Data Analysis
Data Analysis
Analysis answers four kinds of questions: descriptive (what happened), diagnostic (why it happened), predictive (what will happen), and prescriptive (what should we do). Candidates must also be fluent in summary statistics. Measures of central tendency are mean, median, and mode. Measures of dispersion are range, variance, standard deviation, and interquartile range. When data is skewed or has outliers, the median and IQR describe it better than the mean and standard deviation.
Know your sampling methods: simple random, stratified (split the population into groups and sample within each), systematic (every nth record), cluster (sample whole groups), and convenience (non-random and biased). Recognize that sampling bias, survivorship bias, and selection bias undermine otherwise correct math.
Inferential analysis uses hypothesis tests. State a null and alternative hypothesis, choose a significance level (often 0.05), and interpret the p-value as the probability of observing data at least as extreme if the null is true - not the probability that the null is true. A Type I error rejects a true null (false positive); a Type II error fails to reject a false null (false negative). Use t-tests to compare means, chi-square for categorical association, and ANOVA for three or more group means. Correlation measures linear association, not causation.
Traps: reporting the mean for heavily skewed income data; claiming a p-value proves the alternative; confusing statistical significance with practical significance; and forgetting that a confidence interval concerns the parameter, not individual values.
Worked example: response times are 2, 3, 3, 4, and 60 minutes. Mean equals 14.4; median equals 3. Report the median and note the outlier, because the mean is distorted.