Unit 5 of 12
Sampling Distributions and Estimation
- 12 lessons
- Videos 29 to 40
A statistic varies from sample to sample, and its sampling distribution describes how. This unit uses that idea to compare estimators, build confidence intervals and plan sample sizes.
The standard deviation describes spread among individual observations, while the standard error describes how much a statistic varies over repeated samples. Under stated conditions, the law of large numbers says that in a large sample the sample mean is very likely to be close to the population mean, and the central limit theorem says that its distribution is approximately normal. Estimators are compared by bias, variance and mean squared error. A 95% confidence level describes how often the procedure captures the parameter over repeated samples, not a probability for one computed interval.
Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.
Sampling Distributions
Sampling Distributions of Means and Proportions
How a population distribution differs from the sampling distribution of a statistic, how repeated sampling gives the sampling distributions of a sample mean and a sample proportion, and what the finite population correction does.
Video 29
Standard Deviation and Standard Error
How the standard error describes the variability of a statistic over repeated samples, how the standard error of the mean and its estimate depend on sample size, and how cluster dependence lowers the effective sample size.
Video 30
The Law of Large Numbers
What the law of large numbers says about sample averages of independent and identically distributed observations, what convergence in probability means, how Chebyshev's inequality proves it, and why the gambler's fallacy fails.
Video 31
The Central Limit Theorem
What the central limit theorem says about the standardized sample mean, why it needs independent observations with finite positive variance, and how heavy tails slow or break the normal approximation.
Video 32
Student's t, Chi-Square and F Distributions
How the chi-square, Student's t and F distributions are built from independent standard normal variables, what their degrees of freedom mean, and how to read tail areas, quantiles and critical values.
Video 33
Estimators and Likelihood
Estimation, Bias, Precision and Mean Squared Error
The difference between an estimator and an estimate, and how bias, variance, mean squared error with its bias-variance decomposition, and consistency describe and compare estimators of one parameter.
Video 34
Likelihood and Maximum Likelihood Estimation
How a statistical model turns fixed data into a likelihood function of the parameter, how likelihood ratios compare parameter values, and how the maximum likelihood estimate, the log-likelihood and boundary estimates work.
Video 35
Confidence Intervals and Sample Size
Confidence Intervals and Coverage
What a confidence interval is, how its confidence level and coverage probability describe the procedure over repeated samples, and how the margin of error depends on the level, the spread and the sample size.
Video 36
Confidence Intervals for a Mean
How to build a one-sample t interval for a population mean when the population SD is unknown, how t critical values work, what the normal sampling model assumes and how departures from normality affect coverage.
Video 37
Confidence Intervals for a Proportion
How the Wald, Wilson and Clopper-Pearson intervals estimate a binomial proportion, how their actual coverage differs from the nominal level, and what to report when the count is 0 or n.
Video 38
Bootstrap Standard Errors and Intervals
How the bootstrap resamples observed units with replacement to approximate a sampling distribution, and how to compute a bootstrap standard error, bias estimate and percentile interval and choose the resampling unit.
Video 39
Sample Size and Margin of Error
How to turn a target margin of error into a sample size for a proportion or a mean, why 0.5 is the conservative planning proportion, and how pilot estimates, design effects and nonresponse allowances change the plan.
Video 40