MMPC-015 Solved Assignment

Question 1: Why does checking available data help narrow the research problem and the method?

Defining a research problem is often considered the most critical step in the entire research process. A researcher’s understanding of available data strongly shapes both the specific problem they can investigate and the analytical methods they can employ.

Narrowing down the problem

When defining a problem, a researcher might start with a broad or general question. However, the feasibility of answering that question often depends on data availability. If specific data is not available or is too costly to collect, the problem definition must be adjusted to fit what is measurable.

• Feasibility and specificity: A broad problem like “Why is productivity higher in City A than City B?” is too general. By checking available data (for example, labour statistics or manufacturing output reports), the problem can be narrowed down to a specific, answerable question such as: “What factors are responsible for increasing labour productivity in five manufacturing industries in City A compared to City B in 2009?”
• Availability of secondary data: Knowing that certain secondary data (for example, census figures, government reports on mining accidents, or Reserve Bank bulletins) exists allows the researcher to tailor the problem to utilise these reliable sources. If the required data for a complex problem is not available, the researcher may have to redefine the problem to one that can be solved with accessible information.

Determining the technique

The nature of the available data dictates the research techniques and tools.

• Quantitative vs. qualitative: If the available data is numerical (for example, sales figures or census data), quantitative techniques such as regression analysis or hypothesis testing are appropriate. If the data is text-based or observational (for example, interview transcripts), qualitative methods are required.
• Scale of measurement: The type of scale used in data collection (Nominal, Ordinal, Interval) determines the statistical operations possible. For instance, if data is only available on a nominal scale (categories like “yes/no”), one is largely limited to counting and using suitable non-parametric tests (such as Chi-square). One cannot calculate a mean or standard deviation in the same way as with interval data.
• Data availability and method selection: If a researcher knows that data on one dependent variable and multiple independent variables is available, they may choose multivariate techniques like regression analysis. Conversely, if the available information is mainly classification-based (for example, “successful” vs “unsuccessful” salespersons), then a classification-focused method such as discriminant analysis may be more suitable.

In summary, the availability of data acts as a practical constraint that refines the research scope from a vague idea into a specific, manageable problem and simultaneously points the researcher toward the correct methodological toolkit to solve it.

Question 2: What is a sample design? Explain the three key points to consider.

Meaning of sample design

A sample design is a definite plan for obtaining a sample from a given population. It refers to the technique or procedure the researcher adopts to select items for the sample. It is determined before data collection begins. The design lays out how many items are to be included in the sample (sample size) and the method of selection (for example, random or non-random). In simple terms, it acts as a blueprint for collecting, measuring, and analysing data about the target population.

Important points in sample design

• Type of population: Clearly define the population (the aggregate of sampling units). The structure of the population must be understood—whether it is finite or infinite, homogeneous or heterogeneous. For example, is it the population of a city, or the number of workers in a factory?
• Sampling unit: Identify the specific unit to be sampled. This could be a geographical unit (state, district, village), a social entity (family, school), or an individual. The selection of the unit depends on the research objective.
• Type of sample (sampling technique): Decide between probability (random) and non-probability sampling methods.

• Probability sampling (for example, Simple Random, Stratified, Cluster) ensures every unit has a known chance of selection, allowing sampling error estimation.
• Non-probability sampling (for example, Convenience, Quota) may be used when representativeness is not the primary issue or for exploratory work.

Additional practical considerations

• Size of the sample: The sample size must be sufficient to be representative and provide reliable estimates. A larger sample generally improves precision but increases cost.
• Sampling frame: A sampling frame is a list of all units in the population. The frame should be accurate, complete, adequate, and up-to-date. A faulty frame (for example, an outdated directory) leads to sampling errors.
• Budget and time constraints: The design must be viable within available financial resources and time limits. In large geographical surveys, cluster sampling may be chosen over simple random sampling to reduce travel and administrative costs.

Question 3(a): What is an experience survey?

Meaning

An experience survey is an exploratory approach used at an early stage of research where information is collected from knowledgeable and experienced people to gain clarity about the problem. It is closely aligned with methods like expert interviews and depth interviews, which help obtain in-depth information before moving to structured measurement.

Purpose and use

• To understand the background and context of the problem quickly.
• To identify important variables and likely relationships among them.
• To help in framing sharper research questions and (where relevant) workable hypotheses.
• To guide what a later questionnaire or structured study should focus on.

Question 3(b): What is a pilot survey?

Meaning

A pilot survey is a small-scale trial run of the data collection process before the main survey is conducted. In practical terms, it is the pretesting stage of the questionnaire or instrument.

Why it is conducted

• To find weaknesses in the questionnaire: unclear wording, missing response options, wrong sequencing, or questions that respondents misunderstand.
• To test field feasibility: whether respondents can answer comfortably, whether the survey length is reasonable, and whether instructions and routing work correctly.
• To improve reliability of final data: by correcting instrument problems before the main fieldwork begins.

Question 3(c): Explain the components of a research problem.

Main components (decision-oriented view)

• Decision-maker’s question: the immediate question the manager or decision-maker wants answered (what decision is pending?).
• Decision alternatives: the possible courses of action available (what choices are on the table?).
• Decision criteria: how the alternatives will be judged (what standard will be used to decide?).

Supporting components that make it research-ready

• Unit of analysis: what exactly is being studied (for example, individual consumers, households, firms, territories, etc.).
• Information requirement: what data is needed to evaluate alternatives using the criteria (the real “research need” behind the decision).
• Scope and boundaries: practical limits such as time period, geography, and the type of respondents or records to be covered.

Question 3(d): Write the main steps in the research process.

Main steps

1. Define the research problem (clarify what decision or information gap must be addressed).
2. Develop working hypotheses (where applicable, propose expected relationships to be examined).
3. Prepare the research design (decide the overall plan: exploratory/descriptive/other, instruments, and approach).
4. Decide the sampling design (who to study, how to select them, and the sample size).
5. Collect the data (execute fieldwork or gather relevant records/documents).
6. Analyse the data (processing, summarising, and applying appropriate analytical tools).
7. Prepare and present the report (communicate findings in an actionable form for decision-making).

Question 4: What are multivariate techniques? Discuss multiple regression, discriminant analysis, and factor analysis.

Meaning of multivariate techniques

Multivariate techniques refer to statistical procedures used to analyse data involving three or more variables simultaneously. They are used to study relationships and the degree of association among variables. Unlike univariate analysis (one variable) or bivariate analysis (two variables), multivariate analysis handles business problems where multiple independent variables influence a dependent variable, or where variables need to be grouped or reduced.

Important multivariate techniques

• Regression analysis (multiple regression): used to predict one dependent variable from multiple independent variables.
• Discriminant analysis: used to classify observations into two or more mutually exclusive groups based on a set of predictor variables.
• Factor analysis: used to reduce a large number of variables into a smaller set of underlying factors or dimensions.

Explanation of important characteristics: factor analysis

• Data reduction and summarisation: It takes a large set of variables and groups them into a smaller number of factors that account for most of the variance in the original data.
• Search technique: Unlike regression, which separates dependent and independent variables, factor analysis examines the whole set of variables to find underlying strengths of association and does not split variables into criterion and predictor subsets.
• Latent variables: It identifies underlying (latent) variables that are not directly measurable but are reflected in observed variables. For example, variables like “age,” “income,” and “education” may combine into a factor that can be interpreted and labelled meaningfully.
• Factor loadings: It produces factor loadings (coefficients) indicating the correlation between each original variable and the derived factor. A high loading means the variable is strongly linked to that factor.

Question 5: Define descriptive and inferential statistics, and list key statistical measures used to summarise survey/research data.

Descriptive statistics (meaning)

• Focus: describing, summarising, and presenting data in a meaningful way.
• Function: converting raw data into an understandable form using tables, graphs, and summary measures.
• Scope: it does not generalise beyond the data at hand (for example, computing the average income of the survey respondents you actually studied).

Inferential statistics (meaning)

• Focus: drawing conclusions or making predictions about a larger population based on sample data.
• Function: estimation and hypothesis testing, using probability ideas to judge the reliability of findings.
• Scope: generalising beyond the immediate sample to the broader population (for example, testing whether a result found in the sample is likely to hold in the population).

Important statistical measures used for summarising survey/research data

1) Measures of central tendency (averages)

• Mean: the arithmetic average of all values (useful for interval data, but sensitive to extreme values).
• Median: the middle value when data is arranged in order (useful for skewed distributions or ordinal scales).
• Mode: the most frequently occurring value (the only measure suitable for nominal data).

$$ \bar{y}=\frac{1}{n}\left(y_1+y_2+\cdots+y_n\right) $$

2) Measures of dispersion (variation)

• Variance: the average of squared deviations from the mean; it reflects how spread out values are around the average.
• Standard deviation: the square root of variance; it is a widely used measure of spread and supports ideas like standard error and confidence limits.

$$ V(\bar{y})=\frac{\sigma^2}{n} $$

3) Measures of association

• Correlation coefficient: measures the strength and direction of a linear relationship between two variables.
• Regression coefficients: describe the functional relationship, supporting prediction of a dependent variable from one or more independent variables. In multiple regression, explanatory strength is often summarised using R².

$$ \hat{Y}=a+bX_1 $$