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What is the best way to report variation in data? Is there a minimum acceptable sample size? When are multiple comparison adjustments not required? When is a sample size too small? Can a sample size be too large? The proper understanding and use of statistical tools are essential to the scientific enterprise.

This is true both at the level of designing one’s own experiments as well as for critically evaluating studies carried out by others. Unfortunately, many researchers who are otherwise rigorous and thoughtful in their scientific approach lack sufficient knowledge of this field. This methods chapter is written with such individuals in mind. Our intent has been to limit theoretical considerations to a necessary minimum and to use common examples as illustrations for statistical analysis. Our chapter includes a description of basic terms and central concepts and also contains in-depth discussions on the analysis of means, proportions, ratios, probabilities, and correlations.

If I need to rely on statistics to prove my point, then I’m not doing the right experiment. In fact, reading this statement today, many of us might well identify with this point of view. We are perhaps even a bit suspicious of other kinds of data, which we perceive as requiring excessive hand waving. However, the realities of biological complexity, the sometimes-necessary intrusion of sophisticated experimental design, and the need for quantifying results may preclude black-and-white conclusions. Oversimplified statements can also be misleading or at least overlook important and interesting subtleties. The intent of these sections will be to provide C.

Our intent is therefore to aid worm researchers in applying statistics to their own work, including considerations that may inform experimental design. There are numerous ways to describe and present the variation that is inherent to most data sets. It has the advantage that nearly everyone is familiar with the term and that its units are identical to the units of the sample measurement. Its disadvantage is that few people can recall what it actually means. Both have identical average brood sizes of 300. However, the population in Figure 1B displays considerably more inherent variation than the population in Figure 1A. In reality, most biological data do not conform to a perfect bell-shaped curve, and, in some cases, they may profoundly deviate from this ideal.

Nevertheless, in many instances, the distribution of various types of data can be roughly approximated by a normal distribution. The vertical red lines in Figure 1A and 1B indicate one SD to either side of the mean. From this, we can see that the population in Figure 1A has a SD of 20, whereas the population in Figure 1B has a SD of 50. SD to either side of the mean. Often we can never really know the true mean or SD of a population because we cannot usually observe the entire population. Instead, we must use a sample to make an educated guess. In the case of experimental laboratory science, there is often no limit to the number of animals that we could theoretically test or the number of experimental repeats that we could perform.

It is important to note that increasing our sample size will not predictably increase or decrease the amount of variation that we are ultimately likely to record. What can be stated is that a larger sample size will tend to give a sample SD that is a more accurate estimate of the population SD. In particular, these measures usually3 tell you nothing about the shape of the underlying distribution. The data from both panels have nearly identical means and SDs, but the data from panel A are clearly bimodal, whereas the data from Panel B conform more to a normal distribution4. Alternatively, a somewhat more concise depiction, which still gets the basic point across, is shown by the individual data plot in Panel C. Two distributions with similar means and SDs.

Note that both populations have nearly identical means and SDs, despite major differences in the population distributions. Before you become distressed about what the title of this section actually means, let’s be clear about something. Statistics, in its broadest sense, effectively does two things for us—more or less simultaneously. Statistics provides us with useful quantitative descriptors for summarizing our data. This includes fairly simple stuff such as means and proportions. In the preceding section we discussed the importance of SD as a measure for describing natural variation within an entire population of worms. We also touched upon the idea that we can calculate statistics, such as SD, from a sample that is drawn from a larger population.