Solutions for Chapter 12: One-Way Analysis of Variance

A full factorial experiment with k factors and all factors tested at only two levels (settings) each.

A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

A set of rules that probabilities deined on a sample space must follow. See Probability

An estimator for a parameter obtained from a Bayesian method that uses a prior distribution for the parameter along with the conditional distribution of the data given the parameter to obtain the posterior distribution of the parameter. The estimator is obtained from the posterior distribution.

The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

Formulas used to determine the number of elements in sample spaces and events.

In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

A quality tool that graphically shows the location of defects on a part or in a process.

See U chart

A probability distribution for a discrete random variable

A random variable with a inite (or countably ininite) range.

A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

A subset of a sample space.

A series of pair-wise hypothesis tests of treatment means in an experiment to determine which means differ.

In statistical quality control, that portion of a number of units or the output of a process that is defective.

Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications