Class Notes, Chapter 10, second part

One- and Two-Sample Tests of Hypotheses

Tests, in general

Assumptions

Hypotheses

Test statistic - formula - parameters

Distribution of the test statistic

Test statistic - value

Alpha level (significance level)

Critical values - parameter, test statistic, p

Decision

Conclusion

Haven't talked about Random Assignment, an element of the Design of Experiments (DOE). Relevant when there are two groups. We will talk about it later.

Various tests

Mean from a normal distribution, standard deviation "known"

Mean from a normal distribution, standard deviation unknown

Two means from normal distributions, standard deviations "known"

Usually the difference between the two, usually difference = 0, they are equal

Two means from normal distributions, standard deviations unknown, assumed equal

Usually the difference between the two, usually difference = 0, they are equal

Two means from normal distributions, standard deviations unknown, assumed unequal

Usually the difference between the two, usually difference = 0, they are equal

Approximately t-distributed

Must use equal ns!

Paired observations: differences from bivariate normal distribution,

standard deviations and covariance unknown (want positive covariance)

Usually the mean difference = 0, the marginal means are equal

Proportion from a binomial distribution, using the normal approximation

Two proportions from binomial distributions, using the normal approximation

Variance from a normal distribution

Not robust to non-normality

Ratio of variances from normal distributions

Not robust to non-normality