Chapter 11 - Analysis of Variance

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 variable

Ho : A1 = A2 = ... = Aj = 0

The sum of squares formula for a non-replicated two-factor ANOVA is?

SST = SSA + SSB + SSE

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 1 error probability.

Mean squares are found by dividing SSA and SSE each by its ______ ______ ______.

degrees of freedom

The hypotheses tested in a one-factor ANOVA are Ho; All the treatment means are ______ vs H1: At least ______ treatment mean is different

equal; one

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

If the test statistic for a one-way ANOVA is significantly greater than 1, this means that

the between-treatments are significantly greater than the within-treatments variability.

Hartley's test statistic for testing equal variances in the ratio of sample ______ with the larger value in the ______

variances; 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 -Variation in Y = Explained Variation + Unexplained Variation

Analysis of Variance assumes that

-population variances are equal -populations are normally distributed

The random error in the ANOVA linear model, e, is assumed

-to be normally distributed -to have a zero mean and constant variance

A two-factor non-replicated ANOVA design is often used because

1. the observations are expensive 2. repeated treatment observations can be impossible to collect

The Tukey test statistic relies on

1. the sample sizes nj and nk 2. the MSE 3. the difference in groups means, [ybarj-ybark]

How many pairwise comparisons need to be performed when a factor has four treatments or levels?

6

You can find the critical value of the Fdif1,dif2 statistic in Excel using the fucntion

=F.INV.RT(a,df1,df2)

The test for comparing more than two population variances without assuming normal populations is called

Levene's test

Which of the following are NOT assumptions for performing a one-way ANOVA?

The population standard deviations are unknown but assumed unequal.

In ANOVA, a factor is defined as

a categorical independent variable that explains variation in a response, or dependent, variable

Using the Tukey method, there are no significant differences to find if the ANOVA test does not reject the ______ hypothesis of ______ means

null; equal

The one-way ANOVA test is always a

right tailed test

The ANOVA test is considered _____ to departures from the normality assumption and equal variance assumptions.

robust

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.

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.