Null and Alternative Hypotheses

 The null hypothesis ( H0) refers to a given population parameter, such as a population mean of 100 on IQ. Imagine that we ask two groups of students to complete a standardized IQ test, and then we calculate the mean IQ score for each group. We observe that the mean IQ for Group A is 100 ( MA = 100), whereas the mean IQ for Group B is 115 ( MB = 115). Is a mean difference of 15 IQ points statistically significant or just due to chance? The null hypothesis predicts that H0: MA = MB. That is, the null hypothesis predicts no difference between groups. Remember that “null” also means “zero,” so we could also state the null hypothesis as H0: MA − MB = 0. When comparing groups, in general, the null hypothesis predicts that group means will not differ. When testing the strength of a relationship between two variables, such as the correlation between IQ scores and grade point average (GPA), in general, the null hypothesis is that the relationship between variable A and variable B is zero. By contrast, the alternative hypothesis ( H1) does predict a difference between two groups, or in the case of relationships, those two variables are significantly related. An alternative hypothesis can be directional ( H1: Group X has a higher mean score than Group Y) or nondirectional ( H1: Group X and Group Y will differ). In hypothesis testing, you either reject or fail to reject the null hypothesis. Note that this is not stating, “accept the null hypothesis as true.” By default, if you reject the null hypothesis, you accept the alternative hypothesis is true. However, if you do not reject the null hypothesis, you cannot accept the alternative hypothesis is true. You have simply failed to find statistical justification to reject the alternative hypothesis. Type I and Type II Errors If you commit a Type I error, this means that you have incorrectly rejected a true null hypothesis. You have incorrectly concluded that there is a significant difference between groups, or a significant relationship, where no such difference or relationship actually exists. Type I errors have real-world significance, such as concluding that an expensive new cancer drug works when actually it does not work, costing money and potentially endangering lives. Keep in mind that you will probably never know whether the null hypothesis is “true” or not, as we can only determine that our data fail to reject it. If you commit a Type II error, this means that you have not rejected a false null hypothesis when you should have rejected it. You have incorrectly concluded that no differences or no relationships exist when they actually do exist. Type II errors also have real-world significance, such as concluding that a new cancer drug does not work when it actually does work and could save lives. Your alpha level will affect the likelihood of making a Type I or a Type II error. If your alpha level is small (such as .01, less than 1 in 100 chance), you are less likely to reject the null hypothesis, so you are less likely to commit a Type I error. However, you are more likely to commit a Type II error. You can decrease the chances of committing a Type II error by increasing the alpha level (such as .10, less than 1 in 10 chance). However, you are now more likely to commit a Type I error. Since the chances of committing Type I and Type II errors are inversely proportional, you will have to decide which type of error is more grievous. You need to assess the risk associated with each type of error. Your research questions will help in this decision. In standard social sciences research, the alpha level is set to .05 (that is, a 1 in 20 chance of committing a Type I error). An alpha level of .05 is used throughout the remainder of this course.