Statistics MCQs for Lecturer, Assistant Professor & Subject Specialist Exams

Data Types and Scales (Nominal, Ordinal, Interval, Ratio) Sampling Techniques: Probability vs. Non-probability Sampling Survey Methods, Questionnaire Design, and Bias Data Cleaning and Missing Data Mechanisms (MCAR, MAR, MNAR)

Measures of Central Tendency: Mean, Median, Mode, and Quantiles Measures of Dispersion: Variance, Standard Deviation, and Range Skewness and Kurtosis: Moments and Shape of Distribution

Histograms, Boxplots, and Stem-and-Leaf Displays Exploratory Data Analysis (EDA) and Outlier Detection

Probability Laws, Axioms, and Bayes’ Theorem Random Variables: Discrete and Continuous Common Distributions: Binomial, Poisson, Normal, Exponential Generating Functions: MGF, PGF, and Characteristic Functions

Point Estimation: MLE, Method of Moments (MoM), and UMVUE Properties of Estimators: Consistency, Unbiasedness, Efficiency, and Sufficiency Cramer-Rao Lower Bound (CRLB) and Completeness

Laws of Large Numbers (LLN) and Central Limit Theorem (CLT) Convergence in Probability and Distribution

Null and Alternative Hypotheses, Type I & II Errors Power of a Test and p-values Classical Tests: Z-test, T-test, Chi-square (χ²), and F-test Neyman-Pearson Lemma and Likelihood Ratio Tests (LRT)

Interval Estimation for Means, Proportions, and Variances

Sign Test, Wilcoxon Signed-Rank, and Mann-Whitney U Test Kruskal-Wallis and Rank Correlation (Spearman)

OLS Estimation, Assumptions, and Gauss-Markov Theorem Model Diagnostics: Multicollinearity, Heteroskedasticity, and Autocorrelation Model Selection: AIC, BIC, and Cross-Validation

Logistic and Probit Regression for Categorical Data Poisson and Negative Binomial Models for Count Data

Ridge, LASSO, and Elastic Net Regression Fixed Effects, Random Effects, and Multilevel Modeling

Principles of DOE: Randomization, Replication, and Blocking CRD (Completely Randomized Design) and RCBD Latin Square and Factorial Designs

One-way and Two-way ANOVA ANCOVA (Analysis of Covariance) Multiple Comparison Tests (Tukey, Scheffé)

PCA (Principal Component Analysis) and Factor Analysis Cluster Analysis (K-means, Hierarchical) Discriminant Analysis (LDA/QDA) and MANOVA

Stationarity, Autocorrelation (ACF/PACF), and Differencing AR, MA, ARMA, and ARIMA Models ARCH/GARCH Models for Volatility Forecasting Evaluation and Exponential Smoothing

Survival Analysis: Kaplan-Meier and Cox Proportional Hazards Epidemiology: Odds Ratio, Relative Risk, and Clinical Trials Demographic Measures: Birth/Death Rates and Population Growth

Simultaneous Equation Models and Instrumental Variables (IV) Time Series Econometrics and Unit Root Tests

Item Response Theory (IRT) and Reliability/Validity of Tests

Control Charts (X-bar, R, P, C) and Process Capability Risk Assessment and Life Contingencies

Priors (Conjugate/Informative) and Posterior Distributions Credible Intervals and Bayes Factors

Monte Carlo Simulations and MCMC (Gibbs/Metropolis-Hastings) Bootstrapping and Jackknife Resampling Techniques

Statistical Learning: Supervised vs. Unsupervised Learning Programming Tools for Statistics (R, Python, SPSS, STATA)

Methods of Teaching Statistical Concepts Assessment and Evaluation in Statistics

Ethical Issues in Data Reporting and Plagiarism Technical Writing and Statistical Software Usage -----

Nature, Scope, and Applications of Statistics Types of Data and Variables Scales of Measurement Statistical Population and Sampling Units Role of Statistics in Research and Decision-Making

Primary and Secondary Data Collection Census and Sample Surveys Probability Sampling Techniques Non-Probability Sampling Techniques Survey Methods and Questionnaire Design Sampling and Non-Sampling Errors Data Cleaning and Missing Data Mechanisms Ethical Issues in Data Collection

Measures of Central Tendency Measures of Dispersion Quartiles, Deciles, and Percentiles Moments, Skewness, and Kurtosis Coefficient of Variation and Standard Scores Association of Attributes

Frequency Distributions and Tables Histograms and Frequency Polygons Boxplots and Stem-and-Leaf Displays Scatter Plots and Correlation Visualization Exploratory Data Analysis (EDA) Outlier Detection and Treatment Data Transformation and Standardization

Basic Concepts of Probability Conditional Probability and Bayes’ Theorem Random Variables and Probability Distributions Discrete Probability Distributions Continuous Probability Distributions Binomial and Poisson Distributions Normal, Exponential, and Gamma Distributions Joint, Marginal, and Conditional Distributions Expectation, Variance, and Covariance MGF, PGF, and Characteristic Functions

Sampling Distributions Point and Interval Estimation Properties of Estimators Sufficiency and Completeness Cramer-Rao Lower Bound Maximum Likelihood Estimation (MLE) Method of Moments (MoM) UMVUE and Efficiency

Law of Large Numbers Central Limit Theorem Convergence in Probability Convergence in Distribution Slutsky’s Theorem and Applications

Null and Alternative Hypotheses Type I and Type II Errors Level of Significance and Power of Test Z-test and t-test Chi-square and F-tests Likelihood Ratio Tests Neyman-Pearson Lemma Goodness-of-Fit Tests

Confidence Intervals for Means Confidence Intervals for Proportions Confidence Intervals for Variances Confidence Intervals for Regression Parameters

Sign Test Wilcoxon Signed-Rank Test Mann-Whitney U Test Kruskal-Wallis Test Spearman Rank Correlation Kolmogorov-Smirnov Test Runs Test and Median Test

Correlation Coefficients Simple Linear Regression Multiple Regression Analysis OLS Estimation and Assumptions Gauss-Markov Theorem Multicollinearity and Heteroskedasticity Autocorrelation and Diagnostic Testing Model Selection and Validation Residual Analysis and Influence Measures

Logistic Regression Probit Regression Poisson Regression Negative Binomial Regression Link Functions and Exponential Family

Ridge Regression LASSO and Elastic Net Fixed Effects Models Random Effects Models Multilevel and Hierarchical Models

Principles of Experimental Design Completely Randomized Design (CRD) Randomized Complete Block Design (RCBD) Latin Square Design Factorial Experiments Split Plot and Nested Designs Blocking, Randomization, and Replication

One-Way ANOVA Two-Way ANOVA ANCOVA MANOVA Multiple Comparison Procedures Assumptions and Diagnostics of ANOVA

Principal Component Analysis (PCA) Factor Analysis Cluster Analysis Discriminant Analysis Canonical Correlation Analysis MANOVA and Multidimensional Scaling

Components of Time Series Stationarity and Differencing ACF and PACF AR, MA, ARMA, and ARIMA Models Seasonal Models and SARIMA ARCH and GARCH Models Exponential Smoothing Methods Forecast Accuracy and Evaluation

Survival Functions and Hazard Rates Kaplan-Meier Estimator Cox Proportional Hazards Model Clinical Trials and Epidemiological Studies Measures of Morbidity and Mortality Demographic Measures and Population Growth

Simultaneous Equation Models Instrumental Variable Estimation Panel Data Models Unit Root and Cointegration Tests Time Series Econometrics Forecasting and Policy Evaluation

Item Response Theory (IRT) Classical Test Theory Reliability and Validity of Tests Scaling Techniques and Survey Analysis

Statistical Quality Control Control Charts and Process Monitoring Acceptance Sampling Reliability and Life Testing Process Capability Analysis

Risk Theory and Insurance Models Life Tables and Mortality Analysis Life Contingencies and Premium Calculation Pension and Financial Risk Models

Bayesian Inference and Prior Distributions Posterior and Predictive Distributions Bayes Factors and Model Comparison Credible Intervals and Bayesian Estimation Hierarchical Bayesian Models

Monte Carlo Simulation Bootstrap and Jackknife Methods Markov Chain Monte Carlo (MCMC) Gibbs Sampling Metropolis-Hastings Algorithm Numerical Optimization in Statistics

Supervised Learning Unsupervised Learning Classification and Regression Trees Clustering and Dimensionality Reduction Cross-Validation and Model Evaluation Statistical Learning Theory Big Data Analytics and Visualization

R Programming for Statistics Python for Data Analysis SPSS and STATA Applications SAS and MATLAB in Statistics Data Management and Reproducible Research

Census and Vital Statistics Population Growth Models Fertility, Mortality, and Migration Measures National Income and Economic Indicators

Philosophy and Objectives of Statistics Education Methods of Teaching Statistics Lesson Planning and Classroom Activities Bloom’s Taxonomy in Statistics Education Assessment and Evaluation in Statistics ICT and Statistical Visualization Tools

Quantitative Research Methods Research Design and Sampling Frameworks Ethics in Data Collection and Reporting Plagiarism and Academic Integrity Technical Writing and Research Communication Research Proposal and Thesis Writing