Question

Dr. Jones is interested in the effects of caffeine on performance. She randomly splits her statistics class of 15 students into three groups. Prior to the final exam, she has one group take no caffeine prior to taking the exam, students in another group take 100 mg of caffeine, and students in the third group take 200 mg of caffeine. She records the grades in each condition.

0 mg	100 mg	200 mg
65	75	72
62	80	78
70	85	87
80	94	92
78	86	91

a. State the null hypothesis.

b. Identify the appropriate statistical test

c. Calculate the appropriate test statistic. Make sure to report the degrees of freedom for the statistical test (if appropriate). You must show your work to receive full credit.

d. State your conclusions (use a two-tailed test with  = .05 for all tests).

e. Compute an effect size

Answer 1

a. state the null hypothesis:

H0: There is no significance difference between three group (i.e. 0, 100, 200 mg)

Ha: There is significance difference between three group (i.e. 0, 100, 200 mg)

b. Identify the appropriate statistical tet:

In statistics, one-way analysis of variance is a technique that can be used to compare means of two or more samples.

So, to check significance between there groups we should be use one way anova.

c. Calculate the appropriate test statistic.

By using excel data analysis tool we have to calculate one way ANOVA,

First arrange data in excel as,

0 mg	100 mg	200 mg
65	75	72
62	80	78
70	85	87
80	94	92
78	86	91

Then use data analysis tool as,

The output of ANOVA is,

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
0 mg	5	355	71	62
100 mg	5	420	84	50.5
200 mg	5	420	84	75.5
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	563.33	2	281.67	4.49	0.03	3.89
Within Groups	752.00	12	62.67
Total	1315.33	14

d. State your conclusions (use a two-tailed test with alpha = .05 for all tests).

We can see in above output,

P-vlaue = 0.03

Decision: the p-value (0.03) is less than 0.05 then we Reject H0

Conclusion: There is significance difference between three group (i.e. 0, 100, 200 mg)

e. Compute an effect size

Overall effect size = Sqrt(MSbetween / MSwithin)

= sqrt(281.67/62.67)

= sqrt(4.49)

= 2.1200

The effect size is 2.1200