Question

16. The following resting data were collected from three different sports teams (hockey, rugby and football). Ignoring the sport played, run a Kolmogorov–Smirnov test on the age variable. What is the correct expression for the result?

ID	Sport	Age (y)	Body mass (kg)	Stature (m)	Resting heart rate (bpm)	Resting systolic blood pressure (mmHg)	Resting diastolic blood pressure (mmHg)	Resting mean arterial pressure (mmHg)
1	Hockey	18	79	1.83	65	121	79	93
2	Hockey	20	79.9	1.78	50	127	81	96
3	Hockey	25	75.8	1.83	53	120	62	81
4	Hockey	17	63.6	1.7	74	115	75	88
5	Hockey	22	57.4	1.64	68	116	68	84
6	Hockey	22	60	1.65	64	100	30	53
7	Hockey	21	81.2	1.79	65	126	80	95
8	Hockey	19	84.5	1.93	64	120	70	87
9	Rugby	19	71.1	1.77	79	120	80	93
10	Rugby	26	72.8	1.79	82	134	76	95
11	Rugby	29	75.1	1.78	55	130	90	103
12	Rugby	21	69.4	1.74	60	140	71	94
13	Rugby	19	68.8	1.8	76	122	78	93
14	Rugby	19	63.8	1.6	61	119	74	89
15	Rugby	19	87	1.87	60	130	80	97
16	Football	24	74.2	1.77	63	120	64	83
17	Football	26	80.9	1.82	65	110	79	89
18	Football	27	66.5	1.75	63	120	50	73
19	Football	19	83	1.81	49	120	80	93
20	Football	21	89.5	1.78	50	117	80	92
21	Football	19	74.2	1.77	72	114	78	90
22	Football	21	66.6	175	83	122	82	95

	a.	D(22) = .197, p = .026
	b.	D(22) = .026, p = .197
	c.	D(22) = .086, p > .2
	d.	D(22) = .2, p > .086

17. Why does a Shapiro–Wilk test sometimes conclude that the data are not normally distributed (i.e. significant) when a Kolmogorov–Smirnov test is non-significant?

	a.	The Shapiro–Wilk test is more powerful.
	b.	The Shapiro–Wilk test is less powerful.
	c.	The Shapiro–Wilk test does not work well when there are a large number of cases.
	d.	The Shapiro–Wilk test is a more conservative test.

18. Using the data from the table in Q16, what assumption can be made regarding the distribution of the age data?

	a.	They are not normally distributed.
	b.	They are normally distributed.
	c.	It is unclear whether they are normally distributed or not.
	d.	A Shapiro–Wilk test should be run to confirm the result.

20.

Using the data in the table in Q16, split the data according to the sport. Run a Kolmogorov–Smirnov test on the diastolic blood pressure data. Which group’s data cannot assume a normal distribution?

	a.	Football
	b.	Hockey
	c.	Rugby
	d.	All three are normally distributed.

Answer 1

Shapiro-Wilk test, using right-tailed normal distribution

1. H₀ hypothesis
Since p-value<α, H₀ is rejected.
It is assumed that the data is not normally distributed.
In other words, the difference between the data sample and the normal distribution is big enough to be statistically significant.

2. P-value
p-value is 0.0213364, hence, the chance of type1 error (rejecting a correct H₀) is small: 0.02134(2.13%)
The smaller the p-value, the more it supports H₁

3. The statistics
W is 0.892743. It is not in the 95% critical value accepted range: [0.9112: 1.0000]