A Brief Statistics Glossary

This is a much abbreviated version of a very complete glossary (that includes helpful examples) made available by the Department of Statistics, University of Glasgow, at http //www.stats.gla.ac.uk/steps/glossary/ 

Alternative Hypothesis The alternative hypothesis H, is formulated in contrast with the null hypothesis, and usually represents a more radical interpretation than the safer H,. For example, if the experiment is designed to determine whether results from two laboratories for the same sample are in agreement, H would state that indeed they do agree and Hj that the two sets of data are different within some agreed confidence limits at some agreed confidence level. 

Confidence Interval A confidence interval gives an estimated range of values, calculated from a given set of sample data, that is likely to include an unknown population parameter (e.g., mean, standard deviation). The width of the confidence interval gives us some idea about how uncertain we are about the unknown parameter (see precision). Confidence intervals are more informative than the simple results of hypothesis tests that decide reject Ho or do not reject Hg since they provide a range of plausible values for the unknown parameter. 

Confidence Interval for the Difference Between Two Means A confidence interval for the difference between two means specifies a range of values within which the difference between the means of the two populations may lie. The confidence interval for the difference between two means contains all the values of (p, — p-2) that would not be rejected in the two sided hypothesis test of [H F l = 2] s [Hi It] p.2], or alternatively [H (p., — p,2)=0] vs [H, (p., — p.2) 0]. In the latter case if the 

Confidence Level The confidence level (CL) is the probability value (1 — p) associated with a confidence interval. It is often expressed as a percentage, e.g., if / = 0.05, then CL = (1 —0.05) x 100 = 95 %. A confidence interval for a mean of a distribution, calculated at e.g. a 95 % CL, means that we are 95 % confident that the stated interval (limits) contains the true population mean or, in other words, that 95 % of all confidence intervals formed in this manner (from different samples of the population) will include the true population mean. 

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