Question

Question 1

As variation within groups decreases, what should happen to the F ratio, assuming no other changes to variation between groups?

a) F doesn't change

b) F becomes smaller

c) F becomes larger

Question 2

Charlie is testing the mean cuteness scores of a sample of dogs by groups. The groups are pugs, other small dogs, medium dogs, and large dogs (4 groups). We run the one-way ANOVA analysis, our DV is the cuteness scores and the IV is the type of dog. If we were to reject null for the F-test, what would be the appropriate conclusion?

a) All dogs are cuter than pugs.

b) Mean cuteness scores differ by dog type.

c) Large dogs are cuter than small dogs and pugs.

d) Pugs are statistically significantly cuter than all other dogs.

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Let's conduct the ANOVA analysis for Charlie's study.

Charlie is testing the mean cuteness scores of a sample of dogs by groups. The groups are pugs, other small dogs, medium dogs, and large dogs (4 groups). There are 5 ratings (cuteness scores) per breed.

The cuteness scores are:

Pugs (5 observations): 8, 9, 9, 7, 8
Other Small dogs (5 observations): 5, 4, 6, 4, 2
Medium (5 observations): 5, 6, 4, 6, 5
Large (5 observations): 6, 5, 9, 3, 4

In the next few items you will be asked to make calculations to conduct the ANOVA analysis with this data.

Question 3

The first step of conducting our analysis will be to calculate the Overall mean and the Group means. Fill in the blanks below:

Write down the Overall Mean and the Group Means for each category below.

OVERALL MEAN
GROUP MEANS:
Pugs
Other small dogs
Medium
Large

Question 4

WRITE YOUR ANSWER BELOW!

This is the space where you should show your work for the next two items. You must show your work to get full credit.

Put all your work for the ANOVA calculations and the r-squared calculations here, to be evaluated in grading the quiz and assigning partial credit.

You can directly enter your calculations into the response box, insert images of your hand calculations, or insert R code that does MANUAL/"BY HAND" calculations (not using the aov() ) function.

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Question 5

Using Charlie's data, and the means you calculated in the previous question, fill out the ANOVA table with the appropriate degrees of freedom, sum of squares, mean squares, and F-ratio.

You can use excel or R as a calculator, but you MUST calculate them by hand/manually. If you do not provide your work/code for the manual calculations in the previous "question" you will not get full credit.

Degrees of freedom should be provided as integers.
Other values should be rounded to one decimal place.

	DF	SS	MS	F
Group
Residual

Question 6

Calculate the r-squared for the ANOVA analysis you just conducted above.

Express your answer as a proportion. Round your answer to TWO decimal places.

Question 7

Using a critical F-value of 3.24, and the F-ratio you calculated above, is your result statistically significant?

a) yes

b) no

Answer 1

Question 1.

As variation within groups decreases then F value will be increases.

So correcr option is c) F becomes larger.

Since because ,

F= between variation / within variation .

e.g. between variation = 25

And within variation = 15 then

F = 25/15

= 1.6667

Suppose we decrease the within variation as 15 to 10.

Then F = 25/10

= 2.5