Question

Do a traditional oneway analysis of variance to see if the pulse before running depends on activity level. State conclusion in a jargon-free sentence, check assumptions and conditions. Report any problems and discuss how they impact interpretation of the result.

PuBefore	PuAfter	Ran?	Smokes?	Sex	Height	Weight	ActivityL
48	54	no	yes	male	68	150	1
54	56	no	yes	male	69	145	2
54	50	no	no	male	69	160	2
58	70	yes	no	male	72	145	2
58	58	no	no	male	66	135	3
58	56	no	no	female	67	125	2
60	76	yes	no	male	71	170	3
60	62	no	no	male	71	155	2
60	70	no	yes	male	71.5	164	2
60	66	no	no	female	62	120	2
61	70	no	no	female	65.5	120	2
62	76	yes	yes	male	73.5	160	3
62	75	yes	no	male	72	195	2
62	58	yes	no	male	72	175	3
62	100	yes	no	female	66	120	2
62	98	yes	yes	female	62.75	112	2
62	62	no	no	male	74	190	1
62	66	no	no	male	70	155	2
62	68	no	yes	male	73	155	2
62	66	no	no	female	65	122	3
64	88	yes	no	male	66	140	2
64	80	yes	no	male	69	155	2
64	62	no	no	male	75	160	3
64	60	no	no	female	66	130	3
66	78	yes	yes	male	73	190	1
66	82	yes	yes	male	69	175	2
66	102	yes	no	male	70	130	2
66	72	no	no	female	66	125	2
66	76	no	no	female	65	115	2
68	72	yes	no	male	74	190	2
68	76	yes	no	male	67	145	2
68	76	yes	yes	male	74	180	2
68	112	yes	no	female	70	125	2
68	66	no	yes	male	67	150	2
68	68	no	no	male	71	150	3
68	64	no	no	male	69.5	150	3
68	68	no	no	male	72	142	3
68	66	no	no	male	68	155	2
68	68	no	no	female	69	150	2
68	68	no	no	female	62	110	2
70	72	yes	yes	male	73	170	3
70	106	yes	no	male	71	170	2
70	94	yes	yes	male	75	185	2
70	62	no	yes	male	66	130	2
70	70	no	no	male	70	150	2
70	66	no	yes	male	75	190	2
72	80	yes	no	male	66	135	3
72	74	no	yes	male	69	170	2
72	74	no	yes	male	68	155	3
72	70	no	no	male	71	140	2
72	70	no	no	female	63	118	2
72	68	no	no	female	68	110	2
74	84	yes	no	male	73	165	1
74	76	yes	no	male	70	157	2
74	70	no	no	male	73	155	3
74	74	no	no	male	73	155	2
74	76	no	no	male	67	123	2
76	118	yes	no	male	71	138	2
76	76	no	no	male	72	215	2
76	76	no	no	male	74	148	3
76	76	no	yes	female	62	108	3
76	76	no	no	female	61.75	108	2
78	104	yes	yes	female	68	130	2
78	118	yes	no	female	69	145	2
78	76	no	no	male	72	180	3
78	78	no	no	female	67	115	2
78	80	no	no	female	68	133	1
80	96	yes	no	male	72	155	2
80	128	yes	no	female	68	125	2
80	74	no	no	female	64	102	2
82	100	yes	no	female	68	138	2
82	84	no	yes	male	73	180	2
82	80	no	no	female	63	116	1
84	84	yes	no	male	72	150	3
84	84	no	no	male	69	136	2
84	84	no	no	female	66	130	2
84	80	no	no	female	65	118	1
86	84	no	no	female	67	150	3
87	84	no	no	female	63	95	3
88	110	yes	yes	female	69	150	2
88	84	no	no	male	73.5	155	2
88	74	no	yes	female	65	135	2
90	94	yes	yes	male	74	160	1
90	88	no	yes	male	67	140	2
90	90	no	no	male	68	145	1
90	92	no	yes	female	64	125	1
92	84	yes	yes	male	70	153	3
92	94	no	yes	male	69	150	2
94	92	no	yes	female	62	131	2
96	140	yes	no	female	61	140	2
96	116	yes	no	female	68	116	2
100	115	yes	yes	female	63	121	2

Answer 1

Test for Equal Variances

The hypothesis being tested is:

Null hypothesis	All variances are equal
Alternative hypothesis	At least one variance is different
Significance level	α = 0.05

95% Bonferroni Confidence Intervals for Standard Deviations

ActivityL	N	StDev	CI
1	10	14.0412	(8.94479, 29.8808)
2	61	10.9847	(9.00209, 13.9979)
3	21	9.6259	(6.96360, 15.1913)

Individual confidence level = 98.3333%

Tests

Method	Test Statistic	P-Value
Bartlett	1.87	0.393

The p-value is 0.393.

Since the p-value (0.393) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that all variances are equal.

Analysis of Variance

The hypothesis being tested is:

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Factor	Levels	Values
ActivityL	3	1, 2, 3

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
ActivityL	2	161.1	80.54	0.66	0.520
Error	89	10867.3	122.11
Total	91	11028.4

The p-value is 0.520.

Since the p-value (0.520) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude that all means are equal.