- 12-3.1: How does the two-way ANOVA differ from the oneway ANOVA?
- 12-3.2: Explain what is meant by main effects and interaction effect
- 12-3.3: How are the values for the mean squares computed?
- 12-3.4: How are the F test values computed?
- 12-3.5: In a two-way ANOVA, variable A has three levels and variable B has ...
- 12-3.6: In a two-way ANOVA, variable A has six levels and variable B has fi...
- 12-3.7: What are the two types of interactions that can occur in the two-wa...
- 12-3.8: When can the main effects for the two-way ANOVA be interpreted inde...
- 12-3.9: Describe what the graph of the variables would look like for each s...
- 12-3.10: For Exercises 10 through 15, perform these steps. Assume that all v...
- 12-3.11: For Exercises 10 through 15, perform these steps. Assume that all v...
- 12-3.12: For Exercises 10 through 15, perform these steps. Assume that all v...
- 12-3.13: For Exercises 10 through 15, perform these steps. Assume that all v...
- 12-3.14: For Exercises 10 through 15, perform these steps. Assume that all v...
- 12-3.15: For Exercises 10 through 15, perform these steps. Assume that all v...
Solutions for Chapter 12-3: Analysis of Variance
Full solutions for Elementary Statistics: A Step by Step Approach | 7th Edition
Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chi-square with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chi-square random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chi-square random variables.
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
Bivariate normal distribution
The joint distribution of two normal random variables
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
A tabular arrangement expressing the assignment of members of a data set according to two or more categories or classiication criteria
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.
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
A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.
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
Discrete random variable
A random variable with a inite (or countably ininite) range.
Error of estimation
The difference between an estimated value and the true value.
Estimate (or point estimate)
The numerical value of a point estimator.
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.
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
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