Write out the hypothesis your data is supposed to support or disprove. The nature of the hypothesis will tell you whether to use a one-tailed or two-tailed statistical analysis to calculate statistical significance. A one-tailed calculation is used when trying to answer a question that focuses on one variable, such as, "Are women more likely than men to score high on statistics exams?" A two-tailed approach should be used when trying to examine open-ended hypotheses such as, "Are there significant differences between men's scores and women's scores on statistics exams?"

Organize your data. Make two columns on a piece of paper. Put all the results that agree with one outcome of the experiment in one column and all the results agree with the other outcome in another column. Using the statistics test example, for a one-tailed test you might make one column where you put a tally mark for each female student who scored higher on a test and one column to keep track of each male student who scored higher. For a two-tailed calculation, you would put how much higher each female high score was in one column, and how much higher each male high score was in another column.

Calculate the probability of achieving these results by chance. For a one-tailed test, you do this using the calculation for binomial distribution. Use a graphing or statistics calculator to do this calculation. You need to define one outcome as a success (for example, the number of women scoring higher) and plug this number into the calculator along with the number of trials (how many students were in the class.) For a two-tailed test, double the result you get when you do this calculation.

Look up critical values for the number of trials and type of test in a statistics table. Compare this number to the value you got in Step 3. If your statistic is higher than the statistic in the table, the finding is statistically significant. If not, the finding is statistically insignificant.