Question

In: Math

An experiment was conducted to see the effectiveness of two antidotes to three different doses of...

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

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.    

Solutions

Expert Solution

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 F crit
Sample 6.125 1 6.125 4.075786 0.066418 4.747225
Columns 16.91444 2 8.457222 5.627726 0.018877 3.885294
Interaction 4.223333 2 2.111667 1.405176 0.282941 3.885294
Within 18.03333 12 1.502778
Total 45.29611 17

c) ANTIDOTE = SSeffect / SStotal= 6.125/45.2961=0.14 (small)

DOSE =SSeffect / SStotal = 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.    


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