Using statistics to summarise datasets

• Populations and samples
• Sample mean
• Linearity of sample mean
• Deviations
• Sample median
• Sample percentile
• Sample quartiles
• Sample mode
• Sample variance and standard deviation
• Property of sample variance
• Sample correlation coefficient and interpretation

Essential review of probability theory

• random experiment, sample space, events
• defining properties of probability
• frequentist interpretation of probability
• probability of the complement and addition rule
• equally likely outcomes
• independent events
• random variables (RV)
• discrete RVs
• distribution of a RV
• expected value of a discrete RV
• properties of the expectation
• variance of a discrete RV (equivalent definitions)
• Bernoulli RV
• Binomail distribution, with derivation
• Factiorial numbers and binomail coefficient
• continuous RVs
• probability density function of X and P(a<X<b)
• uniform random variable
• normal random variable
• standard normal random variable
• computing normal probabilities
• additivity of normal RVs

Distribution of sampling statistics

• sample from a distribution
• sample mean as a RV
• expected value and variance of sample mean
• simulation study with binomial sample
• approximate areas under the normal curve
• central limit theorem
• normal approximation for the sample mean (for large n)

Estimation

• estimator and estimate
• unbiased estimator of a parameter
• point estimator of population mean
• margins of error via normal approximation
• point estimator of the population variance
• sampling proportions from a finite population
• random sample of size n from a population of size N
• approximate Binomial distribution for the sample when N is much larger than n
• sample proportion as estimator for population proportion
• interval estimator
• point and interval estimate for the sample proportion

Testing statistical hypothesis

• introduction to hypothesis testing
• null and alternative hypothesis
• test statistic
• critical region
• type I and type II errors
• level of significance of a test
• two-sided and one-sided tests
• p-value
• one-sample Z-test (derivation from the distribution of the test statistic)
• T-test

Linear regression

• simple linear regression
• independent and dependent variables
• least square estimates for the parameters of a linear regression model
• estimated regression line
• prediction via the estimated regression line
• confidence intervals for the predicted values
• coefficient of determination

Data analysis with Stata

• Interface of Stata
• Menu system, command windows and Do-files
• Importing and editing datasets
• computing probabilities with Stata
• examples with binomial and normal random variables
• Z-test: practical examples with Stata
• T-test: practical examples with Stata
• test for proportions: practical examples with Stata
• simple linear regression with Stata
• introduction to residual analysis
• multiple linear regression with Stata