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. Thirty minutes later the response was measured as the concentration in the blood. What can the researchers conclude with an α of 0.01?

	Dose
Antidote	5	10	15
1	0.6 6.5 1.1	2.1 1.5 2.4	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) Obtain/compute the appropriate values 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


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Antidote: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Dose: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is an antidote difference in blood concentration.

There is no antidote difference in blood concentration.    

There is a dose difference in blood concentration.

There is no dose different in blood concentration.    

There is an antidote by dose interaction in blood concentration.

There is no antidote by dose interaction in blood concentration.    

Answer 1

Output using excel:

Anova: Two-Factor With Replication
SUMMARY	Dose 5	Dose 10	Dose 15	Total
Antidote 1
Count	3	3	3	9
Sum	8.2	6	13.1	27.3
Average	2.733333	2	4.366667	3.033333
Variance	10.70333	0.21	2.013333	4.3325
Antidote 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	11.6	10.5	20.4
Average	1.933333	1.75	3.4
Variance	5.050667	0.175	2.06
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	8.133889	1	8.133889	3.668504	0.079582	9.330212
Columns	9.814444	2	4.907222	2.21323	0.151993	6.926608
Interaction	1.687778	2	0.843889	0.380606	0.69141	6.926608
Within	26.60667	12	2.217222
Total	46.24278	17

a) Test used: Two way Anova

b) Obtain/compute the appropriate values to make a decision about H₀.

Antidote:

critical value = 6.927

test statistic = 2.213

Decision: Fail to reject H0

Dose:

critical value = 9.330

test statistic = 3.669

Decision: Fail to reject H0

Interaction:

critical value = 6.927

test statistic = 0.381

Decision: Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
Antidote:

η²A = SSA /(SST - SSB - SSAxB) = 9.8144/(46.2428 - 8.1339 - 1.6878) = 0.2695 = 26.95%

Dose:

η²B = SSB /(SST - SSA - SSAxB) = 8.1339/(46.2428 - 9.8144 - 1.6878) = 0.2341 = 23.41%

Interaction:

η²AxB = SSAxB /(SST - SSA - SSB) = 1.6878/(46.2428 - 9.8144 - 8.1339) = 0.0597 = 5.97%

d) Make an interpretation based on the results.

There is no antidote difference in blood concentration.    

There is no dose different in blood concentration.    

There is no antidote by dose interaction in blood concentration.