The dataset valung.csv includes data on 138 lung cancer patients from the Veteran's Administration Lung Cancer Trial. The variables are:

t - survival or follow-up time in days.

dead - dead or not (1 means dead).

therapy - treatment: standard or test.

age - patient's age in years.

kps - Karnofsky score of patient's performance on a scale of 0 to 100.

diag.time - times since diagnosis in months at entry to trial.

cell - one of four cell types.

prior - prior therapy?

Instruction: For this analysis drop the patients that are not dead, and use only the patients who die.

1. Produce a set of side by side boxplots of the time to death grouped by cell type.

2. You'd like to use an ANOVA to compare the groups with respect to time until death. What assumption of the ANOVA seems to be violated, based on this plot?

3. Remake the plot in part (a) using "time" on a log-scale (ie log(t)). Comment on the appropriateness of the assumptions behind an ANOVA comparing the 4 groups with respect to time on the log scale.

4. If you wished to compare cell-types to see if there were differences in time to death, and if so which types were different from which, how would you do it? Please be specific about what test or tests, and any adjustments.

5. Please do the analysis you describe in part d and report your results, in 2-4 full sentences

Remember to provide enough information for (d & e) so we can understand what you did, and hopefully why. Limited computer code or output ok but also full sentences please!

therapy	cell	t	dead	kps	diagtime	age	prior
standard	Squamous	72	dead	60	7	69	no
standard	Squamous	411	dead	70	5	64	yes
standard	Squamous	228	dead	60	3	38	no
standard	Squamous	126	dead	60	9	63	yes
standard	Squamous	118	dead	70	11	65	yes
standard	Squamous	10	dead	20	5	49	no
standard	Squamous	82	dead	40	10	69	yes
standard	Squamous	110	dead	80	29	68	no
standard	Squamous	314	dead	50	18	43	no
standard	Squamous	100	censored	70	6	70	no
standard	Squamous	42	dead	60	4	81	no
standard	Squamous	8	dead	40	58	63	yes
standard	Squamous	144	dead	30	4	63	no
standard	Squamous	25	censored	80	9	52	yes
standard	Squamous	11	dead	70	11	48	yes
standard	Small	30	dead	60	3	61	no
standard	Small	384	dead	60	9	42	no
standard	Small	4	dead	40	2	35	no
standard	Small	54	dead	80	4	63	yes
standard	Small	13	dead	60	4	56	no
standard	Small	123	censored	40	3	55	no
standard	Small	97	censored	60	5	67	no
standard	Small	153	dead	60	14	63	yes
standard	Small	59	dead	30	2	65	no
standard	Small	117	dead	80	3	46	no
standard	Small	16	dead	30	4	53	yes
standard	Small	151	dead	50	12	69	no
standard	Small	22	dead	60	4	68	no
standard	Small	56	dead	80	12	43	yes
standard	Small	21	dead	40	2	55	yes
standard	Small	18	dead	20	15	42	no
standard	Small	139	dead	80	2	64	no
standard	Small	20	dead	30	5	65	no
standard	Small	31	dead	75	3	65	no
standard	Small	52	dead	70	2	55	no
standard	Small	287	dead	60	25	66	yes
standard	Small	18	dead	30	4	60	no
standard	Small	51	dead	60	1	67	no
standard	Small	122	dead	80	28	53	no
standard	Small	27	dead	60	8	62	no
standard	Small	54	dead	70	1	67	no
standard	Small	7	dead	50	7	72	no
standard	Small	63	dead	50	11	48	no
standard	Small	392	dead	40	4	68	no
standard	Small	10	dead	40	23	67	yes
standard	Adeno	8	dead	20	19	61	yes
standard	Adeno	92	dead	70	10	60	no
standard	Adeno	35	dead	40	6	62	no
standard	Adeno	117	dead	80	2	38	no
standard	Adeno	132	dead	80	5	50	no
standard	Adeno	12	dead	50	4	63	yes
standard	Adeno	162	dead	80	5	64	no
standard	Adeno	3	dead	30	3	43	no
standard	Adeno	95	dead	80	4	34	no
standard	Large	177	dead	50	16	66	yes
standard	Large	162	dead	80	5	62	no
standard	Large	216	dead	50	15	52	no
standard	Large	553	dead	70	2	47	no
standard	Large	278	dead	60	12	63	no
standard	Large	12	dead	40	12	68	yes
standard	Large	260	dead	80	5	45	no
standard	Large	200	dead	80	12	41	yes
standard	Large	156	dead	70	2	66	no
standard	Large	182	censored	90	2	62	no
standard	Large	143	dead	90	8	60	no
standard	Large	105	dead	80	11	66	no
standard	Large	103	dead	80	5	38	no
standard	Large	250	dead	70	8	53	yes
standard	Large	100	dead	60	13	37	yes
test	Squamous	999	dead	90	12	54	yes
test	Squamous	112	dead	80	6	60	no
test	Squamous	87	censored	80	3	48	no
test	Squamous	231	censored	50	8	52	yes
test	Squamous	242	dead	50	1	70	no
test	Squamous	991	dead	70	7	50	yes
test	Squamous	111	dead	70	3	62	no
test	Squamous	1	dead	20	21	65	yes
test	Squamous	587	dead	60	3	58	no
test	Squamous	389	dead	90	2	62	no
test	Squamous	33	dead	30	6	64	no
test	Squamous	25	dead	20	36	63	no
test	Squamous	357	dead	70	13	58	no
test	Squamous	467	dead	90	2	64	no
test	Squamous	201	dead	80	28	52	yes
test	Squamous	1	dead	50	7	35	no
test	Squamous	30	dead	70	11	63	no
test	Squamous	44	dead	60	13	70	yes
test	Squamous	283	dead	90	2	51	no
test	Squamous	15	dead	50	13	40	yes
test	Small	25	dead	30	2	69	no
test	Small	103	censored	70	22	36	yes
test	Small	21	dead	20	4	71	no
test	Small	13	dead	30	2	62	no
test	Small	87	dead	60	2	60	no
test	Small	2	dead	40	36	44	yes
test	Small	20	dead	30	9	54	yes
test	Small	7	dead	20	11	66	no
test	Small	24	dead	60	8	49	no
test	Small	99	dead	70	3	72	no
test	Small	8	dead	80	2	68	no
test	Small	99	dead	85	4	62	no
test	Small	61	dead	70	2	71	no
test	Small	25	dead	70	2	70	no
test	Small	95	dead	70	1	61	no
test	Small	80	dead	50	17	71	no
test	Small	51	dead	30	87	59	yes
test	Small	29	dead	40	8	67	no
test	Adeno	24	dead	40	2	60	no
test	Adeno	18	dead	40	5	69	yes
test	Adeno	83	censored	99	3	57	no
test	Adeno	31	dead	80	3	39	no
test	Adeno	51	dead	60	5	62	no
test	Adeno	90	dead	60	22	50	yes
test	Adeno	52	dead	60	3	43	no
test	Adeno	73	dead	60	3	70	no
test	Adeno	8	dead	50	5	66	no
test	Adeno	36	dead	70	8	61	no
test	Adeno	48	dead	10	4	81	no
test	Adeno	7	dead	40	4	58	no
test	Adeno	140	dead	70	3	63	no
test	Adeno	186	dead	90	3	60	no
test	Adeno	84	dead	80	4	62	yes
test	Adeno	19	dead	50	10	42	no
test	Adeno	45	dead	40	3	69	no
test	Adeno	80	dead	40	4	63	no
test	Large	52	dead	60	4	45	no
test	Large	164	dead	70	15	68	yes
test	Large	19	dead	30	4	39	yes
test	Large	53	dead	60	12	66	no
test	Large	15	dead	30	5	63	no
test	Large	43	dead	60	11	49	yes
test	Large	340	dead	80	10	64	yes
test	Large	133	dead	75	1	65	no
test	Large	111	dead	60	5	64	no
test	Large	231	dead	70	18	67	yes
test	Large	378	dead	80	4	65	no
test	Large	49	dead	30	3	37	no