- 11.9.1: Suppose that we wish to study the effect of computer-aided instruct...
- 11.9.2: The KruskalWallis H test is a nonparametric analog of test (11.33) ...
Solutions for Chapter 11.9: Analysiis And Variance
Full solutions for Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
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
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable
Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
Another term for the conidence coeficient.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
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 graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the in-control value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be in-control, or free from assignable causes. Points beyond the control limits indicate an out-of-control process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
In regression, Cook’s distance is a measure of the inluence of each individual observation on the estimates of the regression model parameters. It expresses the distance that the vector of model parameter estimates with the ith observation removed lies from the vector of model parameter estimates based on all observations. Large values of Cook’s distance indicate that the observation is inluential.
Cumulative normal distribution function
The cumulative distribution of the standard normal distribution, often denoted as ?( ) x and tabulated in Appendix Table II.
A subset of effects in a fractional factorial design that deine the aliases in the design.
Deming’s 14 points.
A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality
A matrix that provides the tests that are to be conducted in an experiment.
Estimate (or point estimate)
The numerical value of a point estimator.
A function used in the probability density function of a gamma random variable that can be considered to extend factorials