Question

Researchers were interested in the relationship between mental health and living with a pet. Students were surveyed and grouped by pet type as either “Cats”, “Dogs”, or “No Pets”, and completed a scale on depressive symptoms on a scale of 1-7, where 7 indicates high levels of depressive symptoms. Using the data in the frequency table below, please conduct a one-way ANOVA to determine if there are any significant differences between these groups. Use α = .05, report η², and if the ANOVA is significant conduct a post-hoc test using Scheffe procedure. Finally, please report your answer in words and show all work and calculations step by step (don't forget to include the ANOVA table).

You are strongly encouraged to do your work in tables to help structure your work and keep it easily visible in your images. All work must be done by hand.

Cats		Dogs		No Pets
x	f	x	f	x	f
1	0	1	0	1	4
2	0	2	3	2	5
3	1	3	4	3	2
4	3	4	2	4	1
5	5	5	2	5	0
6	2	6	1	6	0
7	1	7	0	7	0

Answer 1

We are given the following data and are asked to conduct a one-way ANOVA test.

Ca	ts	Do	gs	No	Pets
x	f	x	f	x	f
1	0	1	0	1	4
2	0	2	3	2	5
3	1	3	4	3	2
4	3	4	2	4	1
5	5	5	2	5	0
6	2	6	1	6	0
7	1	7	0	7	0

The data is given in the form of frequency distribution table, we will change it into a frequency table by multiplying x and f column.

Cats	Dogs	No Pets
0	0	4
0	6	10
3	12	6
12	8	4
25	10	0
12	6	0
7	0	0

Null hypothesis

H₀: there is no significant difference between the groups

Alternate hypothesis

H₁: there is a significant difference between the groups.

Types of Pets	Ob	se	rv	at	io	ns		Ti.
Cats	0	0	3	12	25	12	7	59	497.29	971
Dogs	0	6	12	8	10	6	0	42	252	380
No Pets	4	10	6	4	0	0	0	24	82.29	168
							Totals

Correction Factor

  

  

  

ANOVA Table

Source of Variations	S.S.	df	M.SS	F-ratio
Between Process(treatments)	87.53	(k-1=3-1) 2	43.765 (87.53/2)
Within Process(error)	687.42	(N-K=21-3) 18	38.19 (687.42/18)
Total	774.95	(N-1=21-1) 20

Conclusion

Tabulated value of F at 5% level is

=> we fail to reject the null hypothesis

Hence we conclude that there is no significant difference between the groups.