Conduct Web experiments using PHP, Part 2
By Paul Meagher2005-03-18
Null effects model
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One way to compute the expected cell counts is to assume that no effects are associated with any of your experimental factors. Under this null effects model, you would expect to observe similar cell counts among all four cells in your 2x2 contingency table (also know as homogeneity of proportions).
Under this null effects model, you can compute the expected number of responses for each cell with the formula
E(n) = Np
in which N is the total number of Web offers administered and p is the probability of responding. In turn, you can estimate the value to use for p using this formula
p = r/N
in which r denotes the number of visitors who responded to the Web offer in N trials. In other words, the maximum likelihood estimate (MLE) of p is the response percentage to date.
One of the first statistical analyses that you might want to conduct on your Web offer results is apply the two-dimensional chi-square procedure to your contingency table data in which the expected counts to use are derived under the assumption that no effects are present. This is equivalent to assuming that you are sampling from a homogeneous population. When you use the chi-square test procedure to measure the variance between your observed frequencies and expected frequencies, you will discard the null effects model if the summed difference scores are normally too large to be generated by a sampling model consisting of four independent but identically parameterized poisson random deviates (where the lambda parameter is estimated using r/N).
Tutorial Pages:
» Categorical data analysis
» 2x2 contingency tables
» Sampling model
» Discrete probability distributions
» Binomial sampling model
» Poisson sampling model
» Envisioning your results
» Eliciting your prior distribution
» Model fitting with chi-square
» Null effects model
» Independence model
» Prior model
» DOE explorer
» Explorer output
» Conclusions
» Resources
First published by IBM developerWorks
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