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