BA 2120 - LS 12

In one-way ANOVA we are investigating whether or not all group means are different. Select the correct set of hypotheses:

H0: μ1 = μ2 = μ3 Ha: At least one pair of means differ

The competing hypotheses for a one-way ANOVA test that compares the means of three populations are defined as ______

H0: μ1 = μ2 = μ3 Ha: At least one pair of means differ

The test statistic for a one-way ANOVA test is equal to ______.

MST/MSE Reason: The F statistic is based on comparing MST to MSE.

Researchers are often interested in how a factor influences the responses given by participants. In this instance, the participant's response is called the ______ variable.

dependent

In a completely randomized experimental design ______

independent random samples of experimental units are assigned to each treatment.

In one-way ANOVA, we consider one factor having p levels and try to determine if differences exist between the _______ response to the various treatment levels.

means

The one-way ANOVA test simultaneously determines whether differences exist between the population __________.

means

In one-way ANOVA, we consider ___ factor(s) having __ levels and try to determine if differences exist between the means response to the various treatment levels.

one; p

When you apply the same treatment to more than one experimental unit, the process is called ________.

replication

When performing one-way ANOVA, the problem with populations having unequal variances can be mitigated by ______

taking samples that are the same size.

SSE is the sum of the squared differences between each observation and its group's mean. If all cases within a cluster are identical the SSE would then be equal to ______.

0

Suppose the competing hypotheses for a test are H0: μ1 = μ2 = μ3 versus Ha: At least one mean differs. If the value of the test statistic is F = 3.24 and its associated p-value is 0.07, then at the 5% significance level what is the correct conclusion?

Do not reject H0

A one-way ANOVA test is based on the ______ distribution.

F

True or false: The one-way ANOVA test simultaneously determines whether differences exist between the population means and identifies those population means that may differ.

False

In one-way ANOVA, if SST = 137.2, SSE = 190.8, MST = 68.6, and MSE = 15.9, then SSTO = ______

328

A one-way ANOVA was used to test the effects of fuel additives on miles per gallon achieved. An effect of 0 indicates that, on average, an additive has no effect on MPG. Suppose an individual 95% confidence interval for the mean effect of additive C is [-0.28, 2.35]. How would you interpret this result?

Additive C has not been shown to be effective at the 95% confidence level.

Suppose the competing hypotheses for a test are H0: μ1 = μ2 = μ3 versus Ha: At least one mean differs. If the value of the test statistic is F = 5.75 and the critical value at the 5% level of significance is F0.05 = 3.74, what is the correct conclusion?

Reject H0 and conclude that at least one mean differs.

In one-way ANOVA, the ______ is calculated by summing the squared difference between each observed value and its corresponding group mean, over all of the observations.

SSE

In one-way ANOVA, the ______ measures the amount of variability within treatment groups.

SSE Reason: SSE = error sum of squares

In one-way ANOVA, the mean square error (MSE) is calculated as ______.

SSE / n−p

In one-way ANOVA, the ______ measures the amount of variability between treatment groups.

SST Reason: SST = treatment sum of squares

In one-way ANOVA, the treatment mean square (MST) is calculated as ______.

SST / p−1

In one-way ANOVA, the ______ is calculated as the between-treatment variability plus the within-treatment variability.

SSTO Reason: SSTO = SST + SSE

In one-way ANOVA, the ______ measures the total amount of variability in the observed response values.

SSTO Reason: SSTO = total sum of squares

Why are simultaneous confidence intervals preferable to individual confidence intervals?

Simultaneous confidence intervals reduce the overall probability of Type 1 error (or α).

The following formula is used to calculate __________. ∑i=1 3 ni(xi−x)^2

Sum of Squares between treatments

Which of the following assumptions must be true for performing a one-way ANOVA?

The populations have equal variances. The populations are normally distributed. The samples are independent and randomly selected.

In one-way ANOVA, if the variability between treatments is small compared to the variability within treatments, what can we conclude?

There is insufficient evidence to conclude the population means differ.

In one-way ANOVA, if the variability between treatments is large compared to the variability within treatments, what can we conclude?

There is sufficient evidence to conclude that at least one population mean differs.

Simultaneous confidence intervals reduce the overall probability of ________.

Type I Error

A one-way ANOVA tested the effects of various fever reducing medications. A 95% confidence interval for the mean effect of medication B is [-2.31, -0.79] in degrees Fahrenheit. Which of the following is an appropriate interpretation?

We are 95% confident the drug B reduces mean body temperature by at least 0.79 degrees.

In a one-way ANOVA, a Tukey simultaneous 100(1 - α)% confidence interval for a pairwise difference (μi - μh) is ______. (The formula does not assume ni = nh = m.)

[x(bar)i - x(bar)h ± qα √(MSE)/2 (1/ni+1/nh)

If the factor being studied can be controlled, the data obtained are ______.

experimental

If we can assign the value of a factor experienced by different treatment groups, the data obtained are ______.

experimental

The objects (such as people, cars, etc) that are assigned to different levels of an independent variable, are known as ______

experimental units

In a one-way ANOVA test, when can we reject the null hypothesis?

p-value < α F > Fα

Replication occurs when ______

you apply the same treatment to more than one experimental unit.