Unit2 - Subjective Questions

Definition:

A Research Design is the conceptual structure within which research is conducted. It constitutes the blueprint for the collection, measurement, and analysis of data. It answers the questions of what, where, when, how much, and by what means concerning an inquiry or a research study.

Features of a Good Research Design:

• Objectivity: The design should allow the researcher to arrive at objective conclusions, minimizing personal bias.
• Reliability: It should provide consistent results if the research were to be repeated under similar conditions.
• Validity: It must measure what it claims to measure (internal validity) and the results should be applicable to the general population (external validity).
• Generalizability: The findings obtained from the design should be applicable to a larger population.
• Economy: It should yield maximum information with minimum expenditure of effort, time, and money.
• Flexibility: While structured, it should allow for adjustments if unforeseen changes occur during the research process.

The research process consists of a series of actions or steps necessary to effectively carry out research. The typical sequence is:

1. Formulating the Research Problem: Defining the problem clearly and distinguishing it from symptoms.
2. Extensive Literature Survey: Reviewing previous studies, journals, and books related to the problem.
3. Development of Working Hypothesis: Formulating a tentative assumption (Example: and ) to guide the research.
4. Preparing the Research Design: Creating the blueprint (Exploratory, Descriptive, or Experimental).
5. Determining Sample Design: Deciding on the sampling unit, size, and procedure (Probability vs. Non-probability).
6. Collecting the Data: Gathering data via surveys, observation, or experiments.
7. Execution of the Project: Ensuring the project proceeds according to the design.
8. Analysis of Data: Coding, editing, and tabulating data; applying statistical tests.
9. Hypothesis Testing: Using tests like t-test, F-test, or Chi-square to accept or reject the hypothesis.
10. Generalizations and Interpretation: Drawing conclusions from the results.
11. Preparation of the Report: Writing the thesis or research paper formally.

Professor R.A. Fisher outlined three main principles of experimental design:

1. Principle of Replication:

   • The experiment should be repeated more than once. By repeating the experiment, the statistical accuracy of the experiments is increased.
   • It helps in estimating the experimental error.

2. Principle of Randomization:

   • This provides protection, when we conduct an experiment, against the effect of extraneous factors by randomization.
   • It ensures that variations caused by extraneous factors are distributed purely by chance.

3. Principle of Local Control:

   • This is used to eliminate the variability due to extraneous factors from the experimental error.
   • The extraneous factor (e.g., soil fertility in agriculture) is made to vary deliberately over as wide a range as necessary, and this variation is eliminated from the experimental error usually through methods like 'blocking'.

Definition:
A sampling design is a definite plan for obtaining a sample from a given population. It refers to the technique or the procedure the researcher would adopt in selecting items for the sample.

Steps in Developing a Sampling Design:

1. Type of Universe: Define the population clearly (Finite or Infinite).
2. Sampling Unit: Decide the geographical area or specific unit (e.g., state, district, house, or individual) to be sampled.
3. Source List (Sampling Frame): Obtain or create a list of all sampling units from which the sample is to be drawn.
4. Size of Sample: Determine the number of items () to be selected from the universe () to achieve desired precision and confidence.
5. Parameters of Interest: Identify specific population characteristics to be estimated.
6. Budgetary Constraints: Consider cost considerations which may influence sample size and method.
7. Sampling Procedure: Select the specific technique (e.g., Simple Random Sampling, Stratified) to act as the method of selection.

Stratified Random Sampling:
This is a probability sampling technique where the population is divided into subgroups (strata) that are mutually exclusive and collectively exhaustive. Elements are then randomly selected from each stratum. The goal is to ensure subgroups are represented.

• Logic: Strata should be homogeneous within (low variance internal) and heterogeneous between.

Difference from Cluster Sampling:

• Stratified: The population is divided into strata, and a random sample is taken from every stratum. (Homogeneity within, Heterogeneity between).
• Cluster: The population is divided into clusters (groups), and a random sample of clusters is selected. All or some elements within selected clusters are surveyed. (Heterogeneity within, Homogeneity between groups usually desirable for efficiency, though naturally, clusters often mirror the population).

To determine the sample size () for estimating a population mean with a specific margin of error () and confidence level ():

The formula usually used is:

Where:

• = The Z-value corresponding to the desired confidence level (e.g., $1.96$ for confidence).
• = The population standard deviation (estimated from pilot study or past data).
• = The acceptable margin of error (precision).

Logic:

1. We assume the sampling distribution of the mean is normal.
2. The error is defined as Standard Error ().
3. .
4. Therefore, .
5. Rearranging for : .

If the population proportion () is being estimated instead of mean:

Probability Sampling:

• Definition: Every item in the universe has a known, non-zero chance of being selected.
• Basis: Randomization.
• Bias: Eliminates researcher bias.
• Inference: Statistical inferences about the population can be made with calculated confidence limits.
• Examples: Simple Random Sampling, Stratified, Systematic, Cluster.

Non-Probability Sampling:

• Definition: Selection is based on the researcher’s subjective judgment; probability of selection is unknown.
• Basis: Convenience or Judgment.
• Bias: High risk of selection bias.
• Inference: Results cannot be statistically generalized to the whole population with a known margin of error.
• Examples: Convenience Sampling, Quota Sampling, Judgmental Sampling, Snowball Sampling.

Systematic Sampling:
A probability sampling method where researchers select members of the population at a regular interval. It is often used when a complete list of the population is available.

Procedure:

1. Number the units in the population from $1$ to .
2. Decide on the sample size .
3. Calculate the sampling interval .
4. Select a random starting point between $1$ and .
5. Select every element thereafter.

Formula:
The sampling interval () is calculated as:

Where:

• = Total Population Size
• = Required Sample Size

Note: If and , then . We pick a random number between 1-10 (say 3), then select 3, 13, 23, 33, etc.

Sampling Errors:

• These are errors arising because a sample is not a perfect representation of the population. It is the difference between the sample statistic and the true population parameter.
• Relationship with Sample Size: Sampling error is inversely proportional to the square root of the sample size (). As sample size increases, sampling error decreases (approaches zero at Census).

Non-Sampling Errors:

• These are errors not related to the sampling method but due to human error, data collection flaws, faulty instruments, or data processing errors (e.g., bias, non-response, calculation errors).
• Relationship with Sample Size: Non-sampling errors often increase with sample size because handling larger data sets introduces more complexity and administrative challenges.

Description:
Snowball Sampling (also known as Chain Referral Sampling) is a non-probability technique where existing study subjects recruit future subjects from among their acquaintances. The sample group acts like a rolling snowball, growing larger as the process continues.

Process:

1. Identify initial subjects (seeds) who belong to the target population.
2. Collect data from them.
3. Ask them to refer others who fit the criteria.

Appropriate Situations:

• Hidden Populations: When the population is hard to locate (e.g., illegal immigrants, drug users).
• No Sampling Frame: When no list of the population exists.
• Social Networks: When investigating social dynamics or networks.

The Literature Review is a critical step in the research process (Step 2) for the following reasons:

1. Identification of Research Gap: It helps the researcher find out what is already known and what is yet to be explored.
2. Prevents Duplication: Ensures the researcher does not waste time repeating work that has already been done.
3. Methodological Insights: Provides guidance on research methodologies, tools, and statistical techniques used by previous scholars.
4. Theoretical Framework: Helps in establishing the theoretical roots of the study.
5. Refining the Problem: Helps in narrowing down a broad topic into a specific, feasible research problem.
6. Contextualizing Findings: Allows the researcher to compare their eventual findings with existing knowledge.

Concomitant Variation is one of the essential conditions required to establish causality (cause-and-effect relationship) in research.

Explanation:
It refers to the extent to which a cause () and an effect () occur together or vary together in the way predicted by the hypothesis.

• If increases and increases (positive correlation) or if increases and decreases (negative correlation), there is concomitant variation.

Role in Causal Design:
While concomitant variation suggests a relationship, it is not sufficient proof of causation on its own. For a valid Causal Research Design, one must also establish:

1. Time Order of Occurrence: The cause must precede the effect.
2. Absence of Other Causal Factors: Eliminating extraneous variables that could explain the change in .

Census:

• Definition: A complete enumeration of all items in the population.
• Accuracy: theoretically highest accuracy (no sampling error).
• Cost/Time: Very expensive and time-consuming.
• Feasibility: Not feasible for infinite populations or destructive testing (e.g., testing matchsticks).

Sample Survey:

• Definition: Selection of a subset of the population to represent the whole.
• Accuracy: Subject to sampling error, but non-sampling errors may be lower due to better supervision.
• Cost/Time: More economical and faster.
• Feasibility: Practical for almost all types of research.

Quota Sampling:
This is a method where the researcher ensures that specific subgroups of the population are represented in the sample in exact proportion to their presence in the population (similar to Stratified Sampling), but the selection of individuals within those groups is not random.

Process:

1. Divide population into categories (e.g., Gender: 60% Female, 40% Male).
2. Determine sample quotas (e.g., for , select 60 women and 40 men).
3. Select individuals to fill these quotas based on convenience or judgment until the quota is full.

Why it is Non-Probability:
Even though the quotas match the population structure, the actual selection of units within the quota is left to the interviewer's discretion (convenience). There is no random mechanism giving every individual a known chance of selection. Therefore, sampling error cannot be estimated.

Simple Random Sampling (SRS):
It is the most basic probability sampling technique where every member of the population has an equal and independent chance of being selected. If the population size is and sample size is , the probability of selection for any item is .

The Lottery Method:
This is a practical way to conduct SRS manually.

1. Assign Numbers: Every item in the population is assigned a unique number.
2. Token Creation: These numbers are written on identical slips of paper or tokens.
3. Mixing: The slips are placed in a container and thoroughly mixed to ensure randomness.
4. Selection: A blindfolded person or a neutral party picks slips from the container.
5. Result: The individuals corresponding to the picked numbers form the sample.

Selecting the right research design is crucial for the success of a study. The choice depends on:

1. Nature of the Research Problem: If the problem is vague, Exploratory is best. If variables are known and need measurement, Descriptive. If testing causality, Experimental.
2. Objectives of the Study: Whether the goal is to discover new ideas, describe a population, or test a hypothesis.
3. Available Data: Availability of secondary data might reduce the need for primary data collection designs.
4. Time and Cost: Experimental designs are often costly and time-consuming compared to cross-sectional descriptive surveys.
5. Precision Required: If high precision is needed, a rigorous sampling design and structured instrument are required.
6. Ability to Control Variables: If the researcher cannot manipulate variables (e.g., in sociology), experimental design may not be feasible.

Hypothesis:
A hypothesis is a tentative assertion or a logical supposition regarding the relationship between two or more variables. It serves as the focal point for research, guiding data collection.

Differentiation:

• Null Hypothesis ():

  • It is a statement of 'no difference' or 'no effect'.
  • It assumes that any observed difference in data is due to chance.
  • Example: "There is no significant difference in sales between Region A and Region B" ().
  • Statistical tests are designed to reject or fail to reject .

• Alternative Hypothesis ( or ):

  • It is the statement that is accepted if the Null Hypothesis is rejected.
  • It suggests a real effect or difference exists.
  • Example: "Sales in Region A are significantly different from Region B" ().

Multi-stage Sampling:
This is a complex form of cluster sampling where sampling is carried out in several stages. The population is divided into clusters, clusters are selected, and then sub-clusters are selected within those, continuing until the final sampling unit is reached.

Example: Country States Districts Villages Households.

Utility in Large-Scale Surveys:

1. Cost Effective: It significantly reduces travel and administrative costs compared to SRS, as data collectors only visit specific selected areas.
2. Flexibility: Different sampling methods can be used at different stages (e.g., Stratified at stage 1, SRS at stage 2).
3. No Comprehensive Frame Needed: A list of all households in the country isn't needed initially, only a list of states, then a list of districts within selected states, etc.

Definition:
Cluster sampling is a probability sampling method where the researcher divides the population into separate groups, called clusters. A simple random sample of clusters is selected, and data is collected from every unit within the selected clusters.

Preferred Conditions:

1. Geographical Dispersion: When the population is spread over a wide geographical area, making SRS too expensive (travel costs).
2. No Sampling Frame: When a list of individual elements is not available, but a list of groups (clusters) is available (e.g., list of employees is missing, but list of departments exists).
3. Homogeneity between Clusters: Ideally, each cluster should be a mini-representation of the total population (heterogeneous within, homogeneous between), though in practice, this is often used simply for economic efficiency.