Conduct Web experiments using PHP, Part 2
By Paul Meagher2005-03-18
Prior model
|
|
Another way to derive the expected counts to use in the chi-square model-fitting procedure is to base your estimates of pij on subjective probability estimates elicited by simulating and graphing your results during pre-experimental planning. A Bayesian might ultimately formalize prior belief in experimental outcomes as a set of elicited lambda estimates from which expected frequencies can be derived (like lambdaij * N = Eij where N is the number of experimental trials) and fitted to the observed frequencies using the chi-square procedure.
The informational value of the experiment would be proportional to the size of the chi-square score computed when the experiment is over and the observed cell counts are compared to the expected counts derived from your prior distribution for the lambda lambda parameters. The expected counts might be denoted Eijprior to distinguish this way of computing the expected counts from the two different methods used in the null effects model and the independence model.
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
|
