Assertion (A): Single-subject designs are well suited to evaluating a caseworker's intervention with one client. Reason (R): Single-subject designs measure the client's target behaviour repeatedly during a baseline phase and an intervention phase. Choose the correct option.

Both A and R are true, and R is the correct explanation of A

Both A and R are true, but R is not the correct explanation of A

Which of the following statements about paraphrasing is correct?

A paraphrase restates an idea in one's own words and must still be cited

A paraphrase must reproduce the original words in quotation marks

A paraphrase needs no citation because the words are one's own

Replacing a few words with synonyms is an adequate paraphrase

A paraphrase restates an idea in one's own words and must still be cited

Which of the following are assumptions of parametric tests such as the t-test? Select all that apply.

Homogeneity of variance between groups

Data measured at the interval or ratio level

An approximately normal distribution

Homogeneity of variance between groups

Data measured only at the nominal level

Data measured at the interval or ratio level

An approximately normal distribution

Research in Social Work I, Quantitative Research: the Meaning, Nature and Scope of Social Science and Social Work Research, the Steps of Research from Problem to Report with Referencing, Citing and Paraphrasing, and Descriptive and Inferential Statistics with Parametric and Non-Parametric Tests

The fifth unit is titled "Research in Social Work : Quantitative and Qualitative Approaches" and is divided into three sections. This chapter takes Section A, quantitative research: the basics of social science and social work research; the steps of research from the identification and formulation of the problem through literature review, objectives and hypotheses, research and sample design, sources, methods and tools, processing and analysis, to writing the report with its presentation, styles of reference, citing and paraphrasing; and basic statistical concepts, the process of statistical enquiry, descriptive and inferential methods, and parametric and non-parametric tests. Research methods are taught across several subjects on this platform; here they are framed for social work, with single-subject designs and programme evaluation, and five statistics are worked because the paper asks for them.

1. The meaning, nature and scope of social science and social work research

Research is the systematic, controlled and critical investigation of questions in order to produce reliable knowledge. Social science research studies human behaviour and social phenomena using the scientific method: it is empirical, systematic, replicable, open to verification and aware that its subjects are people with meanings, values and rights. Social work research applies these methods to questions that arise from social work practice and policy. Its distinctive purpose is practical: to understand the problems the profession deals with, to assess needs, to develop and test interventions, and to evaluate whether programmes and practice achieve what they claim. It is therefore often applied rather than pure, and it is closely tied to ethics, because its subjects are frequently vulnerable.

The scope of social work research includes studies of social problems and client populations (the extent and causes of child labour, the needs of older persons in a district); needs assessment for planning services; evaluation of programmes, their inputs, processes, outputs, outcomes and impact; studies of practice effectiveness, including single-subject designs; action research and participatory research in which communities are co-researchers; policy research; and studies of the profession itself, its education, workforce and values. The practitioner-researcher is an ideal of the profession: a worker who evaluates their own practice systematically, as evidence-based practice requires.

ℹ️ Single-subject designs

A single-subject (single-system) design measures one client's target behaviour repeatedly, first during a baseline phase (A) and then during intervention (B). An AB design compares the two; an ABA or ABAB design withdraws and reintroduces the intervention to show that change follows it; a multiple-baseline design introduces the intervention at different times across behaviours, settings or clients. They let a caseworker test whether their own intervention works, without a large sample.

2. The steps of social science research

Research begins with the identification and formulation of a problem (the syllabus writes "Identifications and Formulations"): a broad area of concern is narrowed to a researchable question that is significant, feasible, clearly bounded and ethical. The literature review locates the question in existing knowledge, identifies gaps, refines concepts and suggests methods. Objectives state what the study will do; a hypothesis is a testable statement of an expected relationship between variables. The null hypothesis (H0) states that there is no relationship or difference, and the alternative hypothesis (H1) that there is; an alternative may be directional ("girls score higher") or non-directional ("the scores differ"). Variables are independent (the presumed cause), dependent (the presumed effect), intervening, moderating and extraneous. Concepts are operationalised: "family support" might be measured by a scale of specified items.

The research design is the plan that links the question to the evidence. Exploratory designs investigate little-known areas; descriptive designs describe characteristics accurately; diagnostic or explanatory designs examine relationships and causes; experimental designs test causal hypotheses by manipulating an independent variable. Donald Campbell and Julian Stanley (1963) classified experimental designs as pre-experimental (the one-shot case study, the one-group pretest-posttest design and the static-group comparison, all weak on internal validity), true experimental (the pretest-posttest control group design, the posttest-only control group design and the Solomon four-group design, all with random assignment) and quasi-experimental (such as the time-series design and the non-equivalent control group design, used when random assignment is impossible, which is common in social work). The sample design specifies the population, the sampling frame, the method, probability (simple random, systematic, stratified, cluster, multistage) or non-probability (convenience, purposive, quota, snowball), and the size.

Data come from primary sources, collected by the researcher, or secondary sources such as the Census, the National Family Health Survey, National Sample Survey reports and agency records. Methods and tools include the survey with an interview schedule (filled in by the investigator) or a questionnaire (filled in by the respondent), observation, structured scales and tests, and document analysis. Processing involves editing (checking for completeness and consistency), coding, classification and tabulation, now usually with software such as SPSS or R. The report is organised as title, abstract, introduction and statement of the problem, review of literature, methodology, results, discussion, conclusions and recommendations, references and appendices. Presentation uses tables, graphs and oral presentation. Styles of reference include APA (7th edition, 2019), MLA (9th edition, 2021), Chicago and Harvard author-date styles. Citing acknowledges the source of an idea or a quotation; a direct quotation reproduces words verbatim in quotation marks with a page reference; paraphrasing restates an idea fully in one's own words and sentence structure and still requires citation. Presenting another's words or ideas as one's own is plagiarism, which the UGC Regulations of 2018 grade by the percentage of similarity.

⚠️ A paraphrase still needs a citation

Changing the words does not make an idea one's own. A paraphrase must be substantially reworded, not a sentence with a few synonyms swapped in (sometimes called "patchwriting"), and it must be cited. An option claiming that paraphrased material needs no reference is wrong.

3. The process of statistical enquiry and descriptive statistics

A statistical enquiry proceeds through planning (defining the purpose, the units and the scope), collection of data, organisation (editing, classification and tabulation), presentation (tables, bar diagrams, histograms, frequency polygons, pie charts), analysis and interpretation. Descriptive statistics summarise data. Measures of central tendency are the mean (the arithmetic average), the median (the middle value when data are ordered, preferred when there are extreme values, as with incomes) and the mode (the most frequent value, the only measure for nominal data). Measures of dispersion are the range, the quartile deviation, the mean deviation, the variance and the standard deviation, the square root of the mean of squared deviations from the mean; the coefficient of variation, the standard deviation divided by the mean and multiplied by 100, compares variability across groups with different means. Skewness describes asymmetry and kurtosis peakedness. Correlation measures the strength and direction of association, from minus one through zero to plus one: Pearson's r for interval or ratio data, Spearman's rank correlation for ranks.

Three worked examples. The median of 12, 7, 3, 9, 15 and 10: ordered, the values are 3, 7, 9, 10, 12 and 15; with six values the median is the mean of the third and fourth, (9 + 10) ÷ 2 = 9.5. The coefficient of variation of a group with mean income ₹5,000 and standard deviation ₹1,000 is 1,000 ÷ 5,000 × 100 = 20 per cent. Spearman's rank correlation is ρ = 1 − 6Σd² ÷ n(n² − 1), where d is the difference between each pair of ranks; if two social workers rank five families by need and the squared differences sum to 4, then ρ = 1 − (6 × 4) ÷ (5 × 24) = 1 − 24 ÷ 120 = 0.8, a strong positive agreement.

🧠 Which average for which data

Nominal data (religion, district): mode only. Ordinal data (ranks, satisfaction levels): median and mode. Interval and ratio data (age, income, scores): mean, median and mode, with the median preferred when a few extreme values would pull the mean, as with household incomes in a slum where one moneylender lives.

4. Inferential statistics: parametric and non-parametric tests

Inferential statistics draw conclusions about a population from a sample, by estimation (point estimates and confidence intervals) and hypothesis testing. A test calculates the probability (p-value) of obtaining the observed result if the null hypothesis were true; if p is below the chosen level of significance (α, usually 0.05), the null hypothesis is rejected. A Type I error is rejecting a null hypothesis that is true (its probability is α); a Type II error is failing to reject a null hypothesis that is false (probability β), and power (1 − β) is the probability of detecting a real effect. Degrees of freedom are the number of values free to vary: n − 1 for a one-sample t-test, n1 + n2 − 2 for an independent-samples t-test, and (rows − 1) × (columns − 1) for a chi-square test of a contingency table. So a comparison of 12 boys and 15 girls by an independent t-test has 12 + 15 − 2 = 25 degrees of freedom, and a chi-square test on a 2 × 5 table has 1 × 4 = 4.

Parametric tests assume interval or ratio data, approximately normal distributions, homogeneity of variance and independent observations; they are more powerful when the assumptions hold. Non-parametric (distribution-free) tests make fewer assumptions and suit nominal or ordinal data, small samples and skewed distributions, which are common in social work data. The chi-square test, which compares observed and expected frequencies, is the most used non-parametric test in social research, for example to test whether school dropout is associated with caste category.

Parametric tests and their non-parametric counterparts
Purpose	Parametric test	Non-parametric counterpart
Compare two independent groups	Independent-samples t-test	Mann–Whitney U test
Compare two related measurements (before and after)	Paired t-test	Wilcoxon signed-rank test; sign test
Compare three or more independent groups	One-way ANOVA (F test)	Kruskal–Wallis H test
Compare three or more related measurements	Repeated-measures ANOVA	Friedman test
Association between two variables	Pearson's r	Spearman's ρ; chi-square for nominal data

🎯 Why social workers often need non-parametric tests

Social work studies often have small samples (twenty residents of a shelter), ordinal measures (satisfaction rated from very poor to very good) or skewed distributions (income, days of absence). Using a t-test on such data can mislead. Choosing the test by the level of measurement and the distribution, not by habit, is part of research competence.

Key takeaways

Social work research applies scientific method to practice questions: problems and populations, needs assessment, programme evaluation, practice effectiveness (single-subject AB, ABA, ABAB and multiple-baseline designs), action and participatory research, policy and the profession.
Steps: problem, literature review, objectives and hypotheses (H0 and H1, directional or not), variables and operationalisation, design (exploratory, descriptive, diagnostic, experimental; Campbell and Stanley 1963: pre-, true and quasi-experimental, including the Solomon four-group design), sampling, sources, tools, processing, analysis and report.
Reports follow a standard structure; reference styles include APA 7th (2019) and MLA 9th (2021); quotations are verbatim with page numbers, paraphrases are fully reworded and still cited, and plagiarism is graded under the UGC Regulations 2018.
Descriptive statistics: mean, median (of 12, 7, 3, 9, 15, 10 it is 9.5), mode; range to standard deviation; coefficient of variation (SD ÷ mean × 100, 20 per cent for 1,000 on 5,000); Pearson's r and Spearman's ρ (0.8 when Σd² = 4 for five ranks).
Inference: p against α = 0.05, Type I (rejecting a true H0) and Type II errors, power; df of n1 + n2 − 2 for an independent t-test (25 for 12 and 15) and (r − 1)(c − 1) for chi-square (4 for 2 × 5); parametric tests and their non-parametric counterparts (Mann–Whitney, Wilcoxon, Kruskal–Wallis, Friedman, Spearman, chi-square).

Practice questions (10)

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.

In Campbell and Stanley's classification, the Solomon four-group design is a:
1. Quasi-experimental design
2. True experimental design
3. Single-subject design
4. Pre-experimental design
Show answer
Answer: B — True experimental design
The Solomon four-group design is a true experimental design: it uses random assignment and adds groups without a pretest to control for the effect of testing. Pre-experimental designs lack control groups or randomisation, and quasi-experimental designs lack random assignment.
Find the median of the following numbers of home visits made by six caseworkers in a month: 12, 7, 3, 9, 15, 10. Type the number.
Numerical answer — type the value.
Show answer
Answer: 9.5
Ordered, the values are 3, 7, 9, 10, 12, 15. With an even number of values the median is the mean of the two middle ones: (9 + 10) ÷ 2 = 9.5. Taking 9 or 10 alone, or the unordered middle values, is the usual mistake.
An independent-samples t-test compares the scores of 12 boys and 15 girls. How many degrees of freedom does the test have? Type the number.
Numerical answer — type the value.
Show answer
Answer: 25
For an independent-samples t-test, df = n1 + n2 − 2 = 12 + 15 − 2 = 25. Using n − 1 for the combined sample (26) or for either group alone is the common error.
Two social workers rank five families by need. The squared differences between their ranks sum to 4. Using ρ = 1 − 6Σd² ÷ n(n² − 1), what is Spearman's rank correlation? Type the number as a decimal.
Numerical answer — type the value.
Show answer
Answer: 0.8
ρ = 1 − (6 × 4) ÷ (5 × (25 − 1)) = 1 − 24 ÷ 120 = 1 − 0.2 = 0.8, a strong positive agreement between the two workers' rankings.
Which of the following are non-parametric tests? Select all that apply.
1. Kruskal–Wallis H test
2. Paired t-test
3. Mann–Whitney U test
4. One-way ANOVA
Show answer
Answer: A — Kruskal–Wallis H test; C — Mann–Whitney U test
Mann–Whitney U and Kruskal–Wallis H are non-parametric, the counterparts of the independent t-test and one-way ANOVA respectively. ANOVA and the paired t-test are parametric, assuming interval data and approximately normal distributions.
A Type I error in hypothesis testing is:
1. Rejecting a null hypothesis that is true
2. Failing to reject a null hypothesis that is false
3. Recording data inaccurately
4. Using the wrong sampling frame
Show answer
Answer: A — Rejecting a null hypothesis that is true
A Type I error rejects a true null hypothesis; its probability is the significance level α. Failing to reject a false null is a Type II error. Frame and recording problems are sources of error in data, not these statistical decision errors.
Assertion (A): Single-subject designs are well suited to evaluating a caseworker's intervention with one client. Reason (R): Single-subject designs measure the client's target behaviour repeatedly during a baseline phase and an intervention phase. Choose the correct option.
1. Both A and R are true, and R is the correct explanation of A
2. Both A and R are true, but R is not the correct explanation of A
3. A is true, but R is false
4. A is false, but R is true
Show answer
Answer: A — Both A and R are true, and R is the correct explanation of A
Both are true and the reason explains the assertion: repeated measurement across baseline (A) and intervention (B) phases shows whether change follows the intervention in that one case, without the large sample a group experiment needs.
Which of the following statements about paraphrasing is correct?
1. A paraphrase must reproduce the original words in quotation marks
2. A paraphrase needs no citation because the words are one's own
3. Replacing a few words with synonyms is an adequate paraphrase
4. A paraphrase restates an idea in one's own words and must still be cited
Show answer
Answer: D — A paraphrase restates an idea in one's own words and must still be cited
The idea remains the source's, so a paraphrase must be cited. Verbatim words in quotation marks are a quotation, not a paraphrase, and swapping a few synonyms is patchwriting, which counts as plagiarism.
Which of the following are assumptions of parametric tests such as the t-test? Select all that apply.
1. Homogeneity of variance between groups
2. Data measured only at the nominal level
3. Data measured at the interval or ratio level
4. An approximately normal distribution
Show answer
Answer: A — Homogeneity of variance between groups; C — Data measured at the interval or ratio level; D — An approximately normal distribution
Parametric tests assume interval or ratio data, approximate normality and homogeneity of variance, along with independent observations. Nominal data call for non-parametric tests such as chi-square.
A chi-square test of association is run on a table cross-classifying 2 categories of school status by 5 caste categories. How many degrees of freedom does it have?
1. 10
2. 9
3. 4
4. 7
Show answer
Answer: C — 4
df = (rows − 1) × (columns − 1) = (2 − 1) × (5 − 1) = 4. Ten is the number of cells, and 7 and 9 come from adding or subtracting the dimensions wrongly.