Course or series
Introduction to Statistical Hypothesis Testing
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Motivation
Uses manufacturing examples to turn an informal claim into a statement about a population parameter, then introduces the sequence of a statistical test. The examples concern such quantities as a mean rather than a complete scientific explanation.
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Probability and statistics: Review - Part 1
Reviews probability, random variables and distribution functions, including how a cumulative distribution describes probabilities. The later inspected passage demonstrates normal-density commands in R.
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Probability and Statistics: Review - Part 2
Extends the probability review to means, variances and joint distributions. The inspected passages discuss combinations of Gaussian variables and the special relationship between zero correlation and independence for jointly Gaussian variables.
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R Tutorial 1
Demonstrates basic R operations with vectors and matrices, including transposition, matrix multiplication and solving linear systems. The inspected sequence also introduces elementary plotting commands.
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Statistics for Hypothesis Testing - Part 1
Distinguishes a statistic from an estimator and explores how sample means vary across repeated samples. Inspected examples use normal and uniform data in R to make sampling variation visible.
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Statistics for Hypothesis Testing - Part 2
Continues the discussion of sampling distributions, sample size and properties of estimators. The inspected passages connect sample means with central-limit approximations and discuss chi-square examples.
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Statistics for sample mean
Separates the spread of observations from the uncertainty of a sample mean. It compares the normal case with finite-sample exponential examples to show why the distribution of the mean and the distribution of individual measurements differ.
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Statistics for Variance and Proportion
Introduces sampling statistics for variances, variance ratios, differences in means and proportions. A comparison of preferences in two campus populations illustrates how the parameter of interest determines the statistical problem.
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Type I and Type II errors
Explains false-positive and false-negative decisions in hypothesis testing. An R example repeatedly tests generated samples under a specified null model to connect a significance level with a long-run error rate.
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p value
Develops p-values and power using rejection regions and a worked propellant example. The inspected passage relates a p-value to a tail probability under a specified null hypothesis.
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Hypothesis testing of means
Compares tests concerning means, including different treatments of known and unknown variability. The inspected worked material includes paired measurements and R plots, drawing attention to how observations are related.
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Hypothesis testing of variance and proportions
Moves from testing means to tests about variances and proportions. The inspected passages link variance tests with chi-square and F distributions and demonstrate proportion calculations in R.
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Confidence interval construction
Introduces confidence intervals by moving from point estimates to interval estimates. The inspected passages explain how a sampling distribution and knowledge of population variability affect the construction.
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Hypothesis testing using confidence interval
Connects confidence intervals with one-sided and two-sided tests, including R output. The inspected examples compare proposed means or proportions with intervals rather than treating the p-value as the only useful result.
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Hypothesis testing of correlation
“Hypothesis testing of correlation” is listed in Introduction to Statistical Hypothesis Testing. Its place in the course provides the learning context; an individual account of the lecture's content has not yet been checked.
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Statistic for linear regression
Introduces statistical inference for a straight-line regression with an intercept and slope. The inspected passages distinguish the fitted model from assumptions about errors and the properties of its estimates.
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Hypothesis testing in linear regression
Examines inference in linear regression and warns that increasingly flexible polynomial fits can overfit. The checked R discussion also distinguishes uncertainty about a fitted mean from prediction uncertainty for a new observation.
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Power of hypothesis test
Introduces the power of a test through a one-sample mean example. The inspected passages connect power to a specified non-zero effect and to the chance of failing to reject the null under that alternative.
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Factors affecting hypothesis test
Uses a worked example to explore how sample size, effect size, noise and significance level affect a test. The inspected R material demonstrates changing the inputs to a power calculation.