Fig. 3

The frequency distribution of χ² values. The frequency distribution of the proportion of χ² values in a given range corresponding to phenotypic ratios in Mendel’s experiments is shown. The ranges of χ² values are on the x axis and the frequency with which χ² values in each range occur is on the y axis. For comparison the expected frequency distribution of χ² values is also shown as shaded background bars. These are centred at the expected frequency and the three shades of grey correspond to ±1 (dark), 2 (lighter) or 3 (lightest) standard errors. Standard errors for the expected frequencies (p) were estimated as √(p(1-p)/N) where N = 88. Three sets χ² values corresponding to Mendel’s data are plotted: Those with an open circle correspond to 64 values where the data were as Edward’s grouping, except that the data for Mendel’s experiments 1 and 2 are for the combined values. The second, marked as filled circles, correspond to 88 values which disaggregate the values of Mendel’s experiments 1 and 2 into all of the examples he gave for individual plants. The third set, with marked +, correspond to 84 values where experiments 1 and 2 disaggregate only the first 10 plants of each experiment as in Edwards [8]. The data corresponding to these values are given in Additional file 1: Table S1.3. The expected frequencies were calculated in excel using the function CHISQ.DIST(× 1,ν,c)) - CHISQ.DIST(× 2, ν,c)) where × 1 and × 2 correspond to the range of χ² values, ν = 1 (degree of freedom) and c = 1 (cumulative distribution)