**Acknowledgement**

hospitalization or death. In such a case control study, it would be proper to match on preex‐ isting health, even though one would find that health accounts for some of the variability in getting or not getting the risk factor (flu vaccine). BUT: health would also relate to the mor‐ tality outcome, and even more strongly. It is this strong relationship that is key. If the varia‐

To objectively quantify this, one needs to know how strongly M is related to the Risk Factor R; and then how strongly M is related to the probability of response P. A problem is that

Assume that M would be HMO, R would be mcg Thimerosal exposure, and P would be ASD diagnosis. It would be desirable to compare the size of this relationship M to R with the relationship of M to P. It would be ideal if one could simple compute correla‐ tions for M and R and for M and P. However, in most cases this would not work: the scales are not all continual, and even if one were to employ a Spearman correlation, it would not be apparent how to code something like HMO to insure a linear relationship. What if HMO 2 was associated with an increase in thimerosal, and HMO 1 and 3 both had low levels? This would result in a low correlation due to the curvilinear relation‐ ship, even IF much of the variance were in fact associated with HMO. On the other hand, the relationship between HMO and thimerosal (M and R) can be checked via AN‐ OVA easily enough since R is continual and M is categorical. ANOVA would not work for testing association between M and P because both M and P are both categorical in this case. Chi – Square would be appropriate. However, regardless of the correct hypoth‐

The p value is a function of the size of the effect and the sample size. Different types of stat‐ istical tests have different probability distributions, but the total area under the curve has a constant meaning across tests. The percent of area covered means the same thing in any test, regardless of the precise shape of the curve associated with a particular statistical test (corre‐ lation, ANOVA, Chi-square). A small p value could be due to a large effect, or it could be due to a very small effect and a very large sample. It should be stated that when sample sizes are similar, it will not be unduly affected by sample size differences. Since the sample will be the same for testing M to P or testing M to R, we propose the p values are the most

Compute a measure for the relationship of M and P and the associated p value. (e.g., HMO

Compute a measure for the relationship of M and R and the associated p value. (e.g., HMO

The p value in all cases should be smaller for the M to R relationship, compared to the M to P relationship test. This will serve to demonstrate that even if the Matching variable does bear some relationship to the risk factor for the outcome probability, there is clearly a stron‐ ger relationship to the outcome itself, thus objectively justifying the matching. (e.g., the p value of.45 indicates no relationship exists between the matched variable and the outcome of interest, while the p value <.0001 indicates that matched variable is related to the expo‐

ble is more strongly related to the outcome – this serves to justify matching.

108 Recent Advances in Autism Spectrum Disorders - Volume I

esis test, all hypothesis tests are in fact unified by the p value.

readily available means to index the comparison.

and Thimerosal exposure: F (2,1090) = 237, p <.0001).

(2) = 1.59, p =.45 )

and ASD: X2

different types of data can make precise comparisons of effect size hard to judge.

This work was partially funded by a small grant awarded to the second author, Robert T. Hitlan from Safeminds. We thank Safeminds for their support.
