- 13-6.1: Regression If the methods of this section are used with paired samp...
- 13-6.2: Level of Measurement Which of the levels of measurement (nominal, o...
- 13-6.3: Notation What do r, r s , , and s denote? Why is the subscript s us...
- 13-6.4: . Efficiency Refer to Table 132 in Section 131 and identify the eff...
- 13-6.5: In Exercises 5 and 6, use the scatterplot to find the value of the ...
- 13-6.6: In Exercises 5 and 6, use the scatterplot to find the value of the ...
- 13-6.7: Testing for Rank Correlation. In Exercises 712, use the rank correl...
- 13-6.8: Testing for Rank Correlation. In Exercises 712, use the rank correl...
- 13-6.9: Testing for Rank Correlation. In Exercises 712, use the rank correl...
- 13-6.10: Testing for Rank Correlation. In Exercises 712, use the rank correl...
- 13-6.11: Testing for Rank Correlation. In Exercises 712, use the rank correl...
- 13-6.12: Testing for Rank Correlation. In Exercises 712, use the rank correl...
- 13-6.13: Appendix B Data Sets. In Exercises 1316, use the data from Appendix...
- 13-6.14: Appendix B Data Sets. In Exercises 1316, use the data from Appendix...
- 13-6.15: Appendix B Data Sets. In Exercises 1316, use the data from Appendix...
- 13-6.16: Appendix B Data Sets. In Exercises 1316, use the data from Appendix...
- 13-6.17: Finding Critical Values An alternative to using Table A9 to find cr...
Solutions for Chapter 13-6: Rank Correlation
Full solutions for Elementary Statistics | 12th Edition
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
The joint probability distribution of two random variables.
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.
Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
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
Another term for the conidence coeficient.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
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.
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 correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the off-diagonal elements rij are the correlations between Xi and Xj .
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
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
A property of a collection of events that indicates that their union equals the sample space.
The expected value of a random variable X is its long-term average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.
Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications
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 .
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .