FAQ/heterogeneity - CBU statistics Wiki

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What is heterogeneity of variance in SPSS Probit and Logit procedures?

Probit and Logit functions are used to relate predictors to probabilities, e.g. the relationship between hearing thresholds and the proportion of people who registered a stimuli at these thresholds. The probit and logit functions are merely transforms which turn the output of a linear regression into proportions.

The output is slightly different to that from the usual linear regression. In particular a term called the heterogeneity of variance is produced – with very little explanation of what it means. In fact, this is analogous to the error mean square in an ordinary analysis of variance table. It represents the lack of fit of the model and if it is sufficiently small it suggests, for example, that the probability of picking up a stimulus is closely related to the hearing threshold of that stimulus. The quieter the sound the less people pick it up. It also suggests that noting the hearing threshold is sufficient, on its own, to predict the probability of hearing a stimulus.

The lack of fit term is chi-square distributed with N-p degrees of freedom for N observations and p-1 predictors. In our example N is the number of different hearing thresholds and p=2 representing the intercept and hearing threshold regression term. So the lack of fit term will have N-2 degrees of freedom. If the lack of fit term is substantially larger than a chi-square on N-2 df then we know we have a poor model, possibly due to other factors influencing stimulus hearing other than the volume of the sound.

If there is a statistically significant lack of fit SPSS adjusts for this by producing confidence intervals, in our example, for proportions of people hearing a stimulus, at each stimulus threshold, which are very large indicating a lack of confidence, or precision, in predicting the probability of hearing a sound using the volume of that sound.