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 an α of 0.05?

	Dose
Antidote	5	10	15
1	0.6 1.1 1.1	2.1 1.5 2.4	3.1 4.1 5.9
2	1.6 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

Two-way ANOVA: Y versus Antidote, Dore

Source	DF	SS	MS	F	P	effect size
Antidote	1	2.1356	2.13556	4.66	0.052	0.0753
Dore	2	16.6744	8.33722	18.19	0.000	0.5880
Interaction	2	4.0478	2.02389	4.42	0.037	0.1427
Error	12	5.5	0.45833
Total	17	28.3578

S = 0.6770 R-Sq = 80.60% R-Sq(adj) = 72.52%

a) What is the appropriate test statistic?
Ans: Two-way ANOVA

b) Obtain/compute the appropriate values to make a decision about H₀.
Antidote: critical value =4.7472 ; test statistic = 4.66
Decision: Fail to reject H0

Dose: critical value =3.885 ; test statistic = 18.19
Decision:  Reject H0

Interaction: critical value =3.885 ; test statistic = 4.42
Decision: Reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Antidote: η² = 0.0753 ;  small effect
Dose: η² =0.5880 ; large effect
Interaction: η² = 0.1427 ;  large effect


d) Make an interpretation based on the results.

There is no antidote difference in blood concentration.     

There is a dose difference in blood concentration.

There is an antidote by dose interaction in blood concentration.