Ch. 11
Suppose an ANOVA experiment is comparing means across 4 different categories. If one were to perform the necessary paired t tests for all 4 categories with an alpha = .01, what would the overall Type I error probability be?
.0585
You can find the critical value of the Fdf1,df2 statistic in Excel using the function
=F.INV.RT(α, df1,df2)
The acronym ANOVA stands for
Analysis of variance
One-factor ANOVA can be used to answer which of the following questions?
Are the observed differences between four manufacturing plants' defect counts due to chance or too great to be attributed to chance? and Are the observed differences in overtime hours at four different manufacturing plants due to chance or too great to be attributed to chance?
Variation of a dependent random variable about its mean is categorized as either ____________ or ______________
Explained; unexplained
A random variable's variation about its mean can be attributed to known ____________________ called explained variation, or is simply _____________ error, called unexplained variation
Factors; random
True or false: A completely randomized one-factor ANOVA requires that the sample size for each factor level be the same.
False
True or false: A statistically significant result is always of practical importance.
False
True or false: Fixed-effects models are harder to analyze than random-effects models.
False
True or false: If an interaction effect is present between two factors the plot of means will show parallel lines.
False
The test statistic for a one-way ANOVA test follows the
Fdf1,df2 distribution.
The test for comparing more than two population variances without assuming normal populations is called
Levene's test
The test statistic for a one-way ANOVA test =
MSB/MSE.
Using the Tukey method, there are no significant differences to find if the ANOVA test does not reject the ____________ hypothesis of ___________ means
Null; equal
When two factors are studied for effects on population means, the term without replication means that only ____________ observation(s) for each combination of factor levels is collected.
One
Match each variable description to the logical variable type. Instructions
Quantitative response variable:1. recovery time after surgery2. length of orthopedic surgery and Categorical independent variable:1. type of fracture2. hospital location
For an ANOVA test, the critical value is always found in the ___________ tail of the __________ distribution
Right; F
The Sums of Squares formula for a non-replicated two-factor ANOVA is ____________ = SSA + ____________ + _____________
SST; SSB; SSE
The Sums of Squares formula for a replicated two-factor ANOVA is _____________ = SSA + SSB + _______________ + ___________
SST; SSI; SSE
Which of the following are NOT assumptions for performing a one-way ANOVA?
The population standard deviations are unknown but assumed unequal.
True or false: Analysis of variance assume homogeneous variances.
True
True or false: If no interaction exists between factors the plot of means should show parallel lines.
True
The ________________ test was developed by the 20th century statistician John Tukey. It performs pairwise comparisons of _____________simultaneously.
Tukey; means
Hartley's test statistic for testing equal variances is the ratio of sample _____________ with the larger value in the _____________
Variance; numerator
Choose the correct expressions for variation in a response variable Y from the choices given.
Variation in Y = Variation due to factor(s) + Variation from random error and Variation in Y = Explained Variation + Unexplained Variation
Fully crossed factorial designs include ____________ possible combinations of factor levels.
all
To determine if there is a difference between the means of 3 or more populations, we use
analysis of variance.
The reason why we perform an analysis of variance for comparing means rather than conducting multiple two-mean comparisons is
because multiple two-mean comparisons increase the Type I error probability.
The deviation ____________ treatments can be expressed as yj(bar) - y(bar)
between
A three factor ANOVA model ___________ be adapted to a two-dimensional table.
cannot
A two-factor ANOVA without replication is called a
fixed-effects model
Tukey's HSD method ensures that the probability of a Type I error equals α
for any number of pairwise comparisons.
The average response in a treatment category, j, is referred to as the
group
A 2k factorial design means there are ________ factors and ___________ levels for each factor.
k; two
A model such as Completion time = f(product type, Assembly line(Shift #)) would be considered a ___________ model
nested
The ANOVA test is considered ____________________ to departures from the normality assumption and equal variance assumptions.
robust
A fractional factorial design limits the data collection to a _____________ of the possible factor combinations
subset
In an ANOVA, if the SSE is relatively high then this means
the unexplained variation in Y is high and therefore the factor effects are not significant.
GLM ANOVA models allow more than __________ factors
two
When analyzing difference in means between treatments in a single factor, a completely randomized model means that
the subjects or individuals are assigned randomly to each treatment.
Choose the correct null hypotheses for a two-factor, without replication, ANOVA. Assume factor A is the factor to be tested and factor B is the level variable.
H0: A1 = A2 = . . . = Aj = 0
The null hypothesis for a fixed-effects ANOVA model is
H0: A1 = A2 = A3 = . . . = Aj
One-way ANOVA hypotheses are:
H0: μ1 = μ2 = μ3 = μ4; H1: At least one μ is different.
The alternative hypothesis for a fixed-effects ANOVA model is
H1: At least one Aj is different.
The hypotheses H0: σ12 = σ22 = σ32 = . . . = σc2 vs H1: The variances are not all equal can be tested using
Hartley's test
A randomized block design is an experiment where subjects within each ___________________ are randomly assigned to each of the ________________
block; treatments
The acronym GLM, in the context of ANOVA, means _________ ______________ ___________
general linear model
Even if an ANOVA study shows significant factor effects, the magnitude of the effect may not be __________ The researcher or user of the study results will have to determine this.
important
In a data table for a two-factor replicated ANOVA, the ______________ of each row/column is a treatment.
intersection
If all levels of one factor are contained within another factor we say that the design is a __________ or hierarchical design.
nested
Levene's test does not assume a ___________ distribution
normal
Hartley's test for equal variances assumes the populations are ___________ distributed
normally
Analysis of Variance assumes that
population variances are equal and populations are normally distributed
Replication in a two-factor ANOVA can add ________________ to the test.
power
The dependent variable in an ANOVA should be
quantitative
In a fixed-effects ANOVA model, the factor levels are predetermined. In a ___________ effects model, the factor levels are chosen by chance from a pool of possible levels.
random
A fractional factorial design can be used when it is important to
reduce the cost of an experiment and limit data collection.
Experimental design
refers to the number of levels of each factor refers to the number of factors refers to the way levels are defined
A two-factor non-replicated ANOVA design is often used because
repeated treatment observations can be impossible to collect and the observations are expensive.
A two-way ANOVA with interaction uses __________ F tests. One for each ____________ effect and one for the ____________ effect
three; main; interaction
The random error in the ANOVA linear model, εij, is assumed
to be normally distributed and to have a zero mean and constant variance.
The Aj term in the linear model yij = μ + Aj +εij refers to the
treatment
When replication in a two-factor ANOVA has occurred, for each combination of factor A and factor B ___________ we will see multiple observations of the _______________ variable Y
treatments; response
The one-factor ANOVA linear model reduces to yij = μ + εij if the null hypothesis is
true
True or false: It is possible to design a three-factor ANOVA study.
true
Reducing factors to ____________ levels simplifies the data requirements in a replicated experiment.
two
Two-way ANOVA tests simultaneously examine the effect of __________ factors on the population mean.
two
Replication in a two-factor ANOVA allows
us to test for interaction between factors as well as significant effects due to individual factors.
If a two-factor ANOVA study has only one factor of research interest the second factor is
used to control for potential confounding influences.
Identify the correct two-factor, with replication, ANOVA linear model.
yij = μ + Aj + Bk + ABjk + εij
Identify the correct two-factor ANOVA linear model.
yij = μ + Aj + Bk +εij
Identify the correct one-factor ANOVA linear model.
yij = μ + Aj +εij