , motivation, love etc.).
  • 4. Measurements & Scaling (cont.) Scaling  the procedure of measuring and assigning the objects to the numbers according to the specified rules.  Locating the measured objects on the continuum.
  • 5. Measurements & Scaling (cont.) Example Consider a scale from 1 to 10 for locating consumer characteristics (preference for the product). Each respondent is assigned a number from 1 to 10 denoting the degree of unfavourableness for the product, with ‘1’ indicating extremely unfavorable and ’10’ indicating extremely favorable. Here, the Measurement is... the process of assigning the actual number from 1 to 10 to each respondent. And the Scaling is… placing respondents on a continuum with respect to their preference for the product.
  • 6. Concepts  To understand and communicate information about objects and events, there must be a common ground on which to do it. Concepts serve this purpose.  A concept is a generally accepted collection of meanings or characteristics associated with certain events, objects, conditions, situations, and behaviors.  For example, we see a man passing and identify that he is running, walking, skipping, crawling, or hopping. These movements all represent concepts.
  • 7. Constructs  Constructs are mental abstractions that we used to express the ideas, people, organizations, events and/objects/things.  Examples: morality, depression, air pollution, height, secularism etc.  constructs are mental abstractions because seldom are constructs directly observable (e.g., we cannot directly observe depression, even though we may associate depression with signs such as a person that often cries, engages in self-harm, has mood swings, and so forth).
  • 8. Variables When we operationalized a concept, we are creating variables. Variables can be defined as any characteristics that varies (meaning it must have at least two variables) Examples:  Height ( participant or subject variable) Stress ( response variable) Age ( participant or subject variable)
  • 9. Levels of Measurement Scale Four Types Nominal scale Ordinal scale Interval scale Ratio scale
  • 10. Measurement means- The process of applying numbers to objects according to a set of rules. WHY SCALING- Measurement scales are used to categorize and/or quantify variables.
  • 11. NOMINAL SCALE Assign numbers to objects where different number indicates different objects.  No real meanings  Just differentiate between objects Example- -Football players uniform number The number provides no insights into the players position. Generally shown in pie chart.
  • 12. ORDINAL SCALE Assign numbers to objects like nominal but the numbers also have meaningful order. Numbers indicate placement and order. Example- In a race - 1st, 2nd, 3rd and so on. Generally shown in Bar diagram.
  • 13. INTERVAL SCALE Numbers have order like ordinal but there are also equal intervals between adjacent categories. Example- -Temperature in degrees Fahrenheit – The difference between 78 degrees and 79 degrees is the same as 45 degrees and 46 degrees. Generally shown in Histogram.
  • 14. RATIO SCALE Ratio is meaningful like interval. There is a true zero point.(Absence) Regression analysis in thousands , in millions.
  • 15. DIFFERENCE BETWEEN  INTERVAL VS ORDINAL  INTERVAL VS RATIO  NOMINAL VS INTERVAL, ORDINAL, RATIO.
  • 16. Mathematical and Statistical Analysis of Scales 1. Discrete Measures 2. Continuous Measures
  • 17. Discrete Measures -Measures that take only one of a finite number of values. -Include any yes-or-no response, matching, color choice etc. -Do not represent intensity of measures, only membership. -Nominal and Ordinal Scales are discrete measures. Example: Student politics should be banned from Dhaka University Campus-  Disagree  Neutral  Agree
  • 18. Continuous Measures - measures that reflect the intensity of a concept by assigning values that take on any value along some scale range. - ratio measures are continuous measures. Example Strongly Disagre e Disagree Neutral Agree Strongly Agree Political turmoil is the main hindrance for launching a business in Bangladesh. 1 2 3 4 5
  • 20. Index Measure -assigns a value based on how much of the concept being measured is associated with an observation. -are often formed by putting several variables together. Example A researcher is interested in measuring job satisfaction and one of the key variables is job-related depression. Questions:  When I think about myself and my job, I feel downhearted and blue.  When I’m at work, I often get tired for no reason.  When I’m at work, I often find myself restless and can’t keep still.  When at work, I am more irritable than usual.
  • 21. Composite Measure - assigns a value based on a mathematical derivation of multiple variables. Questions Strongly Disagree Disagree Neutral Agree Strongly Agree When I think about myself and my job, I feel downhearted and blue. 1 2 3 4 5 When I’m at work, I often get tired for no reason. 1 2 3 4 5 When I’m at work, I often find myself restless and can’t keep still. 1 2 3 4 5 When at work, I am more irritable than usual. 1 2 3 4 5
  • 22. Comparative Scale A type of scale where one object is compared with another and relative measure of performance is obtained.
  • 23. Types of Comparative Scaling i. Rank Order Scaling ii. Paired Comparison Scaling iii. Constant Sum Scaling iv. Sorting
  • 24. Rank Order Scaling A rank order scale gives the respondent a set of items and ask them to put the items in some form of order. Example: Brand Rank Pepsodent 1 Colgate 2 Whiteplus 3
  • 25. Paired Comparison Scaling The paired comparison scaling is a comparative scaling technique wherein the respondent is shown two objects at the same time and is asked to select one according to the defined criteria.
  • 26. Example of Paired Comparison 10 pairs of soft drink brand out of 5 brands and respondents are asked to indicate the one they prefer: Brand Coke Sprite Pepsi Mojo Dew No. of time preferre d Coke 0 0 1 0 3 Sprite 1 0 1 0 2 Pepsi 1 1 1 1 0 Mojo 0 0 0 0 4 Dew 1 1 0 1 1 No. of time preferred 3 2 0 4 1 1=column brand is preferred to the row brand 0= row brand is preferred to the column brand
  • 27. Constant Sum Scaling Respondents are presented with a list of object and asked to allocate a constant sum of points with respect to some criterion. Example: Allocating 100 points among 4 attributes of Attributes Point Hassle free ride 20 Saving time 30 Reasonable fare 40 Availability 10 Total 100
  • 28. Sorting Respondents are required to indicate their attitudes by sorting object with respect to some criterion. Example: suppose the respondents are given 100 motivational statements on individual cards and are asked to place these in 11 piles, ranging from the “most agreed with” to the “least agreed with”. Generally, the most agreed statement is placed on the top while the least agreed statement at the bottom.
  • 29. Non-comparative Scales 1) Continuous Rating Scale 2) Itemized Rating Scale Likert Semantic Differential Stapel
  • 30. Continuous Rating Scale  It’s a scale where respondents rate the objects by placing a mark at the appropriate position on a line that runs from one extreme to another. For example: How would you rate ‘’Bata’’ as a brand? 1) Extremely Favoured ---------------------------------------------------------- Extremely Unfavoured. 2) Extremely Favoured ---------------------------------------------------------- Extremely Unfavoured. 0 10 20 30 40 50 60 70 80 90 100
  • 31. Likert Scale  It requires the respondents to indicate a degree of agreement or disagreement about a series of statements related to particular object. Strongly agree Strongly Disagree Example: statements Strongly Disagree Disagree Neither disagree nor agree Agree Strongly Agree Advertisements create a sense of deprivation 1 2 3 4 5 Advertisements augment sales revenue 1 2 3 4 5 Advertisements aid to increase market share 1 2 3 4 5 Advertisements create positive perception . 1 2 3 4 5
  • 32. Semantic Differential  It is a seven point rating scale with end points associated with bipolar labels that have semantic meanings. Here, respondents are asked to rate a products, service or organizations with multi-point questions with bipolar adjectives. Example: If you want to rate Walton BD Ltd. , you may use multi-point questions. 1) Low cost products Unlikely ---:---:---:---:---:---:---:--- Likely 2) How is its service? Unattractive ---:---:---:---:---:---:--- Attractive 3) Customer perception Bad ---:---:---:---:---:---:--- Good
  • 33. Stapel Scale  It’s a unipolar scale with 10 categories from -5 to +5 without any neutral point. Respondents are asked to indicate how accurately the term (pole) describes the objects. The higher the positive number, the more accurately the term describes the objects. The lower the negative values, the more inaccurately the term describes the object. Example: Rating a bank. +5 +5 +4 +4 +3 +3 +2 +2 +1 +1 Friendly Personnel Lower interest -1 -1 -2 -2 -3 -3 -4 -4 -5 -5
  • 34. For well constructing itemized scale six decisions must be made: 1.Number of a scale categories to use: -The greater the number of classes, the more the discrimination among stimulus object is possible. -The more the number of classes, the greater is the problem for respondents to handle. - The appropriate number of classes: 5 -10. Example: 1.Strongly agree 2.Somewhat agree 3.Neither 4.Somewhat disagree 5.Strongly disagree
  • 35. 2. Balanced versus unbalanced scale: Balanced scale means: Number of favorable categories =Number of unfavorable categories. Unbalanced scale means: Number of favorable categories ≠ Number of unfavorable categories. Balanced scale Unbalanced scale Extremely good Extremely Good Very good Very Good Good Good Bad Somewhat Good Very bad Bad Extremely bad Very bad
  • 36. 3. Odd or even number of categories:  In an odd number there is a neutral point in the middle -If there are a lot of possible neutral answers then it should be provided. 4. Forced versus non forced scale:  The question is whether there should be any option for no opinion response category. -Depends on the possibility of whether there could be some or more respondents with no opinion.
  • 37. 5. Nature and degree of category label:  The scales may have verbal labels, numerical labels or may be unlabeled. Example: verbal label Strongly disagree Disagree Neither Agree Strongly agree Example: numerical labels Strongly disagree 1 2 3 4 5 Strongly agree Example: Unlabeled Strongly disagree............. Strongly agree
  • 38. 6. Physical form or configuration:  There could be a number of options with respect to form of configuration of a scale. -A scale may be presented vertically or horizontally. -Response may be positive negative or both. -There can be number or without number is category may be specified. -There may be box or without box.