Sampling Errors

Genetic crosses predict expected ratios, such as 3 : 1 or 1 : 1. In real breeding experiments, the observed numbers almost never match these exactly. The main reason is chance.Each fertilisation is a random, independent event. Which gamete fuses with which is down to chance, so a 3 : 1 ratio is really a probability of 0.75 and 0.25 for each individual offspring, not a guarantee. This difference between the observed and expected results caused by chance is called sampling error.Sampling error is largest in small samples. Toss a coin 4 times and getting 3 heads is common; toss it 1000 times and the result will be very close to 50 : 50. In the same way, the larger the number of offspring counted, the closer the observed ratio tends to be to the expected ratio.Worked example: Tt × Tt gives 40 seedlings. The expected numbers are 30 tall and 10 short. The observed numbers are 27 tall and 13 short. This is a ratio of about 2.1 : 1, not 3 : 1, but the difference could easily be due to chance with only 40 plants.Other factors can also affect results, for example some genotypes may survive less well, or the genes may be linked. To decide whether a difference is small enough to be due to chance alone, biologists use a statistical test: the chi-squared test, covered later in this topic.To reduce sampling error, use large numbers of offspring and repeat the cross.