Question

 

The physician wanted to know if conception periods were different due to the degrees of coffee drinking habit. Thus she collected data on the number of month to conception for 3 light coffee drinkers (1-2 cups per day), 4 moderate coffee drinkers (3-4 cups per day), and 3 heavy coffee drinkers (more than 4 cups per day). The table below summarizes the month to conception as a function of the three groups (light, moderate, and heavy coffee drinkers).

Months to conception for people with different coffee drinking
Light coffee drinkers	Moderate coffee drinkers	Heavy coffee drinkers
4	5	8
5	6	9
6	6	10
	7

You are asked to analyze the above data with one-way ANOVA. Please answer the following questions with regards to one-way ANOVA on the above data.

1. State the null and alternative hypotheses (2pts)

2. Identify the degrees of freedom(s). (2pts)

3. Identify the F critical based on the degrees of freedoms above by consulting with F table (2pts)

4. Here is the summary table presenting SSwithin, SS between, and SStotal. Please compute F value based on SSs and Degrees of Freedoms that you identified in the above. This should require computing MSwithin, MSbetween, and F. (2pts each for these three values)

	SS	DF	MS	F
Between	26.4	Use answers for 2 above	??	??
Within	6.00	Use answers for 2 above	??
Total	32.4

5. State your decision on the hypothesis based on the calculation above that led to the F value (2pt).

6. You tried to replicate above study with the exact same number of participants, and you got the following results:

Months to conception for people with different coffee drinking
Light coffee drinkers	Moderate coffee drinkers	Heavy coffee drinkers
2	2	7
5	5	9
8	7	11
	10

You may notice that the means of the three groups are the same as the previous results with three means for L, M, H conditions being 5, 6, and 9 respectively. Please fill out the blank sections of the summary table below based on your understanding/knowledge of how One-way ANOVA works. If you get the correct F value, you will get 9pts. If you do not get the correct F value, 1 pt is given for each of the 6 values (SSs, DFs, and MSs) that is correct.

	SS	DF	MS	F
Between	??	??	??	??
Within	??	??	??
Total	86.4

7. Please compare the two results (and two summary tables), and explain why this difference in F values occurred across the two studies. The explanation should involve the concept of variance between and variance within. (3pt)

Answer 1

Hypothesis:

H0: Means ar same

Ha: Not all means are same

A)

Excel > Data > Data Analysis > Anova: Single Factor

Light coffee drinkers	Moderate coffee drinkers	Heavy coffee drinkers		Anova: Single Factor
4	5	8
5	6	9		SUMMARY
6	6	10		Groups	Count	Sum	Average	Variance
	7			Light coffee drinkers	3	15	5	1
				Moderate coffee drinkers	4	24	6	0.666666667
				Heavy coffee drinkers	3	27	9	1
				ANOVA
				Source of Variation	SS	df	MS	F	P-value	F crit
				Between Groups	26.4	2	13.2	15.4	0.002732888	4.73741413
				Within Groups	6	7	0.857142857
				Total	32.4	9

Fstat = 15.4

F critical = 4.7374

F stat > F critical, Reject H0

There is enough evidence to conclude that claim is true

B)

Excel > Data > Data Analysis > Anova: Single Factor

Light coffee drinkers	Moderate coffee drinkers	Heavy coffee drinkers
2	2	7		Anova: Single Factor
5	5	9
8	7	11		SUMMARY
	10			Groups	Count	Sum	Average	Variance
				Light coffee drinkers	3	15	5	9
				Moderate coffee drinkers	4	24	6	11.33333333
				Heavy coffee drinkers	3	27	9	4
				ANOVA
				Source of Variation	SS	df	MS	F	P-value	F crit
				Between Groups	26.4	2	13.2	1.54	0.279081647	4.73741413
				Within Groups	60	7	8.571428571
				Total	86.4	9

F stat = 1.54

F critical = 4.7374

F stat < F critical, Do not reject H0

There is not enough evidence to conclude that claim is true