Question

Question 1)

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.

Part A)

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

Round your responses to 1 decimal place.

OVERALL MEAN
GROUP MEANS:
Pugs
Other small dogs
Medium
Large

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

Now, 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.

Answer 1

Answer :

By using Excel;

1) Function : average ()

Overall mean and the Group means for given data is ,

	pugs	other small dogs	Medium	large
	8	5	5	6
	9	4	6	5
	9	6	4	9
	7	4	6	3
	8	2	5	4
means	8.2	4.2	5.2	5.4
Overall mean	5.75

2) For Analysis of Variance

Path : data < data analysis < anova for single factor

For ANOVA table with the appropriate degrees of freedom, sum of squares, mean squares, and F-ratio are :

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
pugs	5	41	8.2	0.7
other small dogs	5	21	4.2	2.2
Medium	5	26	5.2	0.7
large	5	27	5.4	5.3
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	44.15	3	14.71667	6.614232	0.004086	3.238871517
Within Groups	35.6	16	2.225
Total	79.75	19

3) r-squared for the ANOVA analysis is

= ss( between groups ) / ss (Total )

= 44.15 / 79.75

= 0.55