Introduction to Applied Statistics
Key concepts, workflow, and practical tools for turning data into insight.
1. What Is Applied Statistics?
| Aspect |
Description |
| Definition |
The use of statistical methods to collect, analyze, interpret, and present data for real‑world problems. |
| Goal |
Turn raw data into actionable information for decision‑making in fields such as business, health, engineering, social sciences, and public policy. |
| Contrast with Theoretical Statistics |
Theoretical statistics focuses on developing new methods and proving their properties; applied statistics emphasizes implementation, model selection, and communication of results. |
2. The Applied‑Statistics Workflow
- Problem Definition – Clarify the research question, objectives, and success criteria.
- Data Collection – Choose a sampling plan, design experiments, or retrieve existing datasets.
- Data Preparation – Clean, transform, and explore data (missing values, outliers, variable types).
- Exploratory Data Analysis (EDA) – Visualize distributions, relationships, and spot patterns.
- Model Building – Select appropriate statistical models (regression, classification, time‑series, etc.).
- Model Assessment – Check assumptions, evaluate fit, and validate with cross‑validation or hold‑out tests.
- Inference & Interpretation – Estimate parameters, test hypotheses, construct confidence intervals, and translate findings into plain language.
- Communication – Create tables, graphs, and reports tailored to the audience; highlight limitations and recommendations.
3. Core Statistical Concepts
| Concept |
Why It Matters |
Typical Tools |
| Population vs. Sample |
Inferences are made about a larger group using a subset. |
Simple random sampling, stratified sampling |
| Variable Types |
Determines which analyses are appropriate. |
Categorical, ordinal, interval, ratio |
| Descriptive Statistics |
Summarize central tendency, spread, and shape. |
Mean, median, mode, variance, standard deviation, IQR, histograms, boxplots |
| Probability Distributions |
Model randomness and underpin inferential methods. |
Normal, binomial, Poisson, exponential, t‑distribution |
| Estimation |
Quantify unknown parameters from data. |
Point estimates, confidence intervals |
| Hypothesis Testing |
Assess evidence for/against a claim. |
p‑values, type I/II errors, power, common tests (t, χ², ANOVA) |
| Regression & Correlation |
Model relationships between variables. |
Simple/Multiple linear regression, logistic regression, Pearson/Spearman correlation |
| ANOVA & MANOVA |
Compare means across multiple groups. |
One‑way, two‑way ANOVA, post‑hoc tests |
| Non‑parametric Methods |
Useful when distributional assumptions fail. |
Wilcoxon, Kruskal‑Wallis, Mann‑Whitney |
| Resampling Techniques |
Estimate sampling variability without strong parametric assumptions. |
Bootstrap, permutation tests |
| Time‑Series & Forecasting |
Analyze data indexed in time order. |
ARIMA, exponential smoothing, seasonal decomposition |
| Multivariate Analysis |
Examine several variables simultaneously. |
Principal Component Analysis (PCA), cluster analysis, discriminant analysis |
4. Common Data Types & Sources
| Domain |
Typical Data |
Collection Methods |
| Business |
Sales, customer churn, web traffic |
Transaction logs, surveys, APIs |
| Health & Medicine |
Patient outcomes, biomarker levels |
Clinical trials, electronic health records |
| Engineering |
|
|