- Chapter 1: Probability
- Chapter 10: Summarizing Data
- Chapter 11: Comparing Two Samples
- Chapter 12: The Analysis of Variance
- Chapter 13: The Analysis of Categorical Data
- Chapter 14: Linear Least Squares
- Chapter 2: Random Variables
- Chapter 3: Joint Distributions
- Chapter 4: Expected Values
- Chapter 5: Limit Theorems
- Chapter 6: Distributions Derived from the Normal Distribution
- Chapter 7: Survey Sampling
- Chapter 8: Estimation of Parameters and Fitting of Probability Distributions
- Chapter 9: Testing Hypotheses and Assessing Goodness of Fit
Mathematical Statistics and Data Analysis 3rd Edition - Solutions by Chapter
Full solutions for Mathematical Statistics and Data Analysis | 3rd Edition
2 k factorial experiment.
A full factorial experiment with k factors and all factors tested at only two levels (settings) each.
Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).
A horizontal line on a control chart at the value that estimates the mean of the statistic plotted on the chart. See Control chart.
Central composite design (CCD)
A second-order response surface design in k variables consisting of a two-level factorial, 2k axial runs, and one or more center points. The two-level factorial portion of a CCD can be a fractional factorial design when k is large. The CCD is the most widely used design for itting a second-order model.
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
Continuous uniform random variable
A continuous random variable with range of a inite interval and a constant probability density function.
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.
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment
A probability distribution for a discrete random variable
Error of estimation
The difference between an estimated value and the true value.
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.
Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
A signal from a control chart when no assignable causes are present
Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
The geometric mean of a set of n positive data values is the nth root of the product of the data values; that is, g x i n i n = ( ) = / w 1 1 .
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.