Agribusiness Management · Functional core · also ABM 540, AEC-509, Research Methods I/II (ABM 602, ABM 604)
How to design, run and report a study: problems, hypotheses, measurement, questionnaires, sampling, analysis and writing up. Examined in agribusiness, agricultural economics and extension PhD entrance papers alike.
In the exams: Research methodology units of agribusiness management PhD entrance and fellowship examinations, agricultural economics PhD entrance and fellowship examinations and agricultural extension PhD entrance and fellowship examinations (heavy in all three)
Research methodology is the discipline of asking a question about the world in a form that data can answer, collecting those data without fooling yourself, and reporting what they show in a way another person can check. In agribusiness, agricultural economics and extension it covers the whole chain: turning a vague concern (why do farmers in this district not use crop insurance?) into a researchable problem, stating hypotheses, measuring things that cannot be weighed, such as attitude or risk perception, designing a questionnaire, drawing a sample, choosing the right statistical test and writing the report.
The subject matters in practice because most decisions in the sector rest on surveys and field studies: a processor sizing a procurement network, a bank judging demand for a new loan product, an extension agency evaluating a training programme, a ministry estimating cost of cultivation. A badly drawn sample or a leading question produces numbers that look precise and are wrong.
Worldwide the content is remarkably uniform. It is taught in Master's and PhD programmes in agricultural economics, agribusiness and extension. India's ICAR PhD entrance examination tests it in all three social-science papers (Agri-Business Management, Agricultural Economics with econometrics, and Agricultural Extension). Master's entrances test the statistical basics: scales, sampling, tests of significance, correlation and regression. PhD qualifying examinations everywhere expect the multivariate material and, increasingly, tree-based machine-learning methods.
This manual follows the order in which a study is actually done. Numerical examples are worked in full because examinations ask for them.
Research is a systematic, controlled and critical inquiry that produces new knowledge or tests existing claims. Textbooks classify research along several axes. By purpose, basic (fundamental) research seeks general knowledge, for example a theory of how farmers form price expectations, while applied research solves a specific problem, such as whether a contract-farming scheme raised members' incomes. By approach, quantitative research measures variables numerically and uses statistics, while qualitative research uses words, observation and interpretation to understand meanings and processes; mixed-methods studies combine the two. By objective, descriptive research describes the state of affairs as it exists (the share of farmers selling through a regulated market), while analytical research uses existing facts to evaluate or explain. Conceptual research works with theory; empirical research with observation and experiment.
By time, a cross-sectional study observes many units once, a panel study follows the same units over time, and a time-series study follows one unit over many periods. By control, research is experimental (treatment randomly assigned), quasi-experimental (a comparison group without random assignment) or non-experimental. Ex post facto research, very common in extension and agricultural economics, studies the effect of a cause that has already happened (for example, adoption of drip irrigation) by comparing units that differ on it; because the researcher did not assign the cause, self-selection is a constant threat to conclusions.
A research design is the plan that links the question to the evidence: what will be observed, on whom, when, and how the data will be analysed. Textbooks group designs into three families. Exploratory (formulative) designs are used when little is known; they rely on literature surveys, experience surveys with knowledgeable people, focus groups and case studies, and their output is usually hypotheses rather than tests. Descriptive and diagnostic designs describe characteristics and associations of a defined population. Causal or hypothesis-testing designs, the experimental family, aim to show that one variable changes another. The classic true experiment has random assignment, a control group and pre- and post-measurement.
Most agribusiness studies are observational. Observational causal work therefore leans on designs that imitate randomisation: difference-in-differences, which compares the change over time in a treated group with the change in an untreated group; matching methods such as propensity score matching, which pair treated and untreated units with similar observed characteristics; instrumental variables; and regression discontinuity. Each rests on assumptions that a good report states. A case study of one or a few units explains process but cannot support statements about a population.
Most textbooks describe the process as a sequence of overlapping steps: (1) identify and formulate the research problem; (2) review the literature, both conceptual and empirical; (3) develop working hypotheses or research questions; (4) prepare the research design; (5) determine the sampling design; (6) develop and pretest instruments; (7) collect data; (8) process data by editing, coding and tabulation; (9) analyse data and test hypotheses; (10) generalise and interpret; and (11) prepare the report. In practice the steps loop back.
Two quality criteria run through the whole process. Internal validity asks whether the observed relationship is really caused by the variable claimed, rather than by a confounding variable, selection, history, maturation, testing or instrumentation effects. External validity asks whether the result generalises beyond the particular sample, place and time. A laboratory-style experiment with volunteer farmers may have high internal but low external validity; a large national survey often has the reverse.
A research problem is a gap or difficulty, in theory or in practice, that a study can resolve with evidence. The source may be a field observation (low repayment in a producer company), a policy change (a new minimum support price regime), a gap in the literature, or a contradiction between earlier findings. The problem becomes researchable when it is narrowed to a defined population, place and period, when its key concepts can be measured, and when data can realistically be obtained within the time and money available. A topic such as 'the problems of agricultural marketing' is a slogan, not a problem. A researchable version might be 'What determines whether tomato growers in a given district sell through commission agents rather than to aggregators, and how do net prices received differ between the two channels?'.
Textbooks list criteria for choosing a problem: it should interest the researcher, be of manageable magnitude, match the researcher's expertise, have relevance for policy or theory, have data available, and raise no ethical difficulty.
Once the problem is fixed, it is broken into specific objectives, each stated with an action verb that implies a method: to estimate, to compare, to identify the determinants of, to examine the constraints in. Each objective should map to one analytical tool and one table in the report. Research questions restate objectives as questions and are preferred in exploratory or qualitative work.
The review of literature serves several purposes: it shows what is already known, prevents duplication, identifies the theories and variables others found relevant, reveals methods and instruments that can be adapted, and positions the study's contribution. A conceptual review covers theory and definitions; an empirical review covers earlier studies and their findings. From the review the researcher builds a conceptual framework, a statement or diagram of which independent variables are expected to affect which dependent variables, possibly through intervening (mediating) variables and conditioned by moderating variables. A systematic review adds a stated search protocol and inclusion criteria; a meta-analysis pools effect sizes across studies.
A variable is a characteristic that takes different values across units. The dependent variable is the outcome the study tries to explain; independent variables are the presumed causes; extraneous variables affect the dependent variable but are not of interest and must be controlled by design or in analysis. A confounding variable is related to both the independent and dependent variable and can create a spurious association. In extension research, for example, farm size may confound the relation between extension contact and adoption.
A conceptual definition states what a concept means in words; an operational definition states exactly how it will be measured. 'Innovativeness' may be defined conceptually as the degree to which an individual adopts new ideas earlier than others, and operationally as the number of years between the release of a practice and its adoption by the respondent. Operational definitions make studies comparable and replicable.
A hypothesis is a tentative, testable statement about the relationship between two or more variables, formulated before the data are examined. Kerlinger defines it as a conjectural statement of the relation between two or more variables. A usable hypothesis is clear, specific, testable, consistent with known facts and simple. 'Farmers with more extension contact have higher adoption scores' is testable; 'extension is good' is not.
Hypotheses are classified in several ways. A descriptive hypothesis states the existence, size or form of a single variable; a relational hypothesis states how two variables are related; a causal hypothesis claims one variable produces change in another. A directional hypothesis states the direction of a difference or relation and leads to a one-tailed test; a non-directional hypothesis states only that a difference exists and leads to a two-tailed test. For statistical testing a research (alternative) hypothesis, H1, is paired with a null hypothesis, H0, which states no difference or no relationship. The test is conducted on H0: we either reject it or fail to reject it. We never prove H1, and failing to reject H0 does not prove H0 true; it may reflect a small sample.
Two kinds of error are possible. A Type I error rejects a true null hypothesis; its probability is the significance level, alpha, set by the researcher before the test, conventionally 0.05 or 0.01. A Type II error fails to reject a false null hypothesis; its probability is beta, and the power of the test is 1 minus beta, the probability of detecting an effect that is really there. For a fixed sample size, lowering alpha raises beta. Power rises with sample size, with the true effect size and with lower variance in the data. A non-significant result from a small, underpowered survey is inconclusive, not evidence of no effect.
The p-value is the probability, computed assuming H0 is true, of obtaining a test statistic at least as extreme as the one observed. If p is less than or equal to alpha, H0 is rejected. The p-value is not the probability that H0 is true, and it says nothing about the size or practical importance of an effect. A tiny effect can be highly significant in a large sample. Modern reporting guidance, including the American Statistical Association's statement on p-values, asks for effect sizes and confidence intervals alongside p-values.
Every classical test follows the same steps: state H0 and H1; choose alpha; choose the test statistic appropriate to the data and assumptions; determine the sampling distribution of the statistic under H0 and the critical region, which lies in one tail for a directional H1 and is split between two tails otherwise; compute the statistic from the sample; and decide, then interpret the result in the language of the problem. For the standard normal distribution the two-tailed critical values are 1.96 at 5 percent and 2.58 at 1 percent; the one-tailed values are 1.645 and 2.33.
A confidence interval gives the same decision in a more informative form. A 95 percent interval for a difference that excludes zero corresponds to rejecting H0 at 5 percent (two-tailed), and also shows the plausible size of the effect. Degrees of freedom, the number of values free to vary once constraints are imposed, fix which t, chi-square or F distribution applies.
Measurement is the assignment of numbers or symbols to characteristics of objects according to rules. Stevens' classification recognises four levels. A nominal scale only classifies: religion, crop grown, marketing channel; numbers are labels, and the permissible statistics are counts, the mode and chi-square tests. An ordinal scale ranks: rank of constraints, grade of produce, socio-economic class; it supports the median, percentiles and rank-order statistics such as Spearman's rho, but differences between ranks are not known to be equal. An interval scale has equal units but an arbitrary zero: temperature in degrees Celsius, many attitude scores; means, standard deviations and Pearson correlation are permissible, but ratios are not meaningful, so 20 degrees is not twice as hot as 10. A ratio scale has equal units and a true zero: yield, income, farm size, price; all arithmetic operations and statistics, including the coefficient of variation and geometric mean, are permissible.
The level of measurement determines which analysis is valid. Common practice treats a summated score from many items as approximately interval, while a single Likert item is treated as ordinal. A report should state which assumption it makes.
Attitudes cannot be observed directly, so they are inferred from responses to a set of statements. Thurstone's method of equal-appearing intervals, developed by Thurstone and Chave, starts with a large pool of statements about the attitude object. A panel of judges sorts each statement into one of eleven piles from most unfavourable to most favourable. The scale value of a statement is the median of the judges' placements, and its ambiguity is measured by the Q value, the interquartile range of those placements. Statements with low Q values and scale values spread across the continuum are retained, typically around twenty. A respondent marks the statements he or she agrees with, and the attitude score is the median (or mean) of the scale values of those statements.
Likert's method of summated ratings, published in 1932, asks respondents to rate each statement on a graded agreement scale, commonly five points from strongly agree to strongly disagree. Scores (for example 5 to 1) are reversed for negatively worded statements so that a high score always means a favourable attitude, and the item scores are summed. Item analysis retains items that discriminate between high and low scorers (by t value or item-total correlation). Likert scales are easier to build than Thurstone scales, need no judges, and usually give comparable or higher reliability. Guttman's scalogram analysis builds a cumulative, unidimensional scale in which agreement with a stronger statement implies agreement with all weaker ones; its coefficient of reproducibility, one minus errors divided by total responses, should be at least 0.90. Osgood's semantic differential rates a concept on bipolar adjective pairs, usually on seven points, which load on evaluation, potency and activity dimensions. Edwards and Kilpatrick's scale-discrimination technique combines Thurstone, Likert and Guttman steps.
Reliability is the consistency of a measure: the extent to which it gives the same result under the same conditions and is free of random error. Test-retest reliability correlates scores from the same respondents at two points in time; too short an interval inflates it through memory, too long an interval lets the attitude really change. Parallel-forms reliability correlates two equivalent versions of the instrument. Split-half reliability correlates scores on two halves of the items (for example odd and even items) and corrects the result for full length with the Spearman-Brown formula, reliability equals 2r divided by (1 plus r). A half-test correlation of 0.6 therefore implies a full-test reliability of 0.75.
Internal consistency is most often reported as Cronbach's alpha, equal to k divided by (k minus 1), multiplied by one minus the ratio of the sum of item variances to the variance of the total score, where k is the number of items. With 10 items whose variances sum to 20 and a total-score variance of 60, alpha is 10/9 times (1 minus 1/3), about 0.74. Values of 0.70 or above are commonly treated as acceptable for research use, following Nunnally, but alpha rises with the number of items and does not show that the scale is unidimensional. Inter-rater reliability is measured by Cohen's kappa, which corrects for chance agreement.
Validity is the extent to which an instrument measures what it claims to measure. A measure can be reliable without being valid, as a scale that consistently reads two kilograms heavy shows, but it cannot be valid without being reliable. Content validity asks whether the items adequately sample the whole domain of the concept; it is judged by experts. Criterion-related validity compares the measure with an external criterion: concurrent validity with a criterion measured at the same time, predictive validity with a future criterion, such as whether an entrepreneurial-orientation score predicts later enterprise growth. Construct validity asks whether the measure behaves as theory predicts: convergent validity means it correlates with other measures of the same construct, and discriminant validity means it does not correlate strongly with measures of different constructs. Factor analysis, covered later, is a central tool for assessing construct validity.
A questionnaire is a set of questions that respondents fill in themselves, delivered by post, by hand or online. A schedule is a similar form filled in by an enumerator who asks the questions face to face and records the answers. In rural surveys of low-literacy populations the schedule is standard; it gives higher response rates, allows clarification and supports probing, but it is costlier and admits interviewer bias. Self-administered questionnaires are cheap and reach dispersed respondents but suffer non-response, cannot be clarified, and exclude those who cannot read. Mailed questionnaires to farmers commonly return low response rates, so follow-up reminders are planned in advance. Computer-assisted personal interviewing (CAPI) on tablets enforces skip patterns and range checks at the point of entry and records the time of each interview, but it does not cure poorly worded questions. Interviews may be structured, semi-structured or unstructured; focus groups and participatory rural appraisal tools serve exploratory stages.
Questions are open-ended, allowing the respondent to answer in his or her own words, or closed-ended, offering fixed alternatives: dichotomous, multiple-choice, ranking, rating scales or checklists. Open questions are hard to code; closed questions can force answers. Closed alternatives must be mutually exclusive and exhaustive, often with an 'other, specify' category.
The standard wording rules are simple and routinely broken. Use the respondent's vocabulary and local units, recording conversions. Ask one thing per question: 'Is the price and quality of seed satisfactory?' is double-barrelled. Avoid leading questions that suggest the answer ('Don't you agree that middlemen exploit farmers?') and loaded words with emotional colour. Avoid double negatives and vague quantifiers such as 'regularly' unless defined. Give a clear reference period: 'in the last kharif season', 'in the last 12 months'. Sensitive questions about income or debt are placed late and asked with ranges. Recall of quantities such as input use declines with the length of the recall period, so shorter periods or diaries are used where accuracy matters.
The questionnaire opens with an introduction that identifies the researcher, states the purpose, explains voluntary participation and confidentiality, and estimates the time required. Easy questions come first. Questions are grouped by topic, and the funnel technique moves from general to specific within a topic. Filter questions with clear skip instructions route respondents past irrelevant sections.
Pretesting on a small number of respondents similar to the target population, and a pilot survey that rehearses the full field procedure, are indispensable. They reveal misunderstood words, missing categories, questions that offend, excessive length, and skip errors. Items in a new attitude scale are also tested for reliability at this stage, and enumerators are trained on the final version with mock interviews so that every question is asked in the same way. When a questionnaire is translated into a local language, back-translation by an independent translator into the original language checks that meaning has been preserved.
The population (universe) is the complete set of units about which conclusions are to be drawn: all paddy-growing households in a district in a given year. The sampling frame is the list or map from which units are drawn: a village land record, a cooperative's member register, a list of licensed input dealers. Frame errors (omissions, duplicates, out-of-date entries) cause coverage error that no statistical formula corrects. Samples are cheaper, faster and often more accurate than a census because closer supervision reduces non-sampling error.
A statistic is a quantity computed from the sample, such as the sample mean; a parameter is the corresponding population value. The sampling distribution of a statistic is its distribution over all possible samples, and its standard deviation is the standard error. For a simple random sample the standard error of the mean is the population standard deviation divided by the square root of n, multiplied by the finite population correction, the square root of (N minus n) over (N minus 1), when sampling without replacement from a finite population. The correction is usually ignored when the sampling fraction n/N is below about 5 percent.
In probability sampling every unit has a known, non-zero chance of selection, which allows sampling error to be estimated. In simple random sampling every possible sample of size n has the same chance; it may be with replacement or without replacement, and selection uses random-number tables or software. In systematic sampling the first unit is chosen at random from the first k units and every k-th unit thereafter, where the sampling interval k is N divided by n; it is simple to run in the field but can be badly biased if the list has a periodic pattern that coincides with k.
In stratified random sampling the population is divided into non-overlapping strata that are internally homogeneous, such as marginal, small, medium and large farm-size classes, and a random sample is drawn from each. It gains precision when strata differ from one another and guarantees representation of small groups. Under proportional allocation each stratum's sample is proportional to its population size. Under optimum (Neyman) allocation, with equal costs per unit, the sample in stratum h is proportional to N_h multiplied by S_h, the stratum size times its standard deviation, so more variable strata are sampled more heavily.
In cluster sampling the population is divided into groups, such as villages, and whole clusters are selected at random, with all units in them enumerated. It cuts travel and listing costs but is usually less precise than a simple random sample of the same number of elements because units within a cluster tend to be alike; ideally clusters should be internally heterogeneous. Multistage sampling selects units in stages, for example districts, then blocks, then villages, then households, and is the usual design for agricultural and rural household surveys. Selecting villages with probability proportional to size (PPS) and then a fixed number of households per village gives households roughly equal selection probabilities.
In non-probability sampling the chance of selection is unknown, so sampling error cannot be estimated and statistical generalisation to a population is not justified. Convenience sampling takes whoever is easiest to reach, such as farmers attending a market day. Purposive or judgement sampling selects units the researcher believes are typical or informative; in Indian agricultural economics theses the district and blocks are often chosen purposively (for concentration of the crop) and households then selected randomly, and the report should say so plainly. Quota sampling fixes the number of respondents in each category, such as gender or farm size, but leaves the choice of individuals to the enumerator. Snowball sampling asks respondents to name others and suits hidden populations such as informal moneylenders. These methods are legitimate for exploratory work, pretests and qualitative research, provided the report states plainly that results describe the respondents studied and cannot be generalised with a known margin of error.
Required sample size depends on the variability of the characteristic in the population, the precision required (the margin of error that can be tolerated), the confidence level, and, for tests, the power wanted and the size of effect to be detected. It also depends on the design: stratification usually reduces the size needed, while cluster sampling increases it. To halve the margin of error the sample must be four times as large.
For estimating a population mean with margin of error E at confidence level with standard normal value z, and population standard deviation sigma (estimated from a pilot or earlier study), n equals (z times sigma divided by E) squared. If the standard deviation of yield is 12 quintals per hectare and the mean must be estimated within 2 quintals with 95 percent confidence, n equals (1.96 times 12 divided by 2) squared, which is 138.3, rounded up to 139.
For estimating a proportion, Cochran's formula gives n0 equals z squared times p times q divided by e squared, where p is the expected proportion, q is 1 minus p and e is the margin of error as a proportion. When p is unknown, 0.5 is used because it maximises pq and gives the most conservative size; at 95 percent confidence and e of 0.05 this gives 384.16, conventionally 384 or 385. If a pilot suggests 40 percent of farmers use crop insurance, n0 equals 1.96 squared times 0.4 times 0.6 divided by 0.0025, which is 368.8, rounded up to 369. Sample sizes are always rounded up.
When the population is finite and the sample is a noticeable fraction of it, the finite population correction gives n equals n0 divided by (1 plus (n0 minus 1) divided by N). With n0 of 384 and a population of 1,200 members of a cooperative, n equals 384 divided by (1 plus 383/1200), about 291.1, rounded up to 292. Yamane's simplified formula, n equals N divided by (1 plus N e squared), is widely used in social-science theses; it assumes p of 0.5 and 95 percent confidence and gives 333 for N of 2,000 and e of 0.05. Krejcie and Morgan's (1970) table levels off at about 384 for very large populations.
In cluster or multistage samples the design effect (deff), the ratio of the variance of an estimate under the actual design to its variance under simple random sampling of the same size, inflates the required size. For clusters of equal size m and intra-cluster correlation rho, deff is approximately 1 plus (m minus 1) times rho. With 20 households per village and rho of 0.05, deff is 1.95, so a simple random sample requirement of 385 becomes about 751.
The calculated size is the number of completed interviews needed, so it is divided by the expected response rate: 300 completed interviews at an expected 75 percent response rate require 400 selected households. For comparing two group means, the size per group for a two-sided test is approximately 2 times (z for alpha over 2 plus z for beta) squared times sigma squared divided by delta squared, where delta is the smallest difference worth detecting. At 5 percent significance and 80 percent power the z values are 1.96 and 0.84.
Total survey error has two parts. Sampling error arises because only a part of the population is observed; it is random, its size can be estimated from a probability sample as a standard error, and it falls as the sample grows. Non-sampling errors arise from everything else and occur in censuses as well as samples. They include coverage (frame) error, where units are omitted or duplicated; non-response error, where selected units are not interviewed or items are left blank and the non-respondents differ from respondents; measurement or response error, from poorly worded questions, recall lapses, deliberate misreporting of income or area, and interviewer effects; and processing error in coding, entry and tabulation. Non-sampling error is usually systematic, so it produces bias rather than random scatter, and it does not fall as the sample grows; a larger survey with weaker supervision can have more of it.
Mean squared error, variance plus squared bias, combines them. Non-sampling error is controlled by good frames, careful questionnaire design, pretesting, enumerator training and supervision, re-interviews of a sub-sample, call-backs, and consistency checks. Non-response bias is assessed by comparing early and late respondents, and corrected by weighting or imputation under stated assumptions.
Data processing turns completed schedules into an analysable data set. Editing examines the forms for completeness, accuracy, consistency and uniformity. Field editing is done by the enumerator or supervisor on the same day, when omissions and illegible entries can still be corrected from memory or by revisiting the respondent. Central editing is done in the office by a trained editor on all forms, applying uniform rules: checking that area sown does not exceed area operated, that ages fit relationships in the household roster, that units are consistent, and marking impossible answers. Editors never invent answers; unresolved entries get a missing-value code.
Coding assigns a number or symbol to each answer so it can be entered and counted. Closed questions are pre-coded on the form; open answers are post-coded by reading a sample of responses, building categories that are mutually exclusive and exhaustive, and then applying them. A codebook records every variable's name, position, question text, codes and missing-value codes and is the essential document for anyone reusing the data. Double entry or computerised range checks catch entry errors, and the cleaned data, codebook and change log are archived.
Classification arranges data into groups with common characteristics. Qualitative (attribute) classification groups by category, such as caste, tenure status or marketing channel. Quantitative classification groups by class intervals of a variable such as farm size or income, producing a frequency distribution. Class intervals may be exclusive (the upper limit excluded) or inclusive; they should not overlap, should be of equal width where possible, and open-ended classes should be avoided if means are to be computed.
Tabulation presents the classified data in rows and columns. A good table has a number, a clear title stating what, where and when, captions (column headings) and stubs (row headings), units of measurement, totals, notes on definitions and the source. Simple tables show one characteristic; complex tables cross-classify two or more, as when adoption is tabulated by farm size and education. Percentages in a cross-table are computed in the direction of the presumed cause, so that the dependent variable's distribution is compared across categories of the independent variable.
Univariate analysis examines one variable at a time. Frequency distributions and percentages suit categorical variables. For numerical variables, measures of central tendency are the arithmetic mean, affected by extreme values; the median, the middle value, preferred for skewed data such as income or land holding; and the mode, the most frequent value. Measures of dispersion are the range, the interquartile range, the variance and standard deviation, and the coefficient of variation, the standard deviation as a percentage of the mean, which compares variability across variables with different units or means and is widely used to compare instability in prices or yields. A crop yield with mean 40 and standard deviation 10 has a CV of 25 percent. Skewness measures asymmetry; income and farm-size distributions are typically positively skewed, with mean greater than median. Kurtosis measures tail heaviness.
Indian agricultural economics and extension studies often summarise constraint rankings with the Garrett ranking technique. For a rank R_ij given by respondent j to item i out of N_j items ranked, the per cent position is 100 times (R_ij minus 0.5) divided by N_j; each per cent position is converted to a Garrett score from Garrett's table, scores are averaged across respondents, and items are ranked by mean score.
The z test for a mean applies when the population standard deviation is known or the sample is large; the z test for a proportion uses the standard error the square root of p0 q0 divided by n. If 56 percent of 400 sampled farmers prefer an aggregator and H0 says 50 percent, z equals 0.06 divided by 0.025, which is 2.4, significant at 5 percent in a two-tailed test.
Student's t test is used when the standard deviation is estimated from a small sample drawn from an approximately normal population. The one-sample t equals the sample mean minus the hypothesised mean, divided by s over the square root of n, with n minus 1 degrees of freedom. The independent two-sample t test compares two group means; the pooled version assumes equal variances and has n1 plus n2 minus 2 degrees of freedom, and Welch's version does not assume equal variances. The paired t test is used when the same units are measured twice (before and after training) or units are matched; it analyses the differences, with t equal to the mean difference divided by its standard error and n minus 1 degrees of freedom.
One-way analysis of variance (ANOVA) tests whether three or more group means are equal by partitioning total variation into between-group and within-group sums of squares. F equals the between-group mean square, SSB divided by (k minus 1), over the within-group mean square, SSW divided by (N minus k). A significant F says only that at least one mean differs; post-hoc tests such as Tukey's or least significant difference identify which. ANOVA assumes independent observations, normality within groups and equal variances.
The chi-square test of independence tests whether two categorical variables are associated. Expected frequency in each cell equals row total times column total divided by the grand total, and chi-square is the sum over cells of (observed minus expected) squared divided by expected, with (r minus 1)(c minus 1) degrees of freedom. Expected frequencies should generally be at least 5; small cells are merged, or Fisher's exact test is used for 2 by 2 tables. Yates' continuity correction is sometimes applied to 2 by 2 tables. It shows association, not its direction or strength; the contingency coefficient or Cramer's V measure strength.
Karl Pearson's correlation coefficient r measures the strength and direction of a linear relationship between two interval or ratio variables; it equals the covariance divided by the product of the standard deviations, lies between minus 1 and plus 1, and r squared is the coefficient of determination. Its significance is tested with t equal to r times the square root of (n minus 2) divided by the square root of (1 minus r squared). Correlation is not causation. In simple linear regression, Y equals a plus bX, the slope b equals r times sy divided by sx and the intercept a equals the mean of Y minus b times the mean of X; b is the change in Y per unit change in X.
Non-parametric (distribution-free) tests make weaker assumptions about the population and suit ordinal data, small samples and clearly non-normal data. The sign test uses only the direction of paired differences. The Wilcoxon signed-rank test uses both direction and rank of paired differences and is the counterpart of the paired t test. The Mann-Whitney U test compares two independent groups using ranks and is the counterpart of the independent t test; U1 equals n1 n2 plus n1(n1 plus 1)/2 minus R1, where R1 is the rank sum of group 1, and the smaller of U1 and U2 is compared with tables. The Kruskal-Wallis H test extends this to three or more independent groups, the counterpart of one-way ANOVA, and is referred to chi-square with k minus 1 degrees of freedom for moderate samples. The Friedman test compares three or more related samples, such as the same respondents rating several varieties. Spearman's rank correlation, rho equals 1 minus 6 times the sum of d squared divided by n(n squared minus 1), and Kendall's tau measure association between ranks; Kendall's coefficient of concordance W measures agreement among several judges ranking the same items, from 0 to 1. When their assumptions hold, parametric tests are more powerful.
Multiple regression models a dependent variable as a linear function of several explanatory variables: Y equals b0 plus b1 X1 plus ... plus bk Xk plus an error term. Each coefficient bj is the expected change in Y for a one-unit change in Xj holding the other variables constant. Ordinary least squares chooses the coefficients that minimise the sum of squared residuals. Under the classical assumptions, a model linear in parameters, errors with zero mean and constant variance, no correlation among errors, and no perfect linear relation among the regressors, the Gauss-Markov theorem states that OLS estimators are best linear unbiased (BLUE).
R squared is the share of variation in Y explained by the model. It never falls when a variable is added, so adjusted R squared, 1 minus (1 minus R squared) times (n minus 1) divided by (n minus k minus 1), is used to compare models with different numbers of regressors. With R squared of 0.64, n of 50 and k of 4 regressors, adjusted R squared is 0.608. Individual coefficients are tested with t equal to the coefficient divided by its standard error; the overall significance of the regression is tested with F equal to (R squared divided by k) divided by ((1 minus R squared) divided by (n minus k minus 1)). In a log-log (Cobb-Douglas type) model the coefficients are elasticities.
Multicollinearity is high correlation among explanatory variables. It does not bias OLS estimates but inflates their standard errors, so individually insignificant coefficients may coexist with a high R squared and a significant F. It is diagnosed with the variance inflation factor, VIF equal to 1 divided by (1 minus R squared j), where R squared j comes from regressing Xj on the other regressors; a VIF above 10 is a common warning threshold and some authors use 5.
Heteroscedasticity, error variance that changes across observations, is common in cross-section farm data because larger farms have larger absolute variation. OLS remains unbiased but its usual standard errors are wrong; it is detected with plots of residuals and tests such as Breusch-Pagan or White's test, and handled with heteroscedasticity-robust standard errors, weighted least squares or a log transformation. Autocorrelation, correlation of errors across time, affects time-series data and is detected with the Durbin-Watson statistic, where a value near 2 indicates no first-order autocorrelation. Qualitative regressors such as tenure status or region enter as dummy variables; a variable with m categories needs m minus 1 dummies when an intercept is included, and including all m creates perfect multicollinearity, the dummy variable trap. Omitting a relevant variable correlated with included regressors biases their coefficients.
Many agribusiness outcomes are binary: adopted or not, sold to a company or not, defaulted or not. A linear probability model can predict outside 0 to 1, so logit or probit is used. The logistic model writes the log of the odds, ln(P/(1 minus P)), as a linear function of the explanatory variables; P is therefore 1 divided by (1 plus e to the power minus z), where z is the linear predictor. If z equals minus 1 plus 0.5 times 4, which is 1, the predicted probability is about 0.73. Parameters are estimated by maximum likelihood, not least squares.
A logit coefficient is the change in log-odds per unit change in X. Exponentiating it gives the odds ratio: a coefficient of 0.693 gives an odds ratio of about 2, meaning the odds of the outcome double for each unit increase in X. Because the effect on probability depends on where it is evaluated, papers report marginal effects. Overall fit is assessed with the likelihood-ratio chi-square test against an intercept-only model, pseudo R squared measures such as McFadden's, the Hosmer-Lemeshow goodness-of-fit test, and the percentage of cases correctly classified. The probit model uses the cumulative normal distribution instead of the logistic and gives very similar predicted probabilities; logit coefficients are roughly 1.6 to 1.8 times probit coefficients. Multinomial logit handles unordered choices such as marketing channel; ordered logit handles ordered categories; Tobit handles outcomes censored at zero; Heckman's two-step procedure addresses sample selection.
Principal component analysis (PCA) is a data-reduction technique that transforms a set of correlated variables into a smaller set of uncorrelated linear combinations, the principal components, which are ordered so that the first explains the largest possible share of total variance, the second the largest share of what remains, and so on. When variables are measured in different units, PCA is performed on the correlation matrix, which is equivalent to standardising each variable to mean zero and variance one. The variance of each component is its eigenvalue; with p standardised variables the eigenvalues sum to p, so a component with eigenvalue 3.2 among 8 variables explains 40 percent of total variance.
How many components to keep is a judgement guided by rules. The Kaiser criterion keeps components with eigenvalues greater than 1, since each then explains more than a single original variable. The scree plot of eigenvalues against component number is inspected for an 'elbow' after which eigenvalues level off. A cumulative variance target, such as 70 to 80 percent, is also used. PCA builds composite indices, such as an asset or market-access index, and removes multicollinearity before regression.
Factor analysis assumes that observed variables are driven by a smaller number of unobserved latent factors plus variable-specific error. Its purpose is to identify and interpret those latent constructs, such as 'risk attitude' or 'market orientation', behind a battery of attitude items. The difference from PCA is conceptual: PCA summarises total variance and components are exact functions of the variables, whereas common factor analysis models only the shared (common) variance and treats the rest as unique. The two are frequently confused in applied papers.
The suitability of the data is checked first. Bartlett's test of sphericity tests whether the correlation matrix is an identity matrix; it should be rejected. The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy compares correlations with partial correlations; values of about 0.6 or higher are commonly required, and values below 0.5 are considered unacceptable. A factor loading is the correlation between a variable and a factor; loadings of about 0.4 or 0.5 and above are usually treated as meaningful. A variable's communality is the sum of its squared loadings across the retained factors, the share of its variance explained by the common factors: loadings of 0.8 and 0.3 give a communality of 0.73.
Unrotated solutions are hard to interpret because most variables load on the first factor. Rotation redistributes variance to achieve simple structure, each variable loading highly on one factor. Varimax is the most used orthogonal rotation and keeps factors uncorrelated; oblique rotations such as promax and direct oblimin allow factors to correlate, which is often more realistic for attitudes. Exploratory factor analysis (EFA) finds structure; confirmatory factor analysis (CFA) tests a pre-specified one. Each factor is named from the content of its high-loading items.
Discriminant analysis classifies units into predefined groups on the basis of several predictors and identifies which predictors separate the groups best. Fisher's linear discriminant function is a weighted combination of predictors chosen to maximise the ratio of between-group to within-group variance. With g groups and p predictors the number of discriminant functions is the smaller of g minus 1 and p; two groups, such as adopters and non-adopters or defaulting and non-defaulting borrowers, give one function. Wilks' lambda, the ratio of within-group to total variation, tests the significance of the functions; values near 0 indicate strong discrimination and values near 1 indicate none.
Classification accuracy is summarised in a classification matrix, and the hit ratio should be judged against chance: the proportional chance criterion is the sum of squared group proportions, and a common rule asks the hit ratio to exceed it by a quarter. Linear discriminant analysis assumes multivariate normality of predictors within groups and equal covariance matrices across groups, tested with Box's M. Logistic regression makes fewer assumptions and is often preferred for two groups.
Cluster analysis groups units so that units within a cluster are similar and clusters differ from each other, without predefined groups; it is used to build farm typologies, segment consumers or classify markets. Similarity is measured by distance, most often Euclidean distance, the square root of the sum of squared differences across variables, or its square; for two farms differing by 3 and 4 units on two variables the Euclidean distance is 5. Variables are standardised first so large units do not dominate.
Hierarchical agglomerative methods start with each unit as its own cluster and merge the closest pair step by step. Single linkage uses the nearest neighbours between clusters and tends to produce long chains; complete linkage uses the farthest; average linkage uses the average distance; and Ward's method merges the pair that gives the smallest increase in within-cluster sum of squares, producing compact clusters of similar size. The merging history is shown in a dendrogram. Non-hierarchical k-means requires the number of clusters k in advance, assigns each unit to the nearest cluster centroid, recomputes centroids and repeats until assignments stabilise; results depend on starting points. Cluster analysis produces clusters even from random data, so solutions must be validated.
A classification or regression tree splits the sample recursively into subgroups using one predictor at a time, choosing at each node the split that makes the resulting groups most homogeneous in the outcome. For classification, homogeneity is measured by Gini impurity, 1 minus the sum of squared class proportions, used in the CART algorithm of Breiman and colleagues, or by entropy and the resulting information gain, used in Quinlan's ID3 and C4.5 algorithms. A node with 30 adopters and 10 non-adopters has Gini impurity 1 minus (0.75 squared plus 0.25 squared), which is 0.375, and entropy of about 0.81 bits. For regression trees the split minimises the residual sum of squares.
Trees are easy to explain to managers and extension staff, as a set of if-then rules, handle mixed numerical and categorical predictors, and capture interactions without being told. Their weakness is instability and over-fitting: a fully grown tree fits noise in the training data, and a small change in the data can change the whole tree. Over-fitting is controlled by stopping rules (a minimum node size, a maximum depth) and by pruning a large tree back using cross-validated error, as in cost-complexity pruning.
A random forest, introduced by Breiman in 2001, averages many trees to reduce the variance of a single tree. Each tree is grown on a bootstrap sample drawn with replacement from the data, a procedure called bagging, and at each split only a random subset of predictors is considered, which de-correlates the trees. Common defaults consider about the square root of the number of predictors at each split for classification and about one third for regression. A bootstrap sample of size n contains on average about 63.2 percent of the distinct original observations, so about 36.8 percent are left out of each tree; these out-of-bag observations give a built-in estimate of prediction error. Predictions are by majority vote for classification and by averaging for regression.
Forests predict better than single trees but are harder to interpret. Variable importance is measured by the mean decrease in impurity or, more reliably, by permutation importance, the loss of accuracy when a predictor's values are randomly shuffled; partial dependence plots show how predictions change with one variable. For any predictive model, performance is judged on data not used for fitting: a train-test split or k-fold cross-validation, with accuracy, sensitivity, specificity and the area under the ROC curve for classification. Prediction is not causal identification.
A research report lets a reader understand, judge and, in principle, repeat the study. Formats vary by institution, but the usual structure has three parts. The preliminary pages contain the title page, certificates and declaration where required, acknowledgements, table of contents, lists of tables and figures, abbreviations, and an abstract. The abstract states the problem, method, main findings and conclusion. The main text contains the introduction (problem, objectives, hypotheses, scope and limitations), the review of literature, the methodology (study area, sampling design, data sources, variables and their measurement, analytical tools with equations), the results and discussion, and the summary and conclusions with implications. The end matter contains references and appendices such as the questionnaire, detailed tables and derivations.
The discussion interprets results against the hypotheses and earlier studies, explains unexpected findings, and states limitations honestly. Tables and figures are numbered, titled and interpreted rather than restated in the text; estimates carry units and standard errors or confidence intervals. Every source used is cited in one consistent style, author-date (APA, Harvard) or numbered (Vancouver); a reference list holds works cited, a bibliography may add works consulted.
Research ethics protects participants, the integrity of knowledge and the public trust on which research depends. The Belmont Report sets out three principles for research with human subjects: respect for persons, which requires informed and voluntary consent and protection of those with limited autonomy; beneficence, which requires minimising harm and maximising benefit; and justice, which requires fair selection of participants and fair distribution of burdens and benefits. Informed consent means participants understand the purpose, procedures, risks, benefits and their right to refuse or withdraw without penalty; for low-literacy respondents it is often obtained orally and recorded. Confidentiality means information is not disclosed in a way that identifies a participant; anonymity means even the researcher cannot link data to identity. Many institutions require ethics-committee review before fieldwork, and data-protection law differs by country.
Research misconduct is usually defined as fabrication (making up data), falsification (manipulating data, materials or processes, or selectively omitting results) and plagiarism (using others' words or ideas without credit). Questionable practices include selective reporting, specification searching, undisclosed conflicts of interest and gift authorship. Payment for respondents' time is acceptable if it is not coercive.
Use this subject to plan a Master's or PhD thesis that survives the viva. Write objectives that each map to one tool, calculate sample size before choosing villages, pretest the schedule, and build attitude scales with item analysis and a reliability check rather than borrowing one untested. In the examination, practise the one-step calculations (sample size, alpha, chi-square, t, F, Spearman's rho, adjusted R squared) until they are quick, and learn which test matches which data type and design, because most wrong answers come from using an independent-samples test on paired data or a parametric test on ranks.
Five years into work in an agribusiness firm, bank, development agency or extension system, the job is commissioning and using surveys. Check the sampling frame and the response rate before trusting any market-size or adoption figure. Size samples for the smallest segment you intend to report, allow for design effect in village-cluster samples, and budget for enumerator training and back-checks, because non-sampling error is usually larger than sampling error. Use logistic regression or a tree to target customers or borrowers, but validate on held-out data and keep the model explainable to field staff.
A senior manager or head of research sets the standards others follow. Insist on a pre-analysis plan for evaluations, stating hypotheses and main specifications before data arrive, so that results are not the product of specification search. Decide when a randomised trial is feasible and when a quasi-experimental design is the honest alternative, and state its assumptions. Protect respondents' data, set rules for ethics review and data sharing that satisfy the law where data are collected, and judge consultants' reports by their methodology section, not their executive summary.
A researcher with a PhD and long field experience works at the frontier of measurement and inference. The open problems are measurement error in self-reported yields, area and income, which objective measurement and remote sensing are beginning to address; valid causal identification in observational farm data; combining machine-learning prediction with causal inference; construct validity of attitude and risk-preference scales across languages and cultures; and reproducibility through shared code and data. Supervising students means teaching them to state limitations plainly and to value a well-measured null result over a fragile significant one.
This manual does not yet cover qualitative data analysis in depth (thematic coding, grounded theory, content analysis software), structural equation modelling beyond a mention of confirmatory factor analysis, panel-data econometrics (fixed and random effects), time-series methods, survey weighting and variance estimation for complex designs, conjoint and choice experiments, or formal power-analysis tables. Garrett's conversion table is described but not reproduced. Ethics-review requirements and data-protection law differ by country and institution and are described only in general terms. Worked examples use round numbers; real studies need software and should report exact p-values.
Original practice questions written to the syllabus and pattern of the exams named in each question's examTags. They are not past papers and do not reproduce any board's questions.
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