Probability and Statistics for Computer Science by David Forsyth

Author:David Forsyth
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

Now assume the factors do not interact. Then we can use the rows to estimate the effect of factor one at L 1 different levels using G × L 2 measurements per cell. Similarly, we can use the columns to estimate the effect of factor two at L 2 different levels using G × L 1 measurements per cell. To obtain the same number of measurements per cell for each factor with independent experiments would take more experiments. You would have to use experiments for factor one and another experiments for factor two.

Randomization is still a strong strategy for assigning groups to cells. Again, we will assume that the experimental equipment doesn’t have a memory, and that changing settings and so on is trivial. We allocate subjects to groups at random, ensuring that each group gets G subjects. You could do this, for example, by permuting the subjects randomly, then allocating the first G to group 1, 1, etc.

We then perform the experiment, by treating each group of subjects at the prescribed level, and recording the results. For each subject, we will observe a measurement. We want to know if there is an interaction between the treatments, and if either treatment has any effect. We can investigate this question using methods like those for one-factor experiments.

We assume that differences in observed values in each group are purely due to noise. Write x ijk for the observed value for the k’th subject in the treatment group that has the i’th level of the first treatment and the j’th level of the second treatment. This means that we could model

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