A confidence interval is a range of values, constructed from sample data, that is likely to contain the true value of an unknown population parameter, such as a mean or a proportion. The confidence level, typically 95%, refers to the long-term success rate of the method, not the probability that a specific interval is correct. As the book clarifies, “We can say with 95 percent confidence that the range […] contains the average” (158), meaning that if we were to repeat the sampling process 100 times, we would expect 95 of the resulting intervals to capture the true population value. This tool provides a crucial way to express the uncertainty inherent in using a sample to estimate a characteristic of a larger population.

Wheelan demonstrates the concept’s application in multiple contexts. In polling, a finding that a candidate has 53% support, with a ±3% margin of error, is a 95% confidence interval, indicating the true level of support is likely between 50 and 56 percent. Similarly, in scientific research, such as the study on autism where children with the disorder had a higher average brain volume, the fact that the 95% confidence intervals for the brain volumes of the autistic and non-autistic groups did not overlap provided strong statistical evidence that the observed difference was not just a result of random chance.

The correlation coefficient, or r, is a concise, unitless metric that summarizes the strength and direction of a linear relationship between two variables. It is expressed as “a single number ranging from -1 to 1” (60). A coefficient of 1 indicates a perfect positive correlation, where the two variables move in lockstep in the same direction. A coefficient of -1 indicates a perfect negative correlation, where they move in lockstep in opposite directions. A coefficient of 0 signifies no linear relationship at all. This tool is powerful because it collapses a complex set of data points into an elegant and easily understood descriptive statistic. 

Wheelan provides the height and weight relationship as a classic example of a strong positive correlation. A more modern application is seen in Netflix’s recommendation algorithm, which suggests films by identifying other users whose viewing history is highly correlated with your own. However, Wheelan also uses the concept to deliver one of the book’s most critical warnings: Correlation does not imply causation. He notes that the number of televisions a family owns is likely correlated with their children’s SAT scores, not because watching TV improves test performance, but because a third factor, such as family income, influences both.

The p-value, a cornerstone of hypothesis testing, is used to determine “the specific probability of getting a result at least as extreme as the one you’ve observed if the null hypothesis is true” (152). In practice, p-value measures how surprising a finding is. If researchers are testing a new drug, their null hypothesis is that the drug has no effect. A very small p-value indicates that the observed results (e.g., a large improvement in patient health) would be highly unlikely to occur by chance if the drug were truly ineffective. This leads researchers to reject the null hypothesis and conclude that the drug likely has a real effect. The book points to the autism study, which found a difference in brain volume between two groups of children with a p-value of .002. This means there was only a 2-in-1,000 chance of seeing such a large difference if no true difference existed. This low probability provides strong evidence against the null hypothesis. The p-value is compared against a predetermined significance level (often .05), and this threshold determines the trade-off between making a Type I error (falsely concluding an effect exists) and a Type II error (failing to detect an effect that does exist).

Regression analysis is a technique used to estimate the relationship between variables. As Wheelan explains, regression analysis “is the tool that enables researchers to isolate a relationship between two variables, such as smoking and cancer, while holding constant (or ‘controlling for’) the effects of other important variables” (11). Its basic form, ordinary least squares (OLS), works by fitting the best possible straight line through a scatterplot of data points, quantifying the association with a regression coefficient. This allows researchers to move beyond simple correlation to model complex phenomena. For example, the Whitehall studies used regression to determine that low job control was linked to heart disease even after accounting for confounding factors like smoking and diet.

The book’s extended example, using the Changing Lives dataset, demonstrates how multivariate regression can explain an outcome like weight by simultaneously considering variables such as height, age, sex, and education. Each coefficient represents the independent contribution of that variable while holding the others constant. 

Wheelan also dedicates significant attention to regression’s potential for misuse. He warns that without careful thought, regression analysis can produce misleading results due to common pitfalls like omitted variable bias (leaving out a key factor), reverse causality (confusing cause and effect), and multicollinearity (including highly correlated explanatory variables).