Question

An experiment was conducted to see the effectiveness of two antidotes to three different doses of a toxin. The antidote was given to a different sample of participants five minutes after the toxin. Twenty-five minutes later the response was measured as the concentration in the blood. What can the researchers conclude with α = 0.01?

	Dose
Antidote	5	10	15
1	0.6 1.1 1.1	2.1 1.5 6.2	3.1 4.1 5.9
2	1.1 1.2 1.1	1.7 1.3 1.5	2.1 3.1 2.1

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
Antidote: critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

Dose: critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

Answer 1

Anova: Two-Factor With Replication
SUMMARY	5	10	15	Total
1
Count	3	3	3	9
Sum	2.8	9.8	13.1	25.7
Average	0.933333	3.266667	4.366667	2.855556
Variance	0.083333	6.543333	2.013333	4.465278
2
Count	3	3	3	9
Sum	3.4	4.5	7.3	15.2
Average	1.133333	1.5	2.433333	1.688889
Variance	0.003333	0.04	0.333333	0.431111
Total
Count	6	6	6
Sum	6.2	14.3	20.4
Average	1.033333	2.383333	3.4
Variance	0.046667	3.569667	2.06
ANOVA
Source of Variation	SS	df	MS	F	P-value
Sample	6.125	1	6.125	4.075786	0.066418
Columns	16.91444	2	8.457222	5.627726	0.018877
Interaction	4.223333	2	2.111667	1.405176	0.282941
Within	18.03333	12	1.502778
Total	45.29611	17

c) ANTIDOTE = SS_effect / SS_total= 6.125/45.2961=0.14 (small)

DOSE =SS_effect / SS_{total =} 16.91/45.296 = 0.37 medium

INTERACTION =  SSeffect / SStotal = 4.22/45.296 = 0.09 (SMALL)

d)

There is no antidote difference in blood concentration.    

There is no  dose difference in blood concentration

There is no antidote by dose interaction in blood concentration.