Frequencies of patients with different numbers of antibodies in diagnostic subgroups at an adult study hospital. The y-axis has a logarithmic scale. Circles represent actual data points. Error bars extend 2 sample SDs from the sample mean. Note that error bars are longer for larger numbers of antibodies first because the number of patients is small and second because the logarithmic scale amplifies length for smaller values. The lines represent least-squares fits to a geometric probability distribution: (1 − p)pn. The distribution parameter p is the risk of forming an (n + 1)th antibody after having formed an nth antibody; 95% confidence intervals for estimates of this parameter are shown in the legend of each panel. Smaller values of p lead to a steeper slope because the slope of this fit on a logarithmic scale is log(p), as can be seen in the top panel for the “pregnancy” patients, where the frequency falls to 10−5 faster than in the other panels.
