Basic Statistics & Research Methodology Concise class notes tailored to the Part-A “General Aptitude” segment of CSIR-UGC NET/JRF/Ph.D. exams.

 

Basic Statistics & Research Methodology

Concise class notes tailored to the Part-A “General Aptitude” segment of CSIR-UGC NET/JRF/Ph.D. exams.

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1. Quick blueprint of topics & weight

Component (Part A)	Core ideas asked	Typical marks
Descriptive stats	Mean, median, mode, range, SD, CV	2–3
Tabulation & graphs	Frequency tables, histograms, pie/bar interpretation	1–2
Correlation & regression	Pearson r, Spearman ρ, lines of best fit	1–2
Probability basics	Classical, conditional P(A	B), Bayes
Inferential tests	t, χ², F/ANOVA (concept—not computation-heavy)	1
Research methodology	Types, steps, sampling, ethics, ICT tools	3–4

Distribution reflects the last ten NET papers and NTA bulletin samples.

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2. Statistics — 10 formulae you must know

Area	Ready-reckoner
Mean (ungrouped)	$\bar{x}= \tfrac{\Sigma x}{n}$
Variance	$\sigma^{2}= \tfrac{\Sigma(x-\bar{x})^{2}}{n}$
Coefficient of variation	$\text{CV}= \tfrac{\sigma}{\bar{x}}\times100\%$
Median (odd n)	Middle term after sorting
Pearson r	$r= \tfrac{\Sigma(x-\bar{x})(y-\bar{y})}{\sqrt{\Sigma(x-\bar{x})^{2}\,\Sigma(y-\bar{y})^{2}}}$
Regression line (Y on X)	$Y-\bar{Y}= r\frac{\sigma_{y}}{\sigma_{x}}(X-\bar{X})$
Conditional probability	$$ P(A
Bayes theorem	$$ P(B_i
t-stat (mean)	$t=\tfrac{\bar{x}-\mu_0}{s/\sqrt{n}}$
χ² (goodness-of-fit)	$\chi^{2}= \Sigma \tfrac{(O-E)^{2}}{E}$

Keep them on a palm-card for 1-minute review before the exam.

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3. Research methodology essentials

1. Types of research

   • Basic vs. applied - Qualitative vs. quantitative - Descriptive, analytical, experimental, survey, case study.

2. Seven steps of the research process

   1. Identify problem

   2. Literature review

   3. Formulate hypothesis

   4. Design (method & sampling)

   5. Data collection

   6. Analysis & interpretation

   7. Conclusions & report.

3. Sampling snapshot

   • Probability: simple random, stratified, cluster.

   • Non-probability: convenience, purposive, snowball.
     Rule-of-thumb: aim for sample size ≥30 to invoke Central-Limit-Theorem for mean-testing.

4. Research ethics (the “HOC” triad)

   • Honesty—no fabrication/falsification.

   • Objectivity—avoid bias; disclose conflicts.

   • Confidentiality—protect participant data.

5. ICT toolkit — at least one MCQ often asks a tool’s purpose.

   Task	Common tools
   Reference management	Zotero, Mendeley
   Statistical analysis	Excel, SPSS, R
   Plagiarism check	Turnitin, Grammarly
   Literature search	Scopus, Google Scholar

4. Worked micro-examples

1. Mean & SD quick-calc
   Marks: 12, 15, 18, 20. $\bar{x}=16.25$; deviations (–4.25,…). $\sigma = 3.27$. CV ≈ 20%.

2. Pearson r
   X = {1,2,3}, Y = {1,3,5}. Cov = 2, σₓ=1, σᵧ=2 ⇒ r = 1. Perfect positive linear relation.

3. Research step sequence MCQ
   Correct order: Problem → Hypothesis → Design → Collection → Analysis → Interpretation.

4. Bayes teaser
   40% projects use Method A with 90% success; 60% use B with 70%. Probability that a successful project used A?
   $P(A|S)= (0.9×0.4)/(0.9×0.4 + 0.7×0.6)=0.36/0.78≈0.462$.

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5. 3-week mastery plan (20 min/day)

Week 1: Revise descriptive stats & practise 30 mean/median/SD MCQs.
Week 2: Alternate days—correlation/regression drills; other days—probability & Bayes.
Week 3: Read Testbook “Research Aptitude” notes twice; attempt two full Part-A mocks, targeting ≥10/15 in stats-research items.

• With these targeted notes and drill schedule you’ll cover every concept the examiner can throw at you—turning a usually neglected 6-8-mark segment into guaranteed scoring territory.