As it happens, this lack of normality in the distribution of the populations from which we derive our samples does not often pose a problem. The reason is that the distribution of sample means, as well as the distribution of differences between two independent sample means (along with many

20 other conventionally used statistics), is often normal enough for the statistics to still be valid. The reason is the

*The Central Limit Theorem*, a “statistical law of gravity”, that states (in its simplest form

21) that the distribution of a sample mean will be approximately normal providing the sample size is sufficiently large. How large is large enough? That depends on the distribution of the data values in the population from which the sample came. The more non-normal it is (usually, that means the more skewed), the larger the sample size requirement. Assessing this is a matter of judgment

22.

Figure 7 was derived using a computational sampling approach to illustrate the effect of sample size on the distribution of the sample mean. In this case, the sample was derived from a population that is sharply skewed right, a common feature of many biological systems where negative values are not encountered (

Figure 7A). As can be seen, with a sample size of only 15 (

Figure 7B), the distribution of the mean is still skewed right, although much less so than the original population. By the time we have sample sizes of 30 or 60 (

Figure 7C, D), however, the distribution of the mean is indeed very close to being symmetrical (i.e., normal).