Statistics / Honors Data Analysis
Think With Data

Data, Inference, Decisions

The most comprehensive agentic Honors Statistics course. From exploring data to statistical inference — master every analysis type, develop data science skills, and communicate findings with confidence — guided by Prof. Nadia Osei and SofAI.

Exploratory Data Analysis

• › Categorical vs. quantitative variables and graphical displays
• › Describing distributions using SOCS: Shape, Outliers, Center, Spread
• › Scatterplots, correlation, and bivariate data patterns

Probability & Distributions

• › Basic probability rules and conditional probability
• › Binomial and geometric distributions
• › Central Limit Theorem and sampling distributions

Statistical Inference

• › Confidence interval structure: statistic ± critical value × SE
• › Four-step hypothesis test: Hypotheses, Conditions, Calculations, Conclusion
• › z-tests, t-tests, and chi-square tests of independence

Regression & Association

• › Least-squares regression line and interpreting slope and intercept
• › Residuals and residual plots for checking linearity
• › r² interpretation and inference for regression slope

Describe and compare distributions using the full SOCS framework in every analysis

Apply probability rules and distributions to model real-world random phenomena

Conduct complete inference procedures with conditions checked and conclusions in context

Communicate findings in writing — every statistical claim supported by evidence and context

Three Assessment Types

Honors Statistics assessments reward statistical communication — defining parameters, checking conditions, and writing conclusions in context — not just correct calculations.

Context every answer: never write a bare number. 'The mean is 42 minutes' is correct. 'The mean is 42' earns no credit.

Use SOCS for every distribution description — Shape, Outliers, Center, Spread — in that order, every time.

Check conditions explicitly before every inference procedure. Random? Normal? Independent? Write them out.

Define your parameter in words before stating hypotheses. 'Let p = the true proportion of all seniors who…'

Sketch the Normal curve when solving probability problems — it helps you verify whether your answer is reasonable.

Review every missed problem by asking two questions: Was my error conceptual or procedural? What's the correct reasoning?

Phase 1: Exploring Data and Collecting Data

• Master SOCS framework until it becomes automatic for every distribution description
• Practice drawing and interpreting boxplots, histograms, scatterplots daily
• Study design: practice identifying confounding variables in 5 studies per week
• Written analysis: 2 data description write-ups per week — check for context in every sentence

Phase 2: Probability and Sampling Distributions

• Master binomial and geometric distribution formulas cold
• Practice sampling distribution problems with Central Limit Theorem applications
• Two probability analysis problems per week with full work shown
• Calculator drills: normalcdf, invNorm, binomcdf, binompdf — master each

Phase 3: Inference — Confidence Intervals and Tests

• Complete all inference types: z-test, t-test, chi-square, regression slope
• Master the four-step HCCC format until it becomes automatic
• One complete inference problem per day — check conditions every time
• Peer review sessions: swap written justifications and evaluate each other's reasoning

Phase 4: Statistical Investigation and Portfolio

• Design and complete a full Statistical Investigation project from question to conclusion
• Compile a Data Analysis Portfolio — one polished report per unit
• Review every missed problem — identify if the error is conceptual or procedural
• Final sessions with Prof. Nadia (SofAI): oral explanation of your reasoning — the highest form of understanding