Statistical Methods for Economics Cheat Sheet

This cheat sheet provides a concise overview of statistical methods essential for economics, covering data collection, summarization, probability, hypothesis testing, and time series analysis.

Core Principles

Statistics is the science that deals with the collection, organization, presentation, and interpretation of data.
Descriptive statistics summarizes data characteristics, while inferential statistics generalizes sample results to a population.
Variables can be discrete (countable) or continuous (infinite values between points), measured using nominal, ordinal, interval, or ratio scales.
Data can be collected through primary (direct observation/inquiry) or secondary (existing data) sources.
Frequency distributions organize data, and graphical methods (histograms, polygons, ogives) and tabular methods (tables) present data visually.
Measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation) summarize data distributions.

Formulas

Mean: $ \bar{X} = \frac{\sum f_i X_i}{N} $
Median (for grouped data): $ M_d = l_m + \frac{\frac{N}{2} - C}{f_m} \times h $
Mode (for continuous data): $ M_0 = l_m + \frac{\Delta_1}{\Delta_1 + \Delta_2} \times h $
Karl Pearson's Coefficient of Skewness: $ S_k = \frac{\text{Mean} - \text{Mode}}{\text{s. d.}} $
Spearman's Rank Correlation: $ \rho = 1 - \frac{6 \sum D_i^2}{n(n^2-1)} $
Correlation Coefficient: $ r = \frac{\sum (X_i - \bar{X})(Y_i - \bar{Y})}{\sqrt{\sum (X_i - \bar{X})^2} \sqrt{\sum (Y_i - \bar{Y})^2}} $
Standard Normal Variate: $ z = \frac{X - \mu}{\sigma} $
Chi-squared Statistic: $ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} $
t-statistic (small samples, unknown variance): $ t = \frac{\bar{X} - \mu}{s / \sqrt{n}} $

People

Abraham de Moivre: Developed the mathematical equation for the normal distribution.
Karl Friedrich Gauss: Independently derived the normal distribution equation.
James Bernoulli: Presented the binomial distribution in 1700.