# Significance of lod scores

The lod score is the log base 10 of the likelihood ratio under the hypotheses of linkage and non-linkage:

Z=log10(LR)

For many likelihood ratio tests twice the natural log of the likelihood ratio is asymptotically distributed as a chi-squared statistic:

T=2ln(LR) => chi-squared

A lod score can be converted into an equivalent chi-squared statistic with the following simple formula:

T=2ln(10)Z

Since 2ln(10) is approximately equal to 4.6 a lod score can be converted into a chi-squared statistic simply by multiplying by 4.6, e.g. a lod of 3 is equivalent to a chi-squared statistic of 13.8.

The number of degrees of freedom will depend on the difference in the number of free parameters used to obtain the numerator and denominator of the likelihood ratio.

For the classical lod score there is one free parameter, the recombination fraction. For other lod scores there may be more degrees of freedom, though often the parameters are confounded with each other and chi-squared tests may tend to be somwhat conservative.

The chi-squared approximation often works well, but under some circumstances the true significance can be as high 1/10 to the power of the lod score (e.g. Z=3, p=0.001).