JB

An example of a Z test on the population mean mu. This test is appropriate when sampling from a normally distributed population, when the population standard deviation sigma is known.

An introduction to the concept of the p-value, in the context of one-sample Z tests for the population mean. Much of the underlying logic holds for other tests as well. I discuss what a p-value is, then using simulation I illustrate its distribution when the null hypothesis is true and when the null hypothesis is … Read more

A discussion of Type I errors, Type II errors, their probabilities of occurring (alpha and beta), and the power of a hypothesis test.

A discussion of when to use a one-sided alternative hypothesis and when to use a two-sided alternative hypothesis in hypothesis testing. I assume that the viewer has already had a brief introduction to the notion of one-sided and two-sided tests.

A brief discussion of the meaning of statistical significance, and how it is strongly related to the sample size.

I discuss the relationship between a (two-sided) confidence interval and a two-sided hypothesis test. I discuss the relationship in terms of inference for one mean, but the same concept holds in many other settings as well.

An example of calculating power and the probability of a Type II error (beta), in the context of a one-tailed Z test for one mean. Much of the underlying logic holds for other types of tests as well.

An example of calculating power and the probability of a Type II error (beta), in the context of a two-tailed Z test for one mean. Much of the underlying logic holds for other types of tests as well.

A look at what factors influence the power of a test. This discussion is in the setting of a one-sample Z test on the population mean, but the concepts hold for many other types of test as well. I discuss what factors affect power, and illustrate the concepts visually using various plots. There are no … Read more

An ultra-brief summary of hypothesis testing.