Question

McAllister et al. (2012) compared varsity football and hockey players with varsity athletes from noncontact sports to determine whether exposure to head impacts during one season have an effect on cognitive performance. In their study, tests of new learning performance were significantly poorer for the contact sport athletes compared to the noncontact sport athletes.

The following presents data similar to the results obtained. Data are the scores of a neurological test. Higher scores indicate better performance.

Type of sport

Noncontact Sport Athletes	Contact Sports Athletes
10, 8, 7, 9, 13, 7, 6, 12	7, 4, 9, 3, 7, 6, 10, 2

Computations by hand

a. What are IV and DV in this study?

b. Compute the mean and the standard deviation for each condition (show your work). (use the definition formula to compute each SS)

c. Are the neurological test scores for contact sport athletes significantly different from the neurological test scores for noncontact sport athletes? Use a two-tailed test with α = .05.

1) State the null hypothesis in words and in a statistical form.

2) State the alternative hypothesis in words and a statistical form.

3) Compute the appropriate statistic to test the hypotheses. Sketch the distribution

with the estimated standard error and locate the critical region(s) with the critical value(s).

4) State your statistical decision

5) Compute Cohen’s d. Interpret what the d really means in this context.  

6) Compute 95% CI (2).

7) What is your conclusion? Interpret the results. Do not forget to include a statistical form (e.g., t-score, df, α, Cohen’s d)

Answer 1

a. What are IV and DV in this study?

IV = exposure to head impacts during one season

DV = cognitive performance

b. Compute the mean and the standard deviation for each condition (show your work). (use the definition formula to compute each SS)

Mean for Noncontact Sport Athletes = (10+ 8+ 7+ 9+ 13+ 7+ 6+ 12)/8 = 9

The standard deviation for Noncontact Sport Athletes = (10-9)2+ (8-9)2+ (7-9)2+( 9-9)2+ (13-9)2+ (7-9)2+ (6-9)2+ (12-9)2)/8-1 = 2.51

Mean for Contact Sports Athletes = (7+ 4+ 9+ 3+ 7+ 6+ 10+ 2)/8 = 6

The standard deviation for Contact Sports Athletes = (7-6)2+ (4-6)2+ (9-6)2+ (3-6)2+ (7-6)2+ (6-6)2+ (10-6)2+ (2-6)2)/8-1 = 2.83

c. Are the neurological test scores for contact sport athletes significantly different from the neurological test scores for noncontact sport athletes? Use a two-tailed test with α = .05.

1) State the null hypothesis in words and in a statistical form.

H0: µ1 = µ2

H0: The neurological test scores for contact sport athletes is not significantly different from the neurological test scores for noncontact sport athletes

2) State the alternative hypothesis in words and a statistical form.

H1: µ1 ≠ µ2

H1: The neurological test scores for contact sport athletes is significantly different from the neurological test scores for noncontact sport athletes

3) Compute the appropriate statistic to test the hypotheses. Sketch the distribution

with the estimated standard error and locate the critical region(s) with the critical value(s).

Group 1	Group 2
9.00	6.00	mean
2.51	2.83	std. dev.
8	8	n
	14	df
	3.000	difference (Group 1 - Group 2)
	7.143	pooled variance
	2.673	pooled std. dev.
	1.336	standard error of difference
	0	hypothesized difference
	2.245	t
	.0414	p-value (two-tailed)

The sketch is:

4) State your statistical decision

The p-value is 0.0414.

Since the p-value (0.0414) is less than the significance level (0.05), we can reject the null hypothesis.

5) Compute Cohen’s d. Interpret what the d really means in this context.  

Cohen’s d = 3/2.673 = 1.122

6) Compute 95% CI (2).

0.134	confidence interval 95.% lower
5.866	confidence interval 95.% upper
2.866	margin of error

7) What is your conclusion? Interpret the results. Do not forget to include a statistical form (e.g., t-score, df, α, Cohen’s d)

Therefore, we can conclude that the neurological test scores for contact sport athletes is significantly different from the neurological test scores for noncontact sport athletes.