Quantitative Reasoning and Data Analysis: Estimation, Uncertainty, and Inference
Core concepts
Be comfortable with descriptive statistics (mean, median, variance, standard deviation, standard error), distributions, and the logic of hypothesis testing: null and alternative hypotheses, Type I and Type II error, p-values as tail probabilities under the null, confidence intervals, and statistical power. Know when to use common tests-t-test, chi-square, ANOVA, correlation versus regression-and understand effect size versus significance. Data literacy matters too: units, significant figures, logarithmic and semilog plots, rates of change, dilution and concentration calculations, and interpreting error bars (SD vs SEM vs CI).
Traps
The most common error is interpreting a p-value as the probability the null is true or the probability results will replicate-both wrong. Another is treating a nonsignificant result as evidence of no effect, which ignores power. Error-bar items punish students who assume bars are always confidence intervals. Questions may also swap correlation with causation or ask for a rate when a cumulative curve is shown.
Worked rule of thumb
When comparing two groups, compute the ratio of the difference in means to the standard error of that difference; if the magnitude is around two or more, the result is typically significant at conventional thresholds. This mental t-statistic lets you sanity-check options quickly. Always confirm the direction of the effect and the sample size before choosing an answer, since large effects in tiny samples can still be noise.
Study strategy
Practice converting a described experiment into a null hypothesis and predicted test statistic, then verify the units of your answer.