Lecture 16: Factorial Crossing

Transcription

1 Chapter 6 Frog Experiment Factorial Crossing. We have actually seen this in the experiment comparing different methods of frog dissection. Experimental Units: Lab sections of biology. Response: Average score on a test on the anatomy of the frog. 1 2 Frog Experiment Factors and Levels Treatments:,, Both, ne. These treatments are really the combination of two factors of interest. Factor 1: Levels:, Factor 2: Levels:, 3 4 Treatments With factorial crossing treatments consist of all possible combinations of the levels of the factors. Both Treatments ne 5 6 1

2 Why use factorial crossing? Why use factorial crossing? Doing one experiment using factorial crossing is more efficient than doing separate experiments, one for each factor of interest. 7 Doing one experiment using factorial crossing allows for the investigation of possible interaction between the factors. 8 Efficiency Two Experiments Experiment I: Compare to. Experiment II: Compare to. 9 Alpha = 0.05 Beta = standard deviation in 10 One Experiment Experiment I: 2 Groups, 12 per group, 24 lab sections. Experiment II: 2 Groups, 12 per group, 24 lab sections. Total of 48 lab sections. 11 Alpha = 0.05 Beta = standard deviation in 12 2

3 One Experiment Different Means Experiment: 4 Groups, 16 per group, 64 lab sections. How is this more efficient? There is a problem as the two situations are referring to different Two experiments: difference in factor level One experiment: difference in treatment Both n = 6 n = n = 6 12 ne n = Comparing real dissection to no real dissection there are 12 lab sections per group. Can detect a 1.4 standard deviation difference in factor level means, Alpha = 0.05, Beta = Greater Efficiency Comparing virtual dissection to no virtual dissection there are 12 sections per group. Can detect a 1.4 standard deviation difference in factor level means, Alpha = 0.05, Beta = One experiment using 24 lab sections can detect the same size difference in factor level means as 48 lab sections used in two experiments

4 Important Distinction Important Distinction When there was only one manipulated factor, the factor levels were the treatments. w that there are several factors there is a difference between factor levels and treatments When using the sample size tables be sure to note the distinction between factor level means and treatment 21 In Stat 301 or 401, two explanatory variables are said to interact if the relationship between the response variable and one of the explanatory variables changes for different values of the second explanatory variable. 22 In Stat 402, two factors are said to interact if the effect of one factor on the response is different for different levels of the second factor. The two definitions are getting at the same idea just with different terminology

5 Example In the experiment with ;, and ;, as the factors what would the treatment means look like with and without interaction? 25 Average Score on test of Frog Anatomy : : 26 In sections with no virtual dissection the effect of real dissection is the same as in sections with virtual dissection. 27 Average Score on test of Frog Anatomy : : 28 In sections with no virtual dissection there is a positive effect due to real dissection. In sections with virtual dissection there is no effect due to real dissection. Interpretation The effect of real dissection on the average score on the frog anatomy test is different for sections using, or not using, virtual dissection. dissection and dissection factors interact