GLOSSARY 693Dispersion.The amount of variability exhibited by data.
Distribution free methods(s).Any method of infer-
ence (hypothesis testing or confidence interval con-
struction) that does not depend on the form of the
underlying distribution of the observations. Sometimes
called nonparametric method(s).
Distribution function.Another name for a cumulative
distribution function.
Efficiency.A concept in parameter estimation that uses
the variances of different estimators; essentially, an esti-
mator is more efficient than another estimator if it has
smaller variance. When estimators are biased, the con-
cept requires modification.
Enumerative study.A study in which a sample from a
population is used to make inference to the population.
SeeAnalytic study.
Erlang random variable.A continuous random vari-
able that is the sum of a fixed number of independent,
exponential random variables.
-error (or -risk).In hypothesis testing, an error in-
curred by failing to reject a null hypothesis when it is
actually false (also called a type II error).
-error (or -risk).In hypothesis testing, an error in-
curred by rejecting a null hypothesis when it is actually
true (also called a type I error).
Error mean square.The error sum of squares divided
by its number of degrees of freedom.
Error of estimation.The difference between an esti-
mated value and the true value.
Error sum of squares.In analysis of variance, this is
the portion of total variability that is due to the ran-
dom component in the data. It is usually based on
replication of observations at certain treatment com-
binations in the experiment. It is sometimes called the
residual sum of squares, although this is really a better
term to use only when the sum of squares is based on
the remnants of a model fitting process and not on
replication.
Error variance.The variance of an error term or com-
ponent in a model.
Estimate (or point estimate).The numerical value of
a point estimator.
Estimator (or point estimator).A procedure for pro-
ducing an estimate of a parameter of interest. An esti-
mator 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.Event.A subset of a sample space.
Exhaustive.A property of a collection of events that
indicates that their union equals the sample space.
Expected value.The expected value of a random vari-
able Xis its long-term average or mean value. In the
continuous case, the expected value of X is
where f(x) is the density function
of the random variable X.
Exponential random variable.A continuous random
variable that is the time between counts in a Poisson
process.
Factorial experiment.A type of experimental design
in which every level of one factor is tested in combina-
tion with every level of another factor. In general, in a
factorial experiment, all possible combinations of factor
levels are tested.
F-distribution.The distribution of the random vari-
able defined as the ratio of two independent chi-square
random variables each divided by their number of
degrees of freedom.
Finite population correction factor.A term in the for-
mula for the variance of a hypergeometric random
variable.
First-order model.A model that contains only first-
order terms. For example, the first-order response
surface model in two variables is y
0
1 x 1
2 x 2 . A first-order model is also called a main
effects model.
Fixed factor (or fixed effect).In analysis of variance,
a factor or effect is considered fixed 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 fit a model to the data for interpolating between these
levels.
Forward selection.A method of variable selection in
regression, where variables are inserted one at a time
into the model until no other variables that contribute
significantly to the model can be found.
Fraction defective control chart.See Pchart.
Fraction defective.In statistical quality control, that
portion of a number of units or the output of a process
that is defective.
Fractional factorial.A type of factorial experiment
in which not all possible treatment combinations are
run. This is usually done to reduce the size of an ex-
periment with several factors.E 1 X 2 xf 1 x 2 dxPQ220 6234F.Glo 5/16/02 5:58 PM Page 693 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH114 FIN L: PPEND