Specifically, hypothesis testing requires two hypotheses: the null hypothesis (often written H0) and the alternative hypothesis (often written Ha or H1). The null hypothesis is a straw man. It is the theory that the researcher is attempting to falsify by experimentation. The alternative hypothesis is a statement of what the researcher believes to be the true state of affairs.
For instance, if a sociologist performs research to determine whether after-school programs reduce the likelihood that participants involved in violent crime, the appropriate null hypothesis is that such programs do not reduce the likelihood that participants involved in violent crime, whereas one alternative hypothesis might be that these programs do, in fact, reduce such crimes.
An educational researcher might want to determine whether preschool attendance increases test scores in at-risk children. That researcher's null hypothesis would be that preschool does not increase test scores, whereas the alternative hypothesis might suggest that it does. In practice, the null hypothesis involves the “equals” sign, whereas the alternative hypothesis employs some sort of inequality. Typically, two types of alternative hypotheses used: one-sided and two-sided.
Although the null hypothesis states the simple and equality that the researcher seeks to disprove, the one-sided alternative hypothesis gives the direction in which the true value differs from the hypothesized value. A one-sided alternative hypothesis can be right-tailed, indicating that the true value of the population parameter under consideration is greater than the value hypothesized in H0, or left-tailed, indicating that the true value is less than the hypothesized value.
For example, if a null hypothesis states that the true mean of a given population is, say, 5, then the corresponding right-tailed alternative hypothesis would be that the true mean is greater than 5, whereas the corresponding left-tailed hypothesis is that the true mean is less than 5. A two-tailed alternative hypothesis is different only in that it does not indicate direction (e.g., the true mean is not equal to 5). These hypotheses must be chosen before the data collected. If the researcher allows the data to influence the choice of hypotheses, then the test for statistical significance will lose accuracy.
Hypothesis tests rely on the calculation of a statistic from the observed data and the determination of the distribution of that statistic under the terms of the null hypothesis. Whereas in modern times, a multitude of software packages created to perform the calculations required for most hypotheses testing, they have not always been available, and they are not necessary to process. They simply programmed with the probability distributions of various test statistics under the user-inputted null hypothesis. Regardless of the details of how a test formed, and the means by which it executed, tests for significance allow a researcher to make a determination regarding statistical significance by means of a p value.
After setting the null and alternative hypotheses, collecting data, choosing the appropriate test, and calculating the appropriate test statistic(s), performing the hypothesis test returns a p value. The p value is a measure of statistical ...