Statistics and quantitative evaluation

Learning objectives

• Identify a variable's level of measurement and the statistics it supports.
• Choose the right measure of central tendency and spread for a dataset, and explain what skew does to the mean.
• Interpret a normal distribution, a correlation coefficient, and R-squared.
• Explain statistical significance, the null hypothesis, and Type I and Type II errors, and match common tests to the questions they answer.
• Calculate percent change, percentage-point change, compound annual growth, and inflation-adjusted dollars.
• Read an estimate's margin of error and confidence interval correctly.
• Calculate present value, interpret a benefit-cost ratio, and know when cost-effectiveness analysis fits better.

Key concepts

Levels of measurement

What you can do with a variable depends on what kind of numbers it holds:

Averaging ordinal ratings ("the mean satisfaction score is 3.4") is common but shaky, because the steps between "satisfied" and "very satisfied" aren't necessarily equal. Reporting the share in each category, or the median, is safer. Only ratio data support statements like "twice as much."

8 more sections follow in the full lesson.

Key terms

• Mean: The arithmetic average of a set of values.
• Median: The middle value of sorted data; resistant to outliers.
• Mode: The most frequently occurring value.
• Right-skewed distribution: A distribution with a long tail of high values; its mean exceeds its median.
• Standard deviation: A measure of how widely values spread around the mean.
• Normal distribution: A symmetric bell curve; about 68% of values lie within one standard deviation of the mean.
• Correlation coefficient (r): A number from −1 to +1 describing the strength and direction of a linear relationship.
• R-squared: The share of variation in a dependent variable explained by a regression model.
• Confounding variable: A third factor that influences both variables in an apparent relationship.
• Statistical significance: A result unlikely to have arisen by chance alone, often judged at p < 0.05.
• Chi-square test: A test of association between two categorical variables.
• Confidence interval: The range (estimate ± margin of error) likely to contain the true value.
• Present value: A future amount converted to today's dollars using a discount rate.
• Benefit-cost ratio: Present value of benefits divided by present value of costs.
• Levels of measurement: Nominal, ordinal, interval, and ratio: the kinds of values a variable holds, which determine the statistics it supports.
• Z-score: The number of standard deviations a value lies above or below the mean.
• Null hypothesis: The assumption of no effect or no difference that a statistical test tries to reject.
• Type I error: A false positive: finding an effect that isn't there.
• Type II error: A false negative: missing an effect that is there.
• Percentage point: The arithmetic difference between two percentages.
• Constant (real) dollars: Money values adjusted for inflation to a common base year.
• Cost-effectiveness analysis: Comparing options by their cost per unit of a non-monetary outcome.