How big a sample do you have to have to get a meaningful result. The power analysis will tell you whether your sample size is large enough to not reject the null hypothesis if it is true. According the Cartoon Guide to Statistics, the null hypothesis is usually that the observations are the result of purely chance. The guide also states that the alternative hypothesis is that there is a real effect---that the observations are the result of this real effect plus chance variation.
Find the Sample Size
State the null hypothesis and its alternative. An example hypothesis: that the 15 skulls that were dug up in the garden were dog skulls not cat skulls.
Figure out the size of the population being studied. The Census Bureau has many different population sizes available for download in xls format. For example, on October 22, 2009, 307,759,123 people are estimated to live in the United States.
Determine the confidence level desired. Most fields of expertise have their own standards of acceptable level of confidence with 95% the common one in use.
Figure out the confidence interval. A confidence interval is how sure that your answer falls between a range. For example, at a confidence level of 95% and a confidence interval of 5, you would need to sample 14 of the skulls to see if they were dog skulls.
Calculate the sample size. Use a statistical software package or online sample size calculator.