Ch. 07: Hypothesis Testing Procedures

Lower-tailed test

- A decrease is hypothesized - H1: μ < μ0

Two-tailed test

- A difference is hypothesized - H1: μ ≠ μ0

Null hypothesis

- A hypothesis with no effect - The process of hypothesis testing involves setting up two competing hypotheses: one reflects no difference, no association, or no effect (null hypothesis)

Hypothesis testing

- A specific statement or hypothesis is generated about a population parameter, and sample statistics are used to assess the likelihood that the hypothesis is true

Upper-tailed test

- An increase is hypothesized - H1: μ > μ0

Two-factor ANOVA

- For example, suppose a clinical trial is designed to compare three different treatments for joint pain in patients with osteoarthritis. Investigators might also hypothesize that there are differences in the outcome by sex - The factors are treatment (with three levels) and sex (with two levels)

Type I error

- Refers to the situation where we incorrectly reject H0 when, in fact, it is true

Alternative hypothesis

- Reflects the investigator's belief (called the research or alternative hypothesis)

P-value

- The exact level of significance and it will be less than the chosen level of significance

Level of significance

- The probability that we reject the null hypothesis (in favor of the alternative) when it is actually true

Analysis of variance (ANOVA)

- The technique to test for a difference in more than two independent means - The ANOVA technique applies when there are more than two independent comparison groups. - The ANOVA procedure is used to compare the means of the comparison groups

Type II error

- When one runs a test of hypothesis and decide not to reject H0 (e.g., because the test statistic is below the critical value in an upper-tailed test), then either make a correct decision because the null hypothesis is true or we commit a Type II error

Balanced design

- When sample sizes in each comparison group are equal