Directional Research Hypothesis
DIRECTIONAL RESEARCH HYPOTHESIS
Let’s consider a different situation—one involving a different alternative or research hypothesis. In this instance, let’s assume that we expect to discover that rural residents have higher religious participation scores than urban residents. Since we’re now hypothesizing (in the form of the research or alternative hypothesis) that the rural residents will have higher religious participation scores than the urban residents, we are specifying the direction of the expected difference. Therefore, we’re relying on a directional research or alternative hypothesis. As it turns out, the selection of a directional alternative or research hypothesis (as opposed to a non-directional one), results in a few changes in how we approach the test. These changes can be summarized as follows:
• The null hypothesis changes slightly. Instead of the null being a statement that we expect the two means to be equal, the null is now a statement that either the two means are equal or the mean score of the rural residents is lower than the mean of the urban residents. Remember, our alternative hypothesis in this case is that we expect the mean score for rural residents to be higher than the mean score for urban residents. Therefore, the null hypothesis (if it truly stands in opposition to the research or alternative hypothesis) is that we expect the mean score of the rural residents to be equal to or lower than the mean score of the urban residents.
• We’re no longer looking for an extreme difference at either end of the distribution. Instead, we’re looking for a t value at only one end of the curve—a t value that falls in only one tail of the distribution. Remember: We’re asserting that we expect the mean score of the rural residents to be higher than the mean score of the urban residents. Assuming that we calculate the difference by subtracting the mean of the urban residents from the mean of the rural residents, we’ll be looking for a positive
Let’s consider a different situation—one involving a different alternative or research hypothesis. In this instance, let’s assume that we expect to discover that rural residents have higher religious participation scores than urban residents. Since we’re now hypothesizing (in the form of the research or alternative hypothesis) that the rural residents will have higher religious participation scores than the urban residents, we are specifying the direction of the expected difference. Therefore, we’re relying on a directional research or alternative hypothesis. As it turns out, the selection of a directional alternative or research hypothesis (as opposed to a non-directional one), results in a few changes in how we approach the test. These changes can be summarized as follows:
• The null hypothesis changes slightly. Instead of the null being a statement that we expect the two means to be equal, the null is now a statement that either the two means are equal or the mean score of the rural residents is lower than the mean of the urban residents. Remember, our alternative hypothesis in this case is that we expect the mean score for rural residents to be higher than the mean score for urban residents. Therefore, the null hypothesis (if it truly stands in opposition to the research or alternative hypothesis) is that we expect the mean score of the rural residents to be equal to or lower than the mean score of the urban residents.
• We’re no longer looking for an extreme difference at either end of the distribution. Instead, we’re looking for a t value at only one end of the curve—a t value that falls in only one tail of the distribution. Remember: We’re asserting that we expect the mean score of the rural residents to be higher than the mean score of the urban residents. Assuming that we calculate the difference by subtracting the mean of the urban residents from the mean of the rural residents, we’ll be looking for a positive
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