Question 1 (1 point) When treatment means are far apart it increases the varianc

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Question 1 (1 point)

When treatment means are far apart it increases the variance (as measured by SSTr), and thereby makes it harder to conclude there is a difference in mean.

Question 1 options:

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Question 2 (1 point)

Which of the following is true?

Question 2 options:

SST = SSE + SSTr

SSTr = SST + SSE

SSE = SST + SSTr

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Question 3 (1 point)

Match each abbreviation with the correct definition

Question 3 options:

123

sum of the squared distances between a treatment mean and the grand mean

123

sum of the squared distances between each point and its respective treatment mean

123

sum of the squared distances between a point and the grand mean

SSE

SSTr

SST

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Question 4 (1 point)

How is a residual {"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#x3B5;</mi></math>"}, or "error", defined?

Question 4 options:

A mistake in the measurement of the response variable

The difference between the grand mean and a treatment mean

The difference between an observed response and its treatment mean

A fault in the design of the experiment that potentially leads to bias

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Question 5 (1 point)

Which of the following are the assumptions for a one-way ANOVA model? (select all that apply)

Question 5 options:

The treatment populations must be normal

There can be no variability in the response variable across treatments.

The sample size of each treatment must be greater than 30

The treatment populations must all have the same variance

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Question 6 (1 point)

What is the definition of a balanced design?

Question 6 options:

The effects across different levels of the factor sum to 1

The standard deviations of each treatment are the same

The ratio of MSTr to MSE is close to one.

The sample size of each treatment is the same

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Question 7 (1 point)

What is the benefit of a balanced (or nearly balanced) experiment?

Question 7 options:

There is no advantage to balanced experiments.

It provides more power. In other words it better allows us to detect a difference when a difference is present

The the design is more efficient, it can result in a smaller sample size

It makes the model robust to minor or moderate violation of assumptions.

Explanation / Answer

1. When the treatments are far apart then their difference is large and so it increases the variance. So it is easier to conclude difference in mean. So the statement is False. (Ans).

2. Correct choice is: SST = SSTr + SSE.

3. Sum of squared difference between treatment and grand mean = SSE.

Sum of squared difference between each point and its respective treatment mean = SSTr.

Sum of squared distances between a point and grand mean = SST.

4.Error term : A fault in the design of the experiment that potentially leads to bias.

5. Assumptions:

The treatment populations must be normal.

The treatment populations must all have the same variance.

6. Balanced design:

the sample size of each treatment is the same.

7. Benefit of balanced experiment:

It provides more power. In other words it better allows us to detect a difference when a difference is present.

It makes the model robust to minor or moderate violation of assumptions.

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