A controversy arose over Mendel’s pea crossing experiments after the statistician R.A. Fisher proposed how these may have been performed and criticised Mendel’s interpretation of his data. Here we re-examine Mendel’s experiments and investigate Fisher’s statistical criticisms of bias. We describe pea varieties available in Mendel’s time and show that these could readily provide all the material Mendel needed for his experiments; the characters he chose to follow were clearly described in catalogues at the time. The combination of character states available in these varieties, together with Eichling’s report of crosses Mendel performed, suggest that two of his F3 progeny test experiments may have involved the same F2 population, and therefore that these data should not be treated as independent variables in statistical analysis of Mendel’s data. A comprehensive re-examination of Mendel’s segregation ratios does not support previous suggestions that they differ remarkably from expectation. The χ2 values for his segregation ratios sum to a value close to the expectation and there is no deficiency of extreme segregation ratios. Overall the χ values for Mendel’s segregation ratios deviate slightly from the standard normal distribution; this is probably because of the variance associated with phenotypic rather than genotypic ratios and because Mendel excluded some data sets with small numbers of progeny, where he noted the ratios “deviate not insignificantly” from expectation.

中文翻译：

---

孟德尔豌豆杂交：品种、性状和统计


在统计学家 RA Fisher 提出这些实验可能是如何进行并批评孟德尔对其数据的解释后，孟德尔的豌豆杂交实验引起了争议。在这里，我们重新审视孟德尔的实验并研究费舍尔对偏见的统计批评。我们描述了孟德尔时代可用的豌豆品种，并表明这些品种可以很容易地提供孟德尔实验所需的所有材料；他选择追随的人物在当时的目录中有清晰的描述。这些品种中可用的性状状态组合，加上艾希林对孟德尔进行的杂交的报告，表明他的两个 F3 后代测试实验可能涉及相同的 F2 群体，因此这些数据不应被视为统计中的自变量孟德尔数据分析。对孟德尔分离率的全面重新检查并不支持先前的建议，即它们与预期存在显着差异。他的偏析比的 χ2 值总和接近于预期值，并且不存在极端偏析比的缺陷。总体而言，孟德尔偏析比的 χ 值稍微偏离标准正态分布；这可能是因为与表型比率而不是基因型比率相关的方差，并且因为孟德尔排除了一些后代数量较少的数据集，他指出这些比率与预期“偏差不显着”。