- 11.1.1: An experiment was carried out to investigate the effect ofspecies (...
- 11.1.2: Four different coatings are being considered for corrosionprotectio...
- 11.1.3: An investigation of the machinability of beryllium-copperalloy usin...
- 11.1.4: In an experiment to see whether the amount of coverageof light-blue...
- 11.1.5: In an experiment to assess the effect of the angle of pullon the fo...
- 11.1.6: A particular county employs three assessors who areresponsible for ...
- 11.1.7: The accompanying data resulted from an experimentinvolving three di...
- 11.1.8: The paper Exercise Thermoregulation andHyperprolac-tinaemia (Ergono...
- 11.1.9: The article The Effects of a Pneumatic Stool and aOne-Legged Stool ...
- 11.1.10: The strength of concrete used in commercial constructiontends to va...
- 11.1.11: For the data of Example 11.5, check the plausibility ofassumptions ...
- 11.1.12: Suppose that in the experiment described in Exercise 6the five hous...
- 11.1.13: a. Show that a constant d can be added to (or subtractedfrom) each ...
- 11.1.14: Use the fact that EsXijd 5 m 1 ai 1 bj withoai 5 obj 5 0 to show th...
- 11.1.15: The power curves of Figures 10.5 and 10.6 can be used toobtain b 5 ...
Solutions for Chapter 11.1: Two-Factor ANOVA with Kij 5 1
Full solutions for Probability and Statistics for Engineering and the Sciences | 9th Edition
Adjusted R 2
A variation of the R 2 statistic that compensates for the number of parameters in a regression model. Essentially, the adjustment is a penalty for increasing the number of parameters in the model. Alias. In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
The probability of an event given that the random experiment produces an outcome in another event.
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made
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.
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the off-diagonal elements are the covariances between Xi and Xj . Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
A model that contains only irstorder terms. For example, the irst-order response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irst-order model is also called a main effects model
Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.
Fraction defective control chart
See P chart
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r
In multiple regression, the matrix H XXX X = ( ) ? ? -1 . This a projection matrix that maps the vector of observed response values into a vector of itted values by yˆ = = X X X X y Hy ( ) ? ? ?1 .