Data Processing, Analysis, and Interpretation in Research

Overview of Data Processing, Analysis and Interpretation

Processing and Analysis Guidelines: Once data is collected, it must be processed and analyzed according to the outline established during the development of the research proposal.
Definition of Processing: Technically, data processing involves the editing, coding, classification, and tabulation of collected data to prepare it for analysis.

Data Processing Operations

1. Editing

Definition: Editing is the process of examining raw data to detect errors and omissions, correcting them whenever possible.
Objectives:
- To ensure data accuracy.
- To maintain consistency with other gathered facts.
- To ensure data is uniformly entered.
- To ensure completeness.
- To arrange data for easier coding and tabulation.
Stages of Editing:
- Field Editing:
  - This involves the investigator reviewing forms to complete abbreviated or illegible entries made by the interviewer (enumerator) during field recording.
  - Timeline: It should be conducted as soon as possible after the interview, ideally on the same day or the following day.
  - Restriction: The investigator must not guess or fill in missing information based on what they think the informant might have said if the question had been asked.
- Central Editing:
  - This occurs after all questionnaires or forms have been completed and returned to the office.
  - Process: Editors correct obvious errors, such as entries in the wrong place or data recorded in the wrong units (e.g., months instead of weeks).
  - Clarification: Respondents may be contacted for clarification if needed.
  - Handling Inappropriate Answers: If an answer is inappropriate and the editor has no basis for determining the correct response, the editor must strike it out and enter "no answer."

2. Coding

Definition: Coding identifies numerals or other symbols assigned to answers to allow responses to be categorized into a limited number of classes.
Essential Characteristics of Categories:
- Exhaustiveness: There must be a class for every piece of data collected.
- Mutual Exclusivity: A specific answer can only be placed in one cell within a category set.
Purpose: Coding is necessary for efficient analysis, reducing numerous replies to a manageable number of classes containing critical information.
Timing: Decisions regarding coding should ideally be made during the questionnaire design stage.
Methods: In hand coding, codes may be written on the margin of the questionnaire with colored pencils or transcribed to a specific coding sheet.

3. Classification

Definition: The process of arranging data into groups based on common characteristics, particularly useful for large volumes of raw data.
Classification by Attributes: Based on descriptive information such as literacy, sex, honesty, income level, prestige, or educational level.
- Binary Classification: Grouping items into two classes: those possessing a specific attribute and those that do not.
Occupational Example of Classification:
- Raw Data: Lawyers, Barbers, Practical nurse, Carpenters, Brokers, Elevator operator, Veterinarian, Migrant farm laborer, Executive, Engineer, Advertising agent, Electrician.
- Coding Scheme/Classification Categories:
  1. Professional and Managerial: Lawyers, Veterinarians, Executive, Engineers.
  2. Service and Skilled Labors: Barbers, Elevator operator, Practical nurse, Electrician, Carpenter.
  3. Professional Technical and Sales: Advertising agent, Broker.
  4. Unskilled Labor: Migrant farm laborer.
- Benefits: This system groups by income level, prestige, and education, allowing the use of four categories instead of dozens of occupations.
Classification by Class-Intervals: Used for numerical characteristics like age, weight, production, or income.
- Example: People with incomes between $Br\,201$ and $Br\,400$ form one group; those between $Br\,401$ and $Br\,600$ form another.
- Class Magnitude: The difference between the two class limits.
- Frequency: The number of items falling within a specific class.

4. Tabulation

Definition: The procedure of arranging assembed data into a concise and logical order by summarizing raw data and displaying it in a compact form.
Reasons for Tabulation:
- Conserves space and minimizes the need for descriptive statements.
- Facilitates comparison.
- Assists in the summation of items and detection of errors.
- Provides the foundation for statistical computations.

Problems in Data Processing

A. The "Don't Know" (DK) Response

Significance: Minor when the group is small, but a major concern when the group is large.
Interpreting DK Responses:
1. Legitimate DK: The respondent truly does not know the answer. In this case, the question design is considered sound.
2. Failure of Questioning: The researcher failed to elicit information properly. This suggests a failure in the questioning process.

B. Use of Percentages

Purpose: To simplify numbers by reducing them to a range of $0$ to $100$ .
Rules for Using Percentages:
1. Do not average percentages unless each is weighted by the specific size of the group from which it was derived.
2. Avoid using unnecessarily large percentages.
3. Remember that percentages hide the base (the total count) from which they were computed; failure to check the base can lead to misinterpretation of differences.
4. Percentage decreases cannot exceed $100\%$ . When calculating percentage decrease, the higher figure must be used as the base.
5. Percentages should usually be worked out in the direction of the causal factor in two-dimensional tables.

Measurement Scales

Measurement scales identify the data type before analysis. There are four basic scales based on three characteristics: numbers are ordered, differences are ordered, and the series has a unique origin (zero).

1. Nominal Scales

Characteristics: Partition a set into mutually exclusive and collectively exhaustive categories. No order, no distance relationship, and no arithmetic origin.
Arithmetic/Statistics: Limited to counting members; the only measure of central tendency allowed is the mode. Numbers are used only as labels and have no quantitative value.
Power: The least powerful scale.
Examples: Student ID numbers, gender, marital status.

2. Ordinal Scales

Characteristics: Includes nominal traits plus an indicator of order. Allows for "greater than" or "less than" statements.
Distance: Does not state "how much" greater or less; the difference between rank $1$ and $2$ may not equal the difference between rank $2$ and $3$ .
Arithmetic/Statistics: The appropriate measure of central tendency is the median.
Examples: Opinion scales, preference scales.

3. Interval Scales

Characteristics: Includes nominal and ordinal traits plus equality of interval (the distance between $1$ and $2$ equals the distance between $2$ and $3$ ).
Origin: Has an arbitrary zero point, not an absolute one.
Arithmetic/Statistics: The measure of central tendency used is the arithmetic mean. Multiplication/division is not valid (e.g., cannot say $6\,A.M.$ is twice as late as $3\,A.M.$ ).
Examples: Calendar time, Centigrade temperature, Fahrenheit temperature.

4. Ratio Scales

Characteristics: Includes all previous strengths plus an absolute zero (origin). Represents actual amounts of a variable.
Arithmetic/Statistics: Allows for multiplication and division.
Examples: Money values, population counts, distances, return rates, weight, height, area.

Summary Table of Scales

Type of Scale	Characteristics	Basic Empirical Operation
Nominal	No order, distance, or origin	Determination of equality
Ordinal	Order but no distance or unique origin	Determination of greater or lesser values
Interval	Both order and distance but no unique origin	Determination of equality of intervals or differences
Ratio	Order, distance, and unique origin	Determination of equality of ratios

Data Analysis Concepts

Definition: Computation of measures and searching for relationship patterns among data groups. It involves estimating unknown population parameters and testing hypotheses.
Categories:
- Descriptive Analysis: Study of the distribution of a single variable (location, spread, shape).
- Inferential Analysis: Statistical analysis used for drawing inferences (estimation and hypothesis testing).

Descriptive Analysis

Descriptive statistics describe and summarize data using indices.

Frequency Distribution

Definition: Shows the distribution or count of individual scores in a sample.
Example Table (Grain Sale by 16 Businesses):

Amount (Scores)	Frequency	Percentages	Valid Percentages	Cumulative Percentages
$30$	$3$	$18.75\%$	$18.75\%$	$18.75\%$
$35$	$4$	$25.00\%$	$25.00\%$	$43.75\%$
$40$	$5$	$31.25\%$	$31.25\%$	$75.00\%$
$45$	$2$	$12.50\%$	$12.50\%$	$87.50\%$
$50$	$2$	$12.50\%$	$12.50\%$	$100.00\%$
Total (N)	16	100%	100.00%

Valid Percentage: The proportion based only on those who answered (ignoring missing observations).
Cumulative Percentage: The combined proportion of scores up to and including a given score.

Group Frequency Distribution

Usage: Necessary for large samples or sensitive data (e.g., annual income, age).
Guidelines:
- Class intervals should range between $10$ and $15$ in total number.
- Too few intervals cause loss of accuracy; too many are inconvenient.
- Intervals should have the same width and be continuous.
- Frequencies of zero must be indicated.
Example Table (Milk Sales by 50 Hypothetical Enterprises):

Class-interval	Frequency	Class Limits	Mid Points
$26 - 30$	$5$	$25.5 - 30.5$	$28$
$21 - 25$	$10$	$20.5 - 25.5$	$23$
$16 - 20$	$15$	$15.5 - 20.5$	$18$
$11 - 15$	$10$	$10.5 - 15.5$	$13$
$6 - 10$	$5$	$5.5 - 10.5$	$8$
$1 - 5$	$5$	$0.5 - 5.5$	$3$
Total (N)	50

Calculations for Interval 1-5:
- Class Limit: $0.5$ to $5.5$
- Class Width: $5$ (representing $1, 2, 3, 4, 5$ )
- Mid-point: $\frac{0.5 + 5.5}{2} = 3$

Measures of Central Tendency

Summary statistics providing average measures of indicators.

Mode:
- Definition: The value or score that appears most frequently.
- Example: Family sizes $3, 4, 5, 5, 6, 7, 8, 9, 10$ ; Mode is $5$ .
- Traits: A quick, crude description. Distribution can have multiple modes or no mode if all scores occur with equal frequency.
Median:
- Definition: The middle score dividing ranked scores into two equal parts.
- Example: Scores $75, 80, 82, 84, 87$ ; Median is $82$ .
- Traits: Does not account for extreme values.
Mean:
- Definition: The average of a set of scores.
- Formula: $\bar{x} = \frac{\sum x}{n}$
- Example: $10, 12, 12, 20, 15, 10, 18, 16, 8, 5$ ; Mean is $\frac{126}{10} = 12.6$ .
- Traits: Includes every score. Vulnerability: Pulled toward outliers or extremely large/small scores.

Measures of Variability (Dispersion)

Measures of variability describe the spread of data; central tendencies alone can be misleading when significant variation exists (e.g., urban vs. rural income).

Range:
- Definition: The difference between the highest and lowest scores.
- Example: Scores $78, 79, 80, 81, 82, 85$ ; Range is $85 - 78 = 7$ .
- Traits: Quick estimation. Small range = tightly packed scores; large range = dispersed. Uses only two scores, thus insensitive to total population.
Variance:
- Definition: The sum of squares of deviation from the mean divided by the degrees of freedom.
- Formula: $S^2 = \frac{\sum (x_i - x_m)^2}{n - 1}$
- Traits: Higher value means greater variance.
Standard Deviation:
- Definition: The square root of the variance.
- Formula: $S = \sqrt{\frac{\sum (x_i - x_m)^2}{n - 1}}$
- Traits: Shows the extent to which scores deviate from the mean. Accounts for all scores but is very sensitive to extremes.

Inferential Analysis

Inferential analysis involves testing hypotheses and estimating population values.

Correlation Analysis: Studies the joint variation of two or more variables to determine the degree of correlation between them.
Causal (Regression) Analysis: Concerned with how one or more variables influence changes in another variable (the study of functional relationships).