The Statistical Investigation Process
Core concepts
The statistical investigation process is a cycle: pose a question → plan and collect data → process and represent → interpret and conclude → communicate. You must understand populations vs samples, census vs survey, sampling methods (simple random, systematic, stratified, cluster, convenience), bias and confounding, types of data (categorical, discrete, continuous), and the two-variable ideas of association, correlation and causation. Know how to choose and interpret displays: histograms, boxplots, scatterplots, and two-way tables.
Traps to watch
- Confusing correlation with causation - a strong (r) is not proof of a causal link.
- Sampling bias: convenience samples from one location rarely represent the population; self-selected online polls are classic traps.
- Misreading a boxplot: the box shows the middle 50% (Q1 to Q3); whiskers extend to non-outlier extremes, and outliers are plotted separately.
- Confusing discrete and continuous - counts are discrete; measurements (heights, times) are continuous.
- Overgeneralising from a small or biased sample to the population.
- Ignoring non-response or missing data which can distort conclusions.
Worked rule of thumb
When asked to evaluate a study, run through the PPDAC checklist: Problem (is the question clear?), Plan (is the sample random and large enough?), Data (are variables measured consistently?), Analysis (is the display appropriate?), Conclusion (does the conclusion match the data?). For a scatterplot, describe direction, form, strength, and outliers - never just "positive". A correlation of (r=0.85) indicates a strong positive linear association but says nothing about which variable causes the other.