Quantitative Methods and Tools
What to master
Quantitative items are the most calculation-heavy, so prioritize the formulas that recur: descriptive statistics (mean, median, standard deviation, coefficient of variation = s/mean), the normal distribution and z-transforms, and sampling distributions with standard error σ/√n.
Distributions: normal for continuous measurements, binomial for defectives in fixed-size samples, Poisson for defect counts per unit or time, hypergeometric for sampling without replacement from a finite lot, exponential for time between failures, Weibull for general life data. The central limit theorem explains why X̄ is approximately normal for reasonably sized subgroups even from non-normal populations.
Inference: hypothesis test structure (H0, H1, test statistic, critical region or p-value, decision), one- versus two-tailed tests, Type I error (α - rejecting a true H0, the producer's risk) and Type II error (β - failing to reject a false H0, the consumer's risk), power = 1 − β. Use t when σ is unknown and estimated by s. Know when to use paired t, two-sample t, chi-square (variances, counts of categorical data), F test, ANOVA (comparing three or more means), and regression/correlation (r, r²).
DOE: factors, levels, runs, replication, randomization, blocking, main effects, interactions, and resolution (III, IV, V).
Worked example. A sample of n = 25 has X̄ = 12.4 and s = 0.5. Test H0: µ = 12.5, two-tailed, α = 0.05. t = (12.4 − 12.5)/(0.5/√25) = −1.00. With df = 24, the critical value is about 2.064, so we fail to reject. Note the trap: a p-value is the probability of data this extreme given H0 - not the probability that H0 is true.