Applied Statistics: From Concept to Practice

Define key terms: distinguish between populations vs. samples; parameters vs. statistics; discrete vs. continuous variables; and the four scales of measurement (nominal, ordinal, interval, ratio).

Describe the role of statistics in business, economics, and science, and identify applications (e.g., stock indices, medical studies, weather forecasting).

Compute and interpret basic descriptive statistics: mean, median, mode, midrange.

Create and read graphical summaries: bar charts, stacked bars, time‑series plots, scatter diagrams—and choose the form that best conveys your message.

Understand inferential ideas: the logic of sampling, confidence intervals, hypothesis testing, and an introduction to regression and correlation.

Identify and apply question types: demographic, behavioural, attitudinal, relational.

Spot and correct sources of bias in wording and sequencing (e.g., leading or double‑barrelled items).

Assess reliability and validity: implement test‑retest, internal consistency (Cronbach’s α), face/content/construct/criterion validity checks.

Build and pilot well‑structured instruments: design logical flows, clear language, and effective skip logic; run pilots to catch misinterpretations.

Compare survey modes (telephone – CATI/IVR vs. mail vs. online) in terms of cost, logistics, and data quality.

Use online tools (Google Forms, Microsoft Forms, SurveyMonkey) for distribution and basic analytics.

Manage sampling and nonresponse: choose probability (SRS, stratified, cluster) vs. non‑probability (convenience, quota, snowball) methods; calculate and apply survey weights.

Maximise response rates & minimise bias: reminders, incentives, personalised invitations, pre‑notification, confidentiality assurances

Identify key survey data sources and understand how to apply for and access confidential microdata (e.g. UKHLS, SOEP, EU‑SILC, Arab/Afro/Eurobarometers) through data archives and ethics agreements.

Navigate software interfaces to load and inspect data:

RStudio: use the Environment, Viewer, and History panes to examine objects

SPSS: switch between Variable View and Data View; use the Output Window for charts and tables

Stata: employ the Command, Results, Review, Variables, and Properties windows; write and run do‑files for reproducibility

Apply Excel’s Analysis ToolPak for quick hypothesis testing and descriptive summaries before importing into statistical software

Understand best practices for data access and management, including ethics, secure licenses, and documentation of transformations

Apply probability rules to compute probabilities of simple and compound events using addition (“or”) and multiplication (“and”) rules, including handling independence and conditional probabilities

Use counting methods and combinatorial formula  to calculate probabilities in finite sample spaces (e.g. card draws, coin‐toss sequences

Define and work with discrete random variables (e.g. Bernoulli, Binomial)

Recognise when to use common distributions—Binomial for two‐outcome experiments, Normal for aggregated independent factors, Poisson for rare events—and compute probabilities via standard tables or software

Distinguish point vs. interval estimates, and understand the trade‐off between bias and precision in choosing estimators

Construct confidence intervals for a single mean (large‑nnn using the zzz-distribution; small‑nnn using the ttt-distribution), for proportions, and for differences between two means or two proportions

Interpret confidence levels correctly—e.g. 95% confidence means 95% of such intervals would contain the true parameter, not that there’s a 95% chance the parameter lies within any one interval

Use statistical software (Stata, R, SPSS, Python, Excel) to calculate CIs via built‑in commands, understanding how to set confidence levels and extract results

Formulate null (H0​) and alternative (H1) hypotheses for means, proportions, and paired/unpaired comparisons

Compute test statistics (z or t) and determine critical values or p-values to decide whether to reject the null hypothesis, accounting for one‑ or two‑tailed tests

Understand Type I and II errors, significance level (α), and the power of a test, and how changing α affects error rates

Implement tests in software: Stata’s ttest, R’s t.test(), SPSS menus, Python’s scipy.stats functions and Excel’s Analysis ToolPak

Use the χ² distribution to

• Estimate a variance’s confidence interval

• Perform goodness‑of‑fit tests comparing observed vs. expected frequencies

• Test independence in contingency tables (χ² test of association)

Apply the F distribution to compare two variances and conduct one‑way ANOVA for comparing means across multiple groups

Run these tests in software: Stata’s tabulate …, chi2 / oneway, SPSS Crosstabs and ANOVA menus, R’s chisq.test() and aov(), Python’s chi2_contingency and statsmodels ANOVA, Excel’s Analysis ToolPak

Calculate Pearson’s r to measure strength and direction of association between two variables, and test its significance

Fit the simple linear regression model Y=α+βX+εY

• Estimate coefficients by least squares.

• Compute and interpret goodness of fit.

• Derive standard errors, confidence intervals, and hypothesis tests for β.

Make predictions from the regression line and assess their precision via prediction intervals.

Use software: Stata’s pwcorr and reg, R’s cor() / lm(), Python’s data.corr() and statsmodels.OLS(), SPSS Bivariate Correlations and Linear Regression menus, Excel’s built‑in functions.

Use software: Applications for multiple regression models with Ordinary least Squares, Discrete Logit and Probit choice models with binary, ordered and multinomial outcomes.