#!/usr/bin/awk -f

BEGIN{
    sum1 = 0;
    sum2 = 0;
    sumsq1 = 0;
    sumsq2 = 0;
    sumpair = 0;
    sumpairsq = 0;
    N = 0;
}

{
    sum1 += $1;
    sumsq1 += $1 * $1;
    sum2 += $2;
    sumsq2 += $2 * $2;
    sumpair += $1 + $2;
    sumpairsq += ( $1 + $2 )*( $1 + $2 );
    N++;
}

END{
    m1 = sum1/N;
    m2 = sum2/N
    SSs = sumpairsq/2 - sumpair*sumpair/( N*2 );
    SSb = ( sum1*sum1 + sum2*sum2 )/N - sumpair*sumpair/( N*2 );
    SSe = ( sumsq1+sumsq2 ) - sumpair*sumpair/ ( N*2 ) - SSs - SSb;
    MSs = SSs/(N-1);
    MSb = SSb;
    MSe = SSe/(N-1);
    F = MSb/MSe;

    printf("F: %1.4f\n", F);
}