- 10.3.1: Chase and Dummer (1992) studied the attitudes of school-aged childr...
- 10.3.2: Show that the statistic Q defined by Eq. (10.3.4) can be rewritten ...
- 10.3.3: Show that if C = 2, the statistic Q defined by Eq. (10.3.4) can be ...
- 10.3.4: Suppose that an experiment is carried out to see if there is any re...
- 10.3.5: Suppose that 300 persons are selected at random from a large popula...
- 10.3.6: Suppose that a store carries two different brands, A and B, of a ce...
- 10.3.7: Consider a two-way contingency table with three rows and three colu...
- 10.3.8: If all the students in a class carry out Exercise 7 independently o...
- 10.3.9: Consider a three-way contingency table of size R C T . For i = 1,.....
- 10.3.10: Consider again the conditions of Exercise 9. For i = 1,...,R, and j...
Solutions for Chapter 10.3: Categorical Data and Nonparametric Methods
Full solutions for Probability and Statistics | 4th Edition
a-error (or a-risk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
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.
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.
An effect that systematically distorts a statistical result or estimate, preventing it from representing the true quantity of interest.
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.
The mean of the conditional probability distribution of a random variable.
A probability distribution for a continuous random variable.
Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.
Formulas used to determine the number of elements in sample spaces and events.
The value of a statistic corresponding to a stated signiicance level as determined from the sampling distribution. For example, if PZ z PZ ( )( .) . ? =? = 0 025 . 1 96 0 025, then z0 025 . = 1 9. 6 is the critical value of z at the 0.025 level of signiicance. Crossed factors. Another name for factors that are arranged in a factorial 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).
Another name for a cumulative distribution function.
A study in which a sample from a population is used to make inference to the population. See Analytic study
Estimate (or point estimate)
The numerical value of a point estimator.
A series of tests in which changes are made to the system under study
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.
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.
In statistical quality control, that portion of a number of units or the output of a process that is defective.