Statistical Methods for Economics Cheat Sheet

This cheat sheet covers essential statistical methods for economics, including data collection, tabulation, graphical representation, probability theory, sampling, statistical inference, hypothesis testing, and index numbers.

Core Principles

Statistics is the branch of 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.
Data can be collected through primary (direct investigation) or secondary sources.
Variables can be classified by measurement scales: nominal, ordinal, interval, and ratio.
Frequency distributions organize data by magnitude and frequency.
Graphical presentation aids in understanding data patterns and comparisons.
Probability theory deals with the likelihood of events occurring.
Sampling allows inferences about a population from a subset.
Statistical inference involves estimation and hypothesis testing.
Index numbers measure changes in variables over time or across locations.
Time series analysis decomposes data into trend, seasonal, cyclical, and irregular components.
Chi-squared tests are used for nominal data to assess independence between variables.

Action Steps

Understand the objectives of the survey.
Design a questionnaire and train investigators.
Define the target population and identify the sampling frame.
Select an appropriate sampling procedure (e.g., simple random, systematic, stratified, cluster).
Collect and process data, checking for incomplete or inaccurate responses.
Analyze data using appropriate statistical tools.
Present findings through tables, graphs, and reports.
Interpret results and draw conclusions about the population.

Formulas

Mean (Discrete): $ \bar{X} = \frac{\sum f_i X_i}{N} $
Mean (Grouped): $ \bar{X} = A + h \frac{\sum f_i u_i}{N} $
Median (Grouped): $ M_d = l_m + \frac{\frac{N}{2} - C}{f_m} \times h $
Mode (Continuous): $ 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.}} $
Bowley's Coefficient of Skewness: $ S_Q = \frac{(Q_3 - M_d) - (M_d - Q_1)}{Q_3 - Q_1} $
Spearman's Rank Correlation: $ \rho = 1 - \frac{6 \sum D_i^2}{n(n^2 - 1)} $
Covariance: $ \sigma_{xy} = \frac{1}{n} \sum_{i=1}^{n} (X_i - \bar{X})(Y_i - \bar{Y}) $
Correlation Coefficient (Pearson): $ r = \frac{\sigma_{xy}}{\sigma_x \sigma_y} $
Linear Regression (Y on X): $ Y = a + bX $
Standard Normal Variate: $ z = \frac{X - \mu}{\sigma} $
Chi-squared Statistic: $ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} $
Crude Birth Rate: $ \text{Crude birth rate} = \frac{\text{Annual Number births}}{\text{Annual mid year population}} \times 1000 $
Crude Death Rate: $ \text{Crude Death Rate} = \frac{\text{Annual number of deaths}}{\text{Annual mid year population}} \times 100 $
Sample Size (Proportion): $ n_i = \frac{P_i (1 - P_i)}{A^2 / Z^2 + P_i (1 - P_i) / N_i} $
Sample Size (Mean): $ n = \frac{Z^2 \sigma^2}{A^2} $

Key Terms

Statistics: The science that deals with the collection, organization, presentation, and interpretation of data.
Population: The entire collection of units of a specified type in a given place and at a particular point of time.
Sample: A subset of the population, drawn scientifically using probability rules to minimize bias.
Parameter: A measure of a population characteristic, usually denoted by Greek letters (e.g., μ, σ).
Statistic: A function of sample values used to estimate a population parameter, typically denoted by English alphabets (e.g., x̄, s).
Sampling Distribution: The probability distribution of a statistic obtained from multiple samples.
Standard Error: The standard deviation of the sampling distribution of a statistic.
Hypothesis Testing: A procedure to test a statement or claim about a population parameter using sample data.
Index Number: A measure of relative changes in a variable over time or across locations, expressed as a percentage relative to a base period.
Time Series: A set of observations on a variable measured at successive points in time.
Chi-Squared Test: A non-parametric test used to analyze categorical data, often for testing independence between variables.

Timeline

1733: Abraham de Moivre gives the mathematical equation for the normal distribution.
1700: James Bernoulli presents the binomial distribution.

People

Abraham de Moivre: Developed the mathematical equation for the normal distribution.
Karl Friedrich Gauss: Independently derived the normal distribution equation.
W.S. Gosset: Presented the t-distribution under the pseudonym 'student'.