Question

Survival	Organ
124	Stomach
42	Stomach
25	Stomach
45	Stomach
412	Stomach
51	Stomach
1112	Stomach
46	Stomach
103	Stomach
876	Stomach
146	Stomach
340	Stomach
396	Stomach
81	Bronchus
461	Bronchus
20	Bronchus
450	Bronchus
246	Bronchus
166	Bronchus
63	Bronchus
64	Bronchus
155	Bronchus
859	Bronchus
151	Bronchus
166	Bronchus
37	Bronchus
223	Bronchus
138	Bronchus
72	Bronchus
245	Bronchus
248	Colon
377	Colon
189	Colon
1843	Colon
180	Colon
537	Colon
519	Colon
455	Colon
406	Colon
365	Colon
942	Colon
776	Colon
372	Colon
163	Colon
101	Colon
20	Colon
283	Colon
1234	Ovary
89	Ovary
201	Ovary
356	Ovary
2970	Ovary
456	Ovary
1235	Breast
24	Breast
1581	Breast
1166	Breast
40	Breast
727	Breast
3808	Breast
791	Breast
1804	Breast
3460	Breast 719 Breast
	Conlumn 1. Survival: The survival time of the patient in days Column 2. Organ: the organ where cancer was present - stomach. Bronchus. Colon, Ovary, Breast (a)Create a groupn plot of Survival by organ type. Does there aooear to be significant differences in the groups? Explain your anwer. (b) Find the sample average of survival by organ type. Do you believe you woulf reject the null hypothesis of single factor anova based on these values? Explain. (c) Do you believe the standard deviations of each population are equal? explain. (d) What level of alpha would you suggest if concluding that the true average survival time was equal when in reality it was not, would be considered the most severe error? II. Continue with problem I. (a) Find the value of SSTO, SSA, SSE. (b) Find the value of MSTO, MSA, MSE. (C) Find the value of the test statistic, and the corresponding p value. (D) State your conclusion in terms of the problem if alpha is equal 0.05. Please show the process, need help! Thank you

Answer 1

Answer:

Based on the given data:

	Survival	Survival	Survival	Survival	Survival
	Stomach	Bronchus	Colon	Ovary	Breast
	124	81	248	1234	1235
	42	461	377	89	24
	25	20	189	201	1581
	45	450	1843	356	1166
	412	246	180	2970	40
	51	166	537	456	727
	1112	63	519		3808
	46	64	455		791
	103	155	406		1804
	876	859	365		3460
	146	151	942		719
	340	166	776
	396	37	372
		223	163
		138	101
		72	20
		245	283
Average	286.00	211.59	457.41	884.33	1395.91
Std dev.	346.31	209.86	427.17	1098.58	1238.97

(a) Create a group plot of Survival by organ type. Does there appear to be significant differences in the groups? Explain your answer.

Error bars represents standard deviation

Based on the survival plot by organ type, it appears that survival time is significantly different in different groups.

b) Find the sample average of survival by organ type. Do you believe you would reject the null hypothesis of single factor Anova based on these values? Explain.

Mean of the sample is calculated using the formula:

Standard deviation of the sample is calculated using the formula:

Survival by Organ type
Organ	Mean	Std dev.
Stomach	286.0	346.3
Bronchus	211.6	209.9
Colon	457.4	427.2
Ovary	884.3	1098.6
Breast	1395.9	1239.0

The mean values differ significantly among different organs, standard deviation also varies a lot by each organ type. Based on the average value of survival days for different organs, it appears that there is significant difference in the mean survival time of the patient depending on the organ affected by cancer.

(c) Do you believe the standard deviations of each population are equal? explain.

• Based on the data analysis, the standard deviations of the sample varies a lot. The population variance of the survival time of patients. for different groups (based on the organ affected) seems to be unequal.

(d) What level of alpha would you suggest if concluding that the true average survival time was equal when in reality it was not, would be considered the most severe error?

Significance level 0.01

II. Continue with problem I.

(a) Find the value of SSTO, SSA, SSE.

(b) Find the value of MSTO, MSA, MSE.

(C) Find the value of the test statistic, and the corresponding p value.

(D) State your conclusion in terms of the problem if alpha is equal 0.05.

Organ	Stomach	Bronchus	Colon	Ovary	Breast
Group no.	1	2	3	4	5	Total
N	13	17	17	6	11	64
	3718	3597	7776	5306	15355	35752
Mean	286.0	211.6	457.4	884.3	1395.9	558.6
	2502512	1465733	6476402	10726650	36784569	57955866
Variance	119930.333	44040.6324	182473.0074	1206875.467	1535038.491	602919.127
Std. Dev	346.31	209.86	427.17	1098.58	1238.97	776.48
Std. Err	96.049	50.90	103.60	448.49	373.56	97.06

Source	SS	df	MS
Between	11535760.52	4	2883940.131
Within	26448144.48	59	448273.6352
Total	37983905	63

F	Fcritical	p-value
6.43	2.53	0.0002	Reject at

Since p-value (0.0002) is less than the significance level (0.05), therefore, Null Hypothesis is rejected.

Therefore, based on the evidence the mean (average value of the dependent variable) is not the same for all groups.