Research methods: Know when your numbers are significant

http://www.nature.com/nature/journal/v492/n7428/fig_tab/492180a_T1.html  

When N is only 2 or 3, it would be more transparent to just plot the independent data points, and let the readers interpret the data for themselves, rather than showing possibly misleading P values or error bars and drawing statistical inferences. 

All experimental biologists and all those who review their papers should know what sort of sampling errors are to be expected in common experiments, such as determining the percentages of live and dead cells or counting the number of colonies on a plate or cells in a microscope field. Otherwise, they will not be able to judge their own data critically, or anyone else's.   Table 1: Statistics glossary: Some common statistical concepts and their uses in analysing experimental results.

Term	Meaning	Common uses
N, number of independent samples; t, the t-statistic; p, probability.
Standard deviation (s.d.)	The typical difference between each value and the mean value.	Describing how broadly the sample values are distributed.  s.d. = √−(∑ (x − mean)2/(N − 1))
Standard error of the mean (s.e.m.)	An estimate of how variable the means will be if the experiment is repeated multiple times.	Inferring where the population mean is likely to lie, or whether sets of samples are likely to come from the same population.  s.e.m. = s.d./√−N
Confidence interval (CI; 95%)	With 95% confidence, the population mean will lie in this interval.	To infer where the population mean lies, and to compare two populations.  CI = mean ± s.e.m. × t(N−1)
Independent data	Values from separate experiments of the same type that are not linked.	Testing hypotheses about the population.
Replicate data	Values from experiments where everything is linked as much as possible.	Serves as an internal check on performance of an experiment.
Sampling error	Variation caused by sampling part of a population rather than measuring the whole population.	Can reveal bias in the data (if it is too small) or problems with conduct of the experiment (if it is too big). In binomial distributions (such as live and dead cell counts) the expected s.d. is √−(N × p × (1 − p)); in Poisson dist