Before collecting data a researcher fixes the level of significance at 0.05. Her t-test yields p = 0.03. The correct statistical decision is:

Reject the null hypothesis at the 5% level of significance

Accept the null hypothesis, since p is small

The null hypothesis is proved true

A Type II error has been committed

Reject the null hypothesis at the 5% level of significance

Research Design, Hypothesis, Sampling & Tools

Unit 2 contributes five questions to Paper-1, and the ones candidates lose are not the definitions but the decisions: given a study, name the dependent variable; given a p-value and a significance level, say what happens to the null hypothesis; given a population with no list, choose the sampling method; given a split-half correlation, compute the reliability of the whole test. This chapter is the decision layer above the vocabulary you already have. Every design is written with its Campbell–Stanley notation, every sampling rule with an arithmetic example, every scale of measurement with the statistic it permits, and every reliability method with the formula NET actually uses. Two marks each, no negative marking — so an educated elimination is always worth making, and the traps flagged here are the ones that make elimination possible.

Variables: Independent, Dependent, Extraneous, Intervening and Their Relatives

A variable is any attribute that varies across units and can be measured or categorised. The exam’s favourite move is to hand you a study title and ask you to label its parts, so hold one running example: "Effect of ICT-based instruction on the science achievement of Class IX students in urban and rural schools." The independent variable (IV) is the presumed cause the researcher manipulates or classifies — here, mode of instruction (ICT-based vs conventional). The dependent variable (DV) is the presumed effect that is measured — science achievement. An extraneous variable is any other factor that could influence the DV and so contaminate the IV–DV link — prior achievement, teacher enthusiasm, time of day; when it is not controlled and its effect gets mixed with the IV’s, it is called a confounding variable. An intervening (mediating) variable is a hypothetical internal process that lies between IV and DV and explains how one produces the other — here, perhaps increased attention or reduced anxiety; it cannot be observed directly, only inferred.

Six kinds of variable in one study — role, example and how the researcher deals with each
Variable	Role in the causal chain	In the ICT study	What the researcher does with it
Independent	Presumed cause; the "treatment" or the classifying attribute.	Mode of instruction (ICT / conventional).	Manipulates it (active IV) or selects groups already differing on it (attribute IV — Kerlinger’s term).
Dependent	Presumed effect; the outcome measured.	Score on a science achievement test.	Measures it with a reliable, valid tool, usually before and after.
Extraneous	Outside factor able to affect the DV; a rival explanation.	Prior achievement, teacher quality, class size, time of testing.	Controls it by randomisation, matching, holding constant, or statistical adjustment (ANCOVA).
Control	An extraneous variable that has been held constant or equalised.	Same teacher, same syllabus, same test, same duration for both groups.	Fixes it by design so it cannot vary with the IV.
Intervening / mediating	Unobservable process between IV and DV explaining how the effect happens.	Heightened attention; lowered test anxiety; motivation.	Cannot measure it directly; infers it, perhaps through a proxy scale.
Moderator	A second IV that changes the strength or direction of the IV–DV effect.	Locality (urban/rural) — ICT may help urban pupils more.	Builds it into the design as a factor and tests the interaction.

Two more distinctions score marks. A continuous variable can take any value within a range (height, reaction time); a discrete variable takes separate values only (number of children); a categorical variable sorts into classes (gender, stream). A dichotomous variable has exactly two categories (pass/fail). And an organismic or attribute variable is a characteristic the subject brings that the researcher cannot assign — age, sex, caste, intelligence — which is why studies of such variables can never be true experiments: nobody can be randomly assigned to be fifteen years old.

⚠️ Intervening is inside, extraneous is outside

Candidates confuse these two because both are "other" variables. The test: can you measure and control it? Teacher enthusiasm, room temperature and prior marks are outside the learner, observable, and can be equalised or randomised — extraneous. Motivation, anxiety, interest and attention are inside the learner, unobservable, and lie on the causal path from treatment to outcome — intervening. A second trap: the DV is what is measured, not what is interesting. In "the influence of parental income on college dropout", dropout is the DV even though income is the more discussed variable.

Hypothesis Testing: Null, Alternative, Errors and Level of Significance

Statistical testing runs on an indirect logic. The researcher wants to show that ICT instruction raises achievement (alternative hypothesis, H₁), but what is tested is its denial, the null hypothesis, H₀: "there is no difference between the two groups". The researcher then asks: if H₀ were true, how likely is a difference at least as large as the one observed? That probability is the p-value. Before collecting data he fixes a cut-off, the level of significance (α) — conventionally 0.05 (5%, the 1-in-20 rule) or 0.01 (1%) — and the rule is mechanical: if p ≤ α, reject H₀ and call the result "significant"; if p > α, fail to reject H₀. Note the wording: the null is rejected or not rejected; it is never "accepted" or "proved", because absence of evidence is not evidence of absence. A directional (one-tailed) H₁ — "ICT group will score higher" — places the whole 5% rejection region in one tail; a non-directional (two-tailed) H₁ — "the groups will differ" — splits it 2.5% each side, so the same data can be significant one-tailed and not two-tailed.

The decision matrix — what happens when a decision meets reality
Researcher’s decision	H₀ is actually TRUE (no real effect)	H₀ is actually FALSE (real effect exists)
Reject H₀ (declare significant)	Type I error — probability = α. A false positive: claiming an effect that is not there.	Correct decision — probability = 1 − β, the power of the test.
Fail to reject H₀ (not significant)	Correct decision — probability = 1 − α, the confidence level.	Type II error — probability = β. A false negative: missing an effect that is there.

Worked example. A researcher fixes α = 0.05 before the study. The t-test on her two groups returns p = 0.03. Since 0.03 ≤ 0.05, she rejects H₀: the difference is significant at the 5% level, and the risk that this is a Type I error is at most 5%. Had she chosen the stricter α = 0.01, then 0.03 > 0.01 and she would fail to reject H₀ on the very same data — nothing changed except the threshold. Suppose instead p = 0.08: at α = 0.05 she fails to reject, and if the effect is in fact real she has committed a Type II error. The relationship between the two errors is a see-saw: lowering α (fewer false alarms) raises β (more misses) for a fixed sample. The only way to shrink both at once is to increase the sample size or use a more precise instrument — larger n reduces the standard error, making real effects easier to detect. Power of 0.80 (β = 0.20) is the conventional target.

Set α before the data, never after — choosing the threshold that makes your result significant is p-hacking, a form of research misconduct.
"Significant" means "unlikely under H₀", not "important" — with a very large sample a trivial difference becomes significant; report an effect size (Cohen’s d, r²) alongside p.
Degrees of freedom (df) — the number of values free to vary; for a two-sample t-test df = n₁ + n₂ − 2; the critical value read from the table depends on df and α.
Parametric vs non-parametric — t, F (ANOVA) and Pearson r assume interval data and normality; chi-square, Mann–Whitney and Spearman rho serve nominal/ordinal data or small non-normal samples.

🧠 α is the alarm you set, p is the reading you get

Keep the two numbers in separate pockets. α is chosen before the study, by the researcher, as the maximum Type I risk she will tolerate. p is computed after the study, from the data, as the probability of a result this extreme under H₀. The decision is simply p ≤ α → reject. Two shortcuts for the error questions: Type I has one letter of blame — the researcher cried wolf; Type II is the two-fold miss — the effect was there and the test missed it. And α = 0.05 ↔ 95% confidence, α = 0.01 ↔ 99% confidence; an option that pairs 0.05 with 99% is wrong.

Research Designs: Experimental Families and Non-Experimental Types

A research design is, in Kerlinger’s words, "the plan, structure and strategy of investigation conceived so as to obtain answers to research questions and to control variance". Experimental designs are graded by how well they control the threats to internal validity that Campbell and Stanley (1963) catalogued: history (an outside event between pre- and post-test), maturation (subjects grow, tire, or get hungry), testing (the pre-test itself teaches), instrumentation (the measure changes), statistical regression (extreme scorers drift to the mean), selection (groups differ to begin with), mortality/attrition (people drop out unequally). Their shorthand is worth learning: R = random assignment, O = observation or measurement, X = treatment. Random assignment is what separates the three experimental families below — pre-experimental designs have no control group worth the name, quasi-experimental designs have a comparison group but no randomisation, and true experimental designs have both.

Experimental designs in Campbell–Stanley notation (each line is one group; time runs left to right)
Family	Design	Notation	Main weakness / strength
Pre-experimental	One-shot case study	X O	No pre-test, no control — nothing to compare the outcome with.
Pre-experimental	One-group pre-test–post-test	O X O	Gain is visible but history, maturation, testing and regression all remain uncontrolled.
Pre-experimental	Static-group comparison	X O / — O	Intact groups, no pre-test — selection bias cannot be ruled out.
Quasi-experimental	Non-equivalent control group	O X O / O — O	Intact classes used as they are; pre-test lets you check initial equivalence — the workhorse of school research.
Quasi-experimental	Time-series	O O O X O O O	Repeated measures before and after show whether the jump coincides with X; history remains a threat.
True experimental	Pre-test–post-test control group	R O X O / R O — O	Randomisation controls selection; pre-test controls initial differences; only testing × treatment interaction remains.
True experimental	Post-test-only control group	R X O / R — O	Drops the pre-test, so no testing effect; relies wholly on randomisation for equivalence.
True experimental	Solomon four-group	R O X O / R O — O / R X O / R — O	Combines the two above; the most rigorous, isolates the pre-test effect itself; costly.

Descriptive / survey (normative) research — describes what is: incidence, distribution, attitudes, conditions; census-type or sample survey; no manipulation. Uses questionnaires, schedules, interviews; the most common design in Indian education research.
Correlational research — measures the degree of relationship (r from −1 to +1) between two or more variables in one group; cannot establish cause because neither variable is manipulated and a third variable may drive both.
Ex-post-facto / causal-comparative research (Kerlinger) — starts from an effect that has already occurred and looks backwards for its cause by comparing groups that differ on the IV (smokers vs non-smokers; first-generation vs other learners). The IV is not manipulable; conclusions are tentative.
Case study — intensive, holistic study of a single unit (a child, a school, a policy) over time using many sources; depth over breadth; generalisation is analytic, not statistical.
Ethnography — anthropological study of a culture-sharing group by prolonged participant observation and field notes; seeks the insiders’ (emic) view; the researcher is the instrument.
Action research — conceived by Kurt Lewin (1946), brought to education by Stephen Corey (1953); the practitioner studies his own problem in a spiral of plan → act → observe → reflect; aims at local improvement, not generalisable theory.
Mixed methods (Creswell) — deliberately combines quantitative and qualitative strands in one study: convergent parallel (both at once, compared), explanatory sequential (QUAN first, then qual to explain the numbers), exploratory sequential (qual first to build an instrument, then QUAN), embedded (one strand nested inside the other).

⚠️ Two designs that dress up as experiments

Ex-post-facto research compares groups and talks about causes, so it looks experimental — but the IV (gender, smoking, medium of schooling) was fixed by nature or history, not by the researcher, and the groups were never randomised. Correlational research produces a coefficient and a scatter plot, and candidates read a high r as proof of cause; it is not — ice-cream sales and drowning correlate through a third variable, summer. Only a design with manipulation of the IV and control of extraneous variables can support a causal claim, and only random assignment makes that control convincing. When an option describes "intact classes assigned to methods without randomisation", the design is quasi-experimental, never true experimental.

Sampling Decisions and Sample Size Logic

The purpose of sampling is to say something about a population from a sample at a known risk of error. Sampling error is the unavoidable gap between a sample statistic and the population parameter that arises purely because a sample, not the whole, was studied; it is random, shrinks as the sample grows, and can be estimated only for probability samples. Non-sampling error — a faulty frame, non-response, interviewer bias, wrong coding — is systematic, does not shrink with sample size, and afflicts censuses too. The standard error of a mean is σ ÷ √n: with n = 100, SE = σ ÷ 10; with n = 400, SE = σ ÷ 20. Quadrupling the sample halves the error — precision rises with the square root of n, which is why very large samples are wasteful beyond a point and why sample size is a matter of precision required, not of a fixed percentage of the population.

Choosing the sampling method from the situation — the form in which NET asks it
Situation described in the stem	Best method	Why, and the trap option
A complete list of 500 employees exists; the researcher wants every one to have an equal chance.	Simple random (lottery / random-number table)	Small, listed, homogeneous population. Trap: systematic is not the same — it gives equal chance to units but not to all combinations.
A register of 1,200 students; the researcher takes a random start and then every 20th name.	Systematic	k = N ÷ n. Danger: periodicity in the list (every 20th name a class monitor) biases it.
Arts, science and commerce students must all be represented in proportion to their numbers.	Stratified random (proportionate)	Heterogeneous population with known strata. Trap: quota sampling fills the same proportions but non-randomly.
Rural households across a state; no household list, only a list of villages.	Cluster (then multistage if villages are further sub-sampled)	Geographically dispersed, no unit-level frame; cheaper fieldwork. Trap: stratified, which needs a list of every unit.
Injecting drug users, undocumented migrants, or members of a secret society — no list can exist.	Snowball (chain referral)	Hidden or stigmatised population; each respondent recruits the next. Trap: purposive, which requires the researcher to already know the units.
A study of "outstanding principals" needs information-rich cases chosen on expert judgement.	Purposive / judgemental	Qualitative depth; typical, extreme or critical cases. Trap: convenience — availability is not judgement.
A lecturer pilots her questionnaire on whichever students happen to be in the library that afternoon.	Convenience / accidental	Acceptable only for pilot testing; no generalisation possible. Trap: calling it "random" because no one was deliberately chosen.

Worked example 1 — systematic sampling. Population N = 1,200 students, required sample n = 60. Sampling interval k = N ÷ n = 1,200 ÷ 60 = 20. Choose a random start between 1 and 20 — say 9. The sample is the 9th, 29th, 49th, 69th … names, i.e. 9 + 20(i − 1) for i = 1 to 60; the last unit is 9 + 20 × 59 = 9 + 1,180 = 1,189. Worked example 2 — proportionate stratified allocation. A college has 2,000 students: 1,200 girls and 800 boys; n = 200. Girls’ share = 1,200 ÷ 2,000 = 0.60, so 0.60 × 200 = 120 girls; boys’ share = 800 ÷ 2,000 = 0.40, so 0.40 × 200 = 80 boys; check 120 + 80 = 200. In disproportionate allocation the researcher deliberately over-samples a small but important stratum (say, 50 from a 100-strong minority) and re-weights at analysis.

Worked example 3 — how large a sample? Four things push sample size up: greater heterogeneity of the population, higher precision wanted (smaller margin of error e), higher confidence level, and plans for sub-group analysis. Yamane’s formula (1967) for a finite population at 95% confidence is n = N ÷ (1 + N e²). For N = 2,000 and e = 0.05: N e² = 2,000 × 0.0025 = 5; 1 + 5 = 6; n = 2,000 ÷ 6 = 333.3, rounded up to 334. Tighten the margin to e = 0.03: N e² = 2,000 × 0.0009 = 1.8; n = 2,000 ÷ 2.8 = 714.3 → 715. Notice that the population size barely matters once it is large: for N = 20,000 at e = 0.05, n = 20,000 ÷ (1 + 50) = 392 — only 58 more respondents for ten times the population. In qualitative research the criterion is different: sampling stops at saturation, the point where new cases add no new themes.

ℹ️ Population, frame, sample, unit — four words, four things

The target population is every unit the conclusions are meant to cover (all Class IX students in Bihar). The sampling frame is the actual list from which units are drawn (the UDISE roll of one district) — every gap between frame and population is coverage error. The sampling unit is what is selected at each stage (a school, then a section, then a student); the element is the unit on which data are finally collected. A representative sample mirrors the population on the variables that matter; random is a procedure, representative is an outcome — a random sample is usually but not guaranteed to be representative, and a large sample can be badly biased if the frame was wrong (the classic 1936 Literary Digest poll of 2.4 million).

Tools, Attitude Scales, Reliability, Validity and Scales of Measurement

Choose the tool from the respondent and the variable. A questionnaire is self-administered — best for literate, dispersed respondents and sensitive topics where anonymity matters; it can carry closed items (fixed alternatives, easy to code) or open items (free response, rich but laborious). An interview schedule is the same instrument read out and filled by the investigator — the choice for illiterate respondents, children and probing. Observation is the only tool that captures behaviour rather than reports of it, and needs a schedule with categories (as in FIACS) or a checklist to be reliable; observer effects (the Hawthorne effect — people change when watched) are its standing threat. Rating scales turn a judgement into a number: numerical, graphic, descriptive, or the forced-choice paired-comparison. Whatever the tool, it goes through pilot testing on a small sample first, to catch ambiguous items, estimate time and compute reliability before the main study.

Attitude scales deserve their own paragraph because NET asks for the constructor of each. Likert (Rensis Likert, 1932) — the summated rating scale: each statement is rated on a 5-point (sometimes 7-point) agree–disagree continuum, scores are summed, and the scale is ordinal though routinely treated as interval. Thurstone (1928) — equal-appearing intervals: a panel of judges sorts statements into 11 piles from least to most favourable, each statement gets the median pile as its scale value, and the respondent simply ticks the statements he agrees with; laborious but yields interval-like values. Guttman (1944) — cumulative scalogram: statements are ordered so that agreeing with a harder one implies agreeing with all easier ones. Osgood’s semantic differential (1957) — 7-point bipolar adjective pairs (good–bad, strong–weak) measuring the connotative meaning of a concept. Bogardus social distance scale (1925) measures willingness to admit members of a group to closer relationships. Sociometry (J. L. Moreno) maps peer choices in a group into a sociogram — stars, isolates, cliques.

Stevens’ four scales of measurement (1946) — properties, examples and the statistics each allows
Scale	Properties	Examples	Permitted central tendency / statistics
Nominal	Names or categories only; numbers are labels; no order.	Gender, religion, roll numbers, jersey numbers, PIN codes.	Mode; frequency counts; chi-square.
Ordinal	Categories with a rank order, but unequal or unknown gaps between ranks.	Merit rank, grades A/B/C, socio-economic class, Likert item responses.	Median, percentiles; Spearman rho; Mann–Whitney.
Interval	Equal intervals, but an arbitrary zero — zero does not mean "none", so ratios are meaningless.	Temperature in °C or °F, calendar years, IQ scores, standardised test scores.	Mean, standard deviation; Pearson r; t-test, ANOVA.
Ratio	Equal intervals and a true zero meaning absence; ratios are meaningful (20 kg is twice 10 kg).	Height, weight, age, income, reaction time, temperature in Kelvin, number of correct answers.	All of the above plus geometric mean and coefficient of variation.

Worked example — reliability. Test-retest administers the same test twice, weeks apart, and correlates the two sets of scores (coefficient of stability); it is inflated by memory and deflated by real change. Parallel forms correlates two equivalent versions (coefficient of equivalence). Split-half needs only one sitting: correlate the odd-numbered items with the even-numbered items. But that correlation is the reliability of half a test, and shorter tests are less reliable, so it is stepped up with the Spearman–Brown prophecy formula: r_full = 2r_half ÷ (1 + r_half). If the odd–even correlation is 0.60, then r_full = (2 × 0.60) ÷ (1 + 0.60) = 1.20 ÷ 1.60 = 0.75. If it were 0.80: (2 × 0.80) ÷ 1.80 = 1.60 ÷ 1.80 = 0.89. Cronbach’s alpha generalises split-half to all possible splits and is the standard for Likert scales (≥ 0.70 acceptable, ≥ 0.90 for high-stakes decisions); Kuder–Richardson KR-20 is its version for right/wrong items; inter-rater reliability (Cohen’s kappa) covers observation and essay marking. All reliability coefficients run from 0 to 1 and are necessary but not sufficient for validity.

Face validity — the tool appears to measure the trait, to a layman or the respondent; weakest, but matters for cooperation.
Content validity — items sample the whole domain in the right proportions; established by expert judgement against a table of specifications (blueprint); the key type for achievement tests.
Construct validity — the tool measures the theoretical construct (anxiety, creativity) it claims to; shown by convergent validity (agrees with other measures of the same construct), discriminant validity (disagrees with measures of different constructs) and factor analysis.
Criterion-related validity — scores agree with an external criterion: concurrent when the criterion is measured at the same time (new IQ test vs an established one), predictive when the criterion lies in the future (entrance-test score vs first-year marks). The difference is purely the timing of the criterion.

🧠 NOIR, and zero decides

The scales ascend N-O-I-R — Nominal, Ordinal, Interval, Ratio — each adding one property: names → order → equal gaps → true zero. Every statistic permitted at a lower scale is permitted at a higher one, never the reverse. The interval/ratio question always turns on zero: 0 °C is not "no temperature" (interval), 0 K is (ratio); year 0 is a convention (interval), age 0 is birth (ratio). A Likert item is ordinal; a summed Likert scale is treated as interval in practice — if an option says a single Likert response is interval data, it is the trap. And keep the constructors straight: Likert 1932 summated, Thurstone 1928 judges, Guttman 1944 cumulative, Osgood 1957 semantic differential.

Key takeaways

IV is manipulated or classified, DV is measured, extraneous variables are outside and controllable, intervening variables are inside and inferred, a moderator changes the strength or direction of the IV–DV link.
Decision rule: p ≤ α → reject H₀. Type I (α) = false alarm, Type II (β) = missed effect, power = 1 − β; lowering α raises β unless n is increased. α = 0.05 ↔ 95% confidence.
Campbell–Stanley: R = random assignment, O = observation, X = treatment. Pre-experimental = no real control; quasi = comparison group without randomisation; true = randomised groups. Ex-post-facto and correlational designs cannot prove cause.
Systematic: k = N ÷ n, random start, then every k-th; stratified proportionate: stratum share × n; Yamane n = N ÷ (1 + N e²). Sampling error falls with √n — quadruple the sample to halve the error; snowball for hidden populations, cluster when no unit list exists.
Spearman–Brown: r_full = 2r ÷ (1 + r); 0.60 → 0.75. Likert = summated 5-point (1932), Thurstone = judges and equal-appearing intervals (1928). Validity: content (experts), construct (convergent/discriminant), criterion (concurrent now, predictive later). NOIR — zero decides interval vs ratio.

Practice questions (8)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

A researcher studies "the effect of hours of sleep on the examination scores of undergraduate students". In this study, examination score is the:
1. Independent variable
2. Dependent variable
3. Extraneous variable
4. Intervening variable
Show answer
Answer: B — Dependent variable
The dependent variable is the presumed effect that the researcher measures to see whether it changes with the cause — here the examination score, which is expected to depend on sleep. Hours of sleep is the independent variable, the presumed cause. The trap is the independent variable, chosen by candidates who confuse the variable that is interesting with the one that is manipulated or classified. An extraneous variable would be an outside factor such as coaching or prior CGPA, and an intervening variable would be an unobservable internal process such as alertness lying between sleep and score.
Before collecting data a researcher fixes the level of significance at 0.05. Her t-test yields p = 0.03. The correct statistical decision is:
1. Accept the null hypothesis, since p is small
2. The null hypothesis is proved true
3. A Type II error has been committed
4. Reject the null hypothesis at the 5% level of significance
Show answer
Answer: D — Reject the null hypothesis at the 5% level of significance
The decision rule is mechanical: if p ≤ α, reject H₀. Here 0.03 ≤ 0.05, so the null hypothesis is rejected and the difference is called significant at the 5% level. The trap is the option about accepting the null because p is small — a small p is evidence against H₀, not for it, and in any case the null is never "accepted", only rejected or not rejected. Nor is any hypothesis ever "proved" by a sample. A Type II error means failing to reject a false null; since the null was rejected here, the only error possible would be a Type I error, whose probability is at most α = 0.05.
Sixty students are randomly assigned to two groups; both groups take a pre-test, one group receives the new teaching method, and both take a post-test. In Campbell–Stanley notation this is "R O X O / R O — O". Which type of design is this?
1. True experimental design
2. Quasi-experimental design
3. Pre-experimental design
4. Ex-post-facto design
Show answer
Answer: A — True experimental design
The letter R — random assignment of subjects to groups — is what makes a design true experimental; combined with a control group and pre- and post-tests, this is the classic pre-test–post-test control group design. The quasi-experimental option is the trap: it has the same "O X O / O — O" shape but uses intact groups without randomisation, so selection bias remains. A pre-experimental design lacks a proper control group altogether (e.g. O X O alone), and an ex-post-facto design manipulates nothing, studying an independent variable that has already occurred.
A population of 1,200 students is listed serially. A researcher wants a systematic sample of 60 and draws the random start 9. The third student selected in the sample bears the serial number:
1. 29
2. 40
3. 49
4. 69
Show answer
Answer: C — 49
Sampling interval k = N ÷ n = 1,200 ÷ 60 = 20. Starting at 9, the selected serial numbers are 9, 9 + 20 = 29, 29 + 20 = 49, 69, and so on; the third is therefore 49. The value 29 is the trap for candidates who count the random start as the "zeroth" unit rather than the first — 29 is the second student selected. The value 69 is the fourth student, and 40 comes from wrongly multiplying the interval by two without adding the random start. In systematic sampling the i-th unit is always start + k(i − 1).
A researcher wants to study the experiences of homeless persons who use a drug for which no register or list exists. Each participant she locates is asked to introduce her to others like them. The sampling technique being used is:
1. Stratified random sampling
2. Quota sampling
3. Systematic sampling
4. Snowball sampling
Show answer
Answer: D — Snowball sampling
When the population is hidden, rare or stigmatised and no sampling frame can exist, the only workable method is snowball (chain-referral) sampling, in which each located respondent recruits the next — exactly the procedure described. Stratified random and systematic sampling are both probability methods that require a complete list of the population, which is precisely what is absent here. Quota sampling is the non-probability trap: it does fill fixed quotas without a list, but the researcher herself picks whoever is available to fill them rather than relying on referral chains from participants.
The scores on the odd-numbered items of a 40-item test correlate 0.60 with the scores on the even-numbered items. Using the Spearman–Brown formula, the estimated reliability of the full test is:
1. 0.60
2. 0.75
3. 0.80
4. 0.36
Show answer
Answer: B — 0.75
The odd–even correlation is the reliability of a half-length test; the Spearman–Brown prophecy formula steps it up to full length: r_full = 2r ÷ (1 + r) = (2 × 0.60) ÷ (1 + 0.60) = 1.20 ÷ 1.60 = 0.75. The value 0.60 is the trap for candidates who report the split-half correlation itself as the reliability, forgetting that a shorter test is always less reliable than the whole. The value 0.36 is r² (0.60 × 0.60), the coefficient of determination, which has nothing to do with reliability estimation, and 0.80 is simply a plausible round number with no arithmetic basis here.
Temperature recorded in degrees Celsius is an example of which scale of measurement?
1. Interval scale
2. Ratio scale
3. Ordinal scale
4. Nominal scale
Show answer
Answer: A — Interval scale
Celsius has equal intervals (the gap from 10° to 20° equals that from 20° to 30°) but an arbitrary zero — 0 °C is the freezing point of water, not the absence of temperature — so 40 °C is not "twice as hot" as 20 °C. That combination defines the interval scale. The ratio scale is the trap: it needs a true zero, which only the Kelvin scale supplies. Ordinal would mean merely ranked categories with unknown gaps (hot, warm, cold), and nominal would mean unordered labels; Celsius readings carry far more information than either.
Consider the following statements about measurement tools:
1. A test can be highly reliable and yet not valid.
2. Predictive validity is a form of criterion-related validity.
3. The Thurstone attitude scale requires a panel of judges to assign scale values to statements.
Which of the statements are correct?
1. 1 and 2 only
2. 2 and 3 only
3. 1, 2 and 3
4. 1 and 3 only
Show answer
Answer: C — 1, 2 and 3
All three statements are correct. Reliability is consistency and validity is truthfulness; a stuck weighing machine gives the same wrong reading every time, so reliability is necessary but not sufficient for validity (statement 1). Criterion-related validity has two forms distinguished only by when the criterion is measured — concurrent (now) and predictive (later) — so statement 2 holds. Thurstone’s method of equal-appearing intervals (1928) depends on judges sorting statements into eleven piles and taking the median as each statement’s scale value (statement 3). The option "1 and 2 only" is the trap for candidates who confuse Thurstone with Likert, whose summated scale needs no judges.