How the one-way analysis of variance model is affected by the degree of precision of the data

The underlying theory upon which many statistical tests are based, assumes that the variables sampled are continuous. However, the data are often subject to rounding. Here we consider the effect of rounding on the significance level and power of the F test in the one-way analysis of variance with fixed effects, with respect to the degree of precision of recorded data, sample size and normality of the population. Even for coarse rounding the effects are small.