Unit3 - Subjective Questions

Measurement scales categorize the different ways in which variables are defined and quantified. There are four primary levels:

1. Nominal Scale: The simplest level where numbers serve only as labels or tags for identifying and classifying objects. There is no intrinsic ordering.
   • Example: Gender (Male, Female), Jersey numbers of football players.
2. Ordinal Scale: A ranking scale in which numbers are assigned to objects to indicate the relative extent to which the objects possess some characteristic. The difference between ranks is not necessarily equal.
   • Example: Quality ranking (Good, Better, Best), Education level (High School, Bachelor's, Master's).
3. Interval Scale: A scale where numerically equal distances on the scale represent equal values in the characteristic being measured. It has an arbitrary zero point, not a true zero.
   • Example: Temperature in Celsius or Fahrenheit.
4. Ratio Scale: The highest level of measurement. It possesses all the properties of the nominal, ordinal, and interval scales, plus an absolute zero point. Ratios of numbers on this scale are meaningful.
   • Example: Weight, Height, Income, Age.

Distinction between Primary and Secondary Data:

Advantages of Secondary Data:

• Resource Saving: It saves significant time and money compared to primary data collection.
• Accessibility: Some data (like census data) cannot be collected by individuals and must be sourced secondarily.
• Basis for Comparison: It helps in comparing primary data results with existing benchmarks.
• Longitudinal Analysis: Allows for the analysis of trends over time using historical records.

Scaling techniques are classified into two broad categories:

1. Comparative Scaling:

• Definition: In this technique, there is a direct comparison of stimulus objects. The data obtained is interpreted in relative terms and generally has only ordinal or rank order properties.
• Characteristics:
  • Respondents compare one item against another (e.g., "Do you prefer Brand A over Brand B?").
  • It forces a choice between options.
  • Examples: Paired Comparison, Rank Order, Constant Sum Scale.

2. Non-Comparative Scaling:

• Definition: Also known as monadic scales, each object is scaled independently of the others in the stimulus set. The resulting data are generally assumed to be interval or ratio scaled.
• Characteristics:
  • Respondents evaluate only one object at a time (e.g., "Rate Brand A on a scale of 1 to 10").
  • No direct comparison is made with other objects.
  • Examples: Continuous Rating Scales, Likert Scale, Semantic Differential Scale.

Likert Scale:
It is a widely used non-comparative rating scale, often referred to as a summated scale. It requires respondents to indicate a degree of agreement or disagreement with each of a series of statements regarding the stimulus objects.

Construction:

• The scale typically consists of 5 or 7 response categories.
• Standard descriptors range from "Strongly Disagree" to "Strongly Agree".
• Format:
  1. Strongly Disagree
  2. Disagree
  3. Neutral / Neither Agree nor Disagree
  4. Agree
  5. Strongly Agree

Analysis:

• Each response category is assigned a numerical score (e.g., 1 to 5 or -2 to +2).
• The analysis can be done on an item-by-item basis (profile analysis) or by calculating a total (summated) score for each respondent.
• It generates interval data, allowing for the calculation of the mean and standard deviation.

A well-designed questionnaire is crucial for accurate data collection. The essential steps are:

1. Specify the Information Needed: Clearly define the problem and the objectives of the research to determine what data is required.
2. Determine the Type of Interviewing Method: Decide if the questionnaire is for personal interviews, mail, telephone, or online surveys, as this affects the design.
3. Determine Individual Question Content: Assess if the question is necessary and if respondents are informed and willing to answer.
4. Design the Question Structure: Choose between unstructured (open-ended) and structured (closed-ended/multiple choice) questions.
5. Determine Question Wording: Use simple, unambiguous, and unbiased language. Avoid double-barreled questions.
6. Arrangement of Questions: Organize questions logically (e.g., easy questions first, sensitive questions later, funnel approach).
7. Form and Layout: Ensure the questionnaire is visually appealing and easy to read.
8. Pre-testing: Test the questionnaire on a small sample to identify and fix errors or confusion before the full launch.

Arithmetic Mean:
It is the most popular measure of central tendency, often referred to simply as the "average." It is defined as the sum of all observations divided by the number of observations.
Formula:

Mathematical Properties:

1. Sum of Deviations: The algebraic sum of the deviations of a set of numbers from their arithmetic mean is always zero.
2. Sum of Squared Deviations: The sum of the squared deviations of the observations from their mean is minimum (less than the sum of squared deviations from any other value).
3. Combined Mean: If we have the means and number of items of two or more groups, we can calculate the combined mean of the entire group.
4. Linearity: If every observation is increased or multiplied by a constant, the mean is also increased or multiplied by that same constant.

Data preparation is the process of converting raw data into a structured format suitable for analysis.

1. Editing:

• Definition: The process of reviewing the data collection forms to ensure accuracy, consistency, and completeness.
• Purpose: To detect and correct errors and omissions. For example, checking if a respondent skipped a question or ticked two options for a single-choice question.
• Types:
  • Field Editing: Done immediately after the interview.
  • Central Editing: thorough review at the office.

2. Coding:

• Definition: The process of assigning numerical or other symbols to answers so that responses can be put into a limited number of categories or classes.
• Process:
  • For closed-ended questions (e.g., Male/Female), pre-coding is often done (1=Male, 2=Female).
  • For open-ended questions, categories are created based on the responses received, and codes are assigned to these categories.
• Outcome: A codebook is usually created to map the raw data to the codes entered into the software (SPSS, Excel).

Calculation Table:

1. Arithmetic Mean ():

2. Median:

• Determine Median Class: . Look for . The class is 20-30.
• (Lower limit) = 20
• (frequency of median class) = 15
• (cumulative freq of preceding class) = 15
• (class width) = 10

Formula:

A good measure of central tendency (average) should possess the following characteristics to be statistically sound and useful:

1. Rigidly Defined: It should have a clear, fixed definition so that different people calculate the same value from the same data.
2. Based on All Observations: The calculation should take into account every single item in the series (like the Mean).
3. Easy to Understand and Calculate: It should not be overly complex mathematically.
4. Capable of Further Algebraic Treatment: It should be usable in further statistical analysis (e.g., Mean is used in Standard Deviation, Correlation).
5. Least Affected by Sampling Fluctuations: If different samples are drawn from the same population, the measure should remain relatively stable.
6. Not Unduly Affected by Extreme Values: Ideally, a few very small or very large values (outliers) should not skew the average significantly (Median is better than Mean in this regard).

Mode:
The Mode is the value in a distribution that occurs most frequently. It is the point of maximum density in the data.

Calculation for Grouped Data:
First, identify the Modal Class, which is the class interval with the highest frequency.

Formula:

Where:

• = Lower limit of the modal class.
• = Frequency of the modal class.
• = Frequency of the class preceding the modal class.
• = Frequency of the class succeeding the modal class.
• = Width (magnitude) of the class interval.

Note: This formula applies when class intervals are continuous and equal.

Semantic Differential Scale:
This is a non-comparative 7-point rating scale used to measure the psychological meaning of an object to an individual.

Structure:

• It consists of a series of bipolar adjectives (opposites) placed at the ends of the scale.
• Examples of bipolar pairs: Good-Bad, Powerful-Weak, Modern-Old Fashioned, Clean-Dirty.
• Respondents mark the point on the continuum that best describes their feelings toward the object.

Example:
Please rate the Service Quality:
Reliable --- --- --- --- --- --- --- Unreliable
Fast --- --- --- --- --- --- --- Slow

Analysis:

• The scale measures direction and intensity of attitude.
• Numerical values (e.g., +3 to -3 or 1 to 7) are assigned to the spaces.
• It helps in plotting an image profile to compare different brands or products visually.

Paired Comparison Scaling:
A comparative scaling technique where a respondent is presented with two objects and asked to select one according to some criterion.

Mechanism:

• If there are brands to be evaluated, the respondent has to make paired comparisons.
• It creates ordinal data.

Example:
A researcher wants to determine preference among 4 brands of Toothpaste (A, B, C, D).
Number of pairs = pairs.
The pairs presented would be: {A,B}, {A,C}, {A,D}, {B,C}, {B,D}, {C,D}.

For each pair, the user asks: "Which brand do you prefer?"

Advantages: It closely mimics the marketplace selection process.
Disadvantages: If the number of objects () is large, the number of comparisons becomes unmanageable for the respondent.

Empirical Relationship:
For a moderately skewed (asymmetrical) frequency distribution, there exists an approximate relationship between the Mean, Median, and Mode.

The Formula:

OR

Application:

• Missing Value: It is used to estimate one measure when the other two are known.
• Skewness Check:
  • If Mean = Median = Mode, the distribution is Symmetrical (Normal).
  • If Mean > Median > Mode, the distribution is Positively Skewed.
  • If Mean < Median < Mode, the distribution is Negatively Skewed.

Observation Method:
A method of data collection where the researcher observes the behavior, actions, or events of the subjects directly without asking them questions.

Types:

• Structured vs. Unstructured.
• Disguised (participants don't know they are watched) vs. Undisguised.
• Human vs. Mechanical observation.

Advantages:

• Objectivity: Removes the bias of the respondent (e.g., lying about their habits).
• Current Behavior: Captures behavior as it happens, rather than relying on memory.
• Non-Verbal Data: Useful for subjects who cannot articulate (e.g., children, animals).

Disadvantages:

• Limited Scope: Cannot observe underlying motives, beliefs, or feelings.
• Time-Consuming: Researchers must wait for the event to occur.
• Hawthorne Effect: If subjects know they are being observed, they may alter their behavior.

Characteristics of Interval Scale:

1. Order and Distance: It has the properties of the ordinal scale (ranking) but also ensures that the distance between adjacent points on the scale is equal.
2. Difference is Meaningful: The difference between 20 and 30 is the same as the difference between 40 and 50.
3. Statistical Operations: You can calculate the Mean and Standard Deviation.

Arbitrary Zero:

• The Interval scale lacks a "true" or "absolute" zero. The zero point is defined arbitrarily.
• Example (Temperature): does not mean "no temperature" or "absence of heat"; it is just the freezing point of water. Therefore, is not "twice as hot" as in a physical sense (ratios are invalid).
• This contrasts with a Ratio scale (like weight), where 0 kg means "no weight," and 20kg is indeed double 10kg.

The Weighted Arithmetic Mean is calculated when the importance (weight) of items in a series is different.

Formula:

Calculation Table:

Calculation:

The Weighted Mean Cost is 270.

Power of Ratio Scale:

1. Absolute Zero: It is the only scale with a true, meaningful zero point (origin), representing the total absence of the variable.
2. All Mathematical Properties: It supports all mathematical operations: addition, subtraction, multiplication, and division. Statements like "Variable A is twice as large as Variable B" are valid.
3. Comprehensive: It encompasses all properties of Nominal (labeling), Ordinal (ranking), and Interval (equal distance) scales.

Statistical Tests Applicable:
Because it provides the most detailed data, almost all statistical techniques can be applied, including:

• Descriptive: Geometric Mean, Harmonic Mean, Coefficient of Variation.
• Inferential: t-test, F-test, Correlation, Regression Analysis.

Step 1: Arrange the data in ascending order.
12, 14, 15, 18, 21, 22, 25, 29

Step 2: Count the number of observations ().
(which is an even number).

Step 3: Apply the formula for Even series.
When is even, the Median is the average of the term and the term.

• term.
• term.

Step 4: Identify values.

• term = 18
• term = 21

Step 5: Calculate Average.

Median = 19.5