Glossary for exam 3 α: The symbol for level of significance (probability of making a type I error) β: The probability of failing to reject (accepting) a false null hypothesis (probability of making a type II error) Alternative hypothesis: The hypothesis that the researcher wants to prove or verify; a statement about the value of a parameter that is either “less than,” “greater than,” or “not equal to.”
ANOVA (Analysis of Variance): a statistical procedure for testing the equality of multiple means using variances. Central Limit Theorem: The name of the statement telling us that when sampling from a non-Normal population, the sampling distribution of ¯ is approximately Normal whenever the sample is large and x random.
Claimed parameter value: The value of the parameter given in the null hypothesis. E.g., μ0 is a claimed parameter value.
Conditions: The basic premises for inferential procedures. If the conditions are not met, the results may not be valid.
Conditions necessary for a one-sample t procedure (using t* for C.I. or getting P-value from t table):
Conditions: (1) Randomization and (2) Normality of population distribution. Check (1) SRS and (2) if n
< 40, check for outliers in data plot; if n ≥ 40, apply CLThm.
Conditions necessary for a two-sample pooled t procedure (using t* for C.I. or getting P-value from t table): Conditions: (1) Randomization, (2) Normality of both population distributions and (3) equality of both population standard deviations. Check (1) Two separate SRS’s or random allocation and (2) if n1 + n2 < 40, check for outliers in both data plots; if n1 + n2 ≥ 40, apply CLThm and (3) largest standard deviation divided by smallest standard deviation < 2.
Conditions necessary for matched pairs t procedure (using t* for C.I. or getting P-value from t table):
Conditions: (1) Randomization and (2) Normality of population of differences Checks: (1) Either SRS or random order of treatments (two measurements on each individual) or random allocation (two matched individuals). (2) if number of pairs < 40, check for outliers in plot of differences; if number of pairs ≥ 40, apply CLThm.
Conditions necessary for ANOVA:
Conditions: (1) Randomization, (2) Normality of all populations and (3) equality of all population standard deviations. Checks: Either independent SRS’s or random allocation. (2) if n1 + n2 + . . . + nk <
40, check for outliers in all k data plots; if n1 + n2 + . . . + nk ≥ 40, apply CLThm and (3) largest standard deviation divided by smallest standard deviation < 2.
Confidence interval: An estimate of the value of a parameter in interval form with an associated level of confidence; in other words, a list of reasonable or plausible values for the parameter based on the value of a statistic. E.g., a confidence interval for μ gives a list of possible values that μ could be based on the sample mean with associated confidence.
Conservative two-sample t test: A test for comparing the means from two independent samples or two treatments where the degrees of freedom are taken to be the minimum of (n1 - 1) and (n2 - 1).
Decreased: What happens to the width of a confidence interval when sample size is increased (or level of confidence is decreased.)
Degrees of freedom: A characteristic of the t-distribution (e.g., n – 1 for a one-sample t); a measure of the amount of information available for estimating σ using s.
Equal population standard deviation: A condition for the pooled two-sample t-test and ANOVA; the condition is met when the largest standard