🎯 Learning Objectives
- Explain when descriptive analysis is sufficient.
- Explain when inferential tools become necessary.
- Map business questions to statistical objectives.
- Anticipate the role of uncertainty in decision making.
3.1 Descriptive analysis
Descriptive analysis answers the question "What does the data in my hands say?"
Exploratory mindset
Use descriptive tools when exploring a new dataset, preparing dashboards, or communicating trends without generalising beyond the data.
Common outputs
- Frequency tables and pivot charts.
- Summary statistics (mean, median, quartiles).
- Visualisations such as time series plots and heatmaps.
Example: summarising this semester's quiz scores to identify the toughest question types.
3.2 Inferential analysis
Inferential analysis extends insight beyond the observed sample. We estimate unknown quantities and assess the strength of evidence.
Parameter estimation
Estimating the population mean house price or the proportion of satisfied customers by using the sample statistics as point estimates and pairing them with confidence intervals.
Hypothesis testing
Framing competing claims (null vs alternative hypothesis) and using test statistics to quantify support for one claim over another.
Inferential conclusions are always probabilistic. Communicate both the estimates and the associated uncertainty.
3.3 How descriptive and inferential work together
- Profile the sample. Look for impossible values, missingness, and basic trends.
- Pose the inferential question. Translate the business problem into a statistical statement (e.g., "Has the new ad campaign increased click-through rate?").
- Select an appropriate model. Choose parametric or non-parametric tools depending on the data type and assumptions.
- Communicate results. Report conclusions with an explanation of assumptions and limitations.
3.4 Decisions under uncertainty
Every statistical conclusion feeds a decision. To make responsible decisions:
- Quantify uncertainty with intervals, prediction bands, or risk levels.
- Perform sensitivity analysis — how would the decision change if the estimate shifts by a small amount?
- Consider the cost of errors (false positives vs false negatives).
- Document assumptions for future audits.