Exam 3 Glossary R F2010

Exam 3 Glossary R F2010 - Glossary for exam 3 The symbol...

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Glossary for exam 3 α : The symbol for level of significance. β : The probability of failing to reject a false null hypothesis. 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.” Approximate two-sample t test : A test for comparing the means of two independent samples or two treatments where the test statistics has an approximate t distribution. ANOVA (Analysis of Variance) : A statistical procedure for testing the equality of means using variances. Central Limit Theorem: When sampling from a non-Normal population, the sampling distribution of is approximately Normal whenever the sample is large and random. Claimed parameter value: The value of the parameter given in the null hypothesis. E.g. µ 0 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) : Normality of the original population & SRS. (Note: We can use a t- distribution procedure when n < 40 provided the data have no outliers. We must have an SRS, however.) Check (1) data collection and (2) if n < 40, check the outliers in data plot; if n ≥ 40, apply CLT. Conditions necessary for a two-sample t procedure (using t * for C.I. or getting P- value for t table): Normality of both populations & either stratified sample (independent SRS’s) or random allocation. Check (1) data collection and (2) if n 1 + n 2 < 40, check for outliers in both data plots; if n 1 + n 2 ≥ 40, apply CLT. Conditions necessary for ANOVA: Normality of all populations, equality of variances & either stratified random sample (independent SRS’s) or random allocation. Check (1) data collection, (2) if n 1 + n 2 +…+ n k < 40, check for outliers in all k data plots; if n 1 + n 2 + … n k ≥ 40, apply CLT, 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. 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 (n 1 -1) and (n 2 -1).
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