Much naturally occurring data falls in a normal distribution, shaped like a bell, called a bell curve or normal curve. For instance, the number of headaches occurring would vary from very low to very high, with the bulk of the measures falling in the middle. In a bell curve, the mean and the mode both fall in the center. When testing an hypothesis, the population variance is used; this is the measure of how much the experimental group varies from the mean.
The amount of spread in a set of data is known as its standard deviation. On a normal distribution, a large standard deviation means a wide bell curve; a small standard deviation signifies a narrow bell curve. Comparisons of the variance of the subset that received the treatment versus the variance of the control group will be conducted.
To see if the hypothesis is validated or if the null hypothesis is more likely, the standard deviation, or how much the data varies, must be calculated. The subset, the incidence of headaches in those who took medication, is measured against the incidence of those who did not. A mathematical test is conducted to see how many standard variations away from the mean each data set lies. The empirical rule states that 68% of the scores will lie within one standard deviation of the mean, 95% within two standard deviations and over 99% will lie within three.
The likelihood that something will occur by chance rather than because of treatment is calculated by statistical tests. A commonly used test for small collections of data, less than 30 measures, is the student's t-test. A variety of other statistical tests exist, but the common goal is to determine how much samples vary from the mean. Statistical tests show what the probability is of a particular outcome occurring by chance. Usually a figure of less than 10% likelihood by chance is chosen. Test results that do not fall under 10% would be in the rejection region.