Question

Background: Anorexia is well known to be difficult to treat. The data set provided below contains data on the weight gain for three groups of young female anorexia patients. These groups include a control group, a group receiving cognitive behavioral therapy and a group receiving family therapy. Source: Hand, D. J., Daly, F., McConway, K., Lunn, D. and Ostrowski, E. eds (1993) A Handbook of Small Data Sets. Chapman & Hall, Data set 285 (p. 229).

Directions: Click on the Data button below to display the data. Copy the data into a statistical software package and click the Data button a second time to hide it. Then perform an analysis of variance (ANOVA) to determine whether or not the differences in weight gain between the treatment groups is statistically significant.

Data

Control	CBT	Family
-0.5	1.7	11.4
-9.3	0.7	11
-5.4	-0.1	5.5
12.3	-0.7	9.4
-2	-3.5	13.6
-10.2	14.9	-2.9
-12.2	3.5	-0.1
11.6	17.1	7.4
-7.1	-7.6	21.5
6.2	1.6	-5.3
-0.2	11.7	-3.8
-9.2	6.1	13.4
8.3	1.1	13.1
3.3	-4	9
11.3	20.9	3.9
0	-9.1	5.7
-1	2.1	10.7
-10.6	-1.4
-4.6	1.4
-6.7	-0.3
2.8	-3.7
0.3	-0.8
1.8	2.4
3.7	12.6
15.9	1.9
-10.2	3.9
	0.1
	15.4
	-0.7

1. State the null and alternative hypotheses.
   
   
   
2. Compute the test statistic. Document how SSTr and SSE were computed. Use 4 decimal places for the sample means, sample standard deviations and the grand mean and round your answers for SSTr and SSE to 2 decimal places

   Use the values for SSTr and SSE to complete the following ANOVA table. Round each of your answers to 2 decimal places.

   Source	S.S.	df	M.S.	F
   Treatment
   Error
   Total

3. Compute the p-value. Provide the name of the distribution and the parameters used to compute the p-value. Then enter your answer rounded to 4 decimal places.
   
   
   
4. Interpret the results of the significance test. Is this result statistically significant? Is this result important from a practical perspective?
   

Answer 1

using excel>data>data analysis>one way anova

we have

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Control	29	3.1	0.106897	65.64567
CBT	26	72.4	2.784615	52.74135
Family	17	123.5	7.264706	51.22868
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
treatment	549.1148	2	274.5574	4.764378	0.011529	3.129644
error	3976.271	69	57.62712
Total	4525.386	71

Ans a )

the null and alternative hypotheses is

Ho: there is no significant differences in weight gain between the treatment groups .

Ha: there is significant differences in weight gain between the treatment groups .

Source of Variation	SS	df	MS	F
treatment	549.12	2	274.56	4.76
error	3976.27	69	57.63
Total	4525.39	71

the p-value is 0.0115

since p value is less than 0.05 so we reject Ho and conclude that there is significant differences in weight gain between the treatment groups .