Segregation

Qstats also tests for adherence to Mendelian segregation at all marker loci. For a given locus, suppose there are $r$ genotypic classes. Let $p_i$ be the expected frequency, and $n_i$ the observed count for the $i$th class. For a sample of size $n$, the expected counts will be $n p_i$ and the observed frequencies will be $n_i / n$. We can construct a test statistics based on a contigency table

$$T_1 = \sum_{i=1}^r \frac{ (n_i - np_i)^2}{np_i}= n \sum_{i=1}^r \frac{ (n_i/n - p_i)^2}{p_i}$$

or a comparison of likelihoods

$$T_2 = -2 \sum_{i=1}^r n_i (\ln n_i - \ln np_i)$$

Both $T_1$ and $T_2$ should have a $\chi^2$ distribution with one degree of freedom for backcrosses and recombinant inbred lines and two degrees of freedom for intercrosses. Both statistics are calculated and presented in a table in the Qstats output.