Nondirectional Hypotheses

A nondirectional hypothesis is a type of alternative hypothesis used in statistical significance testing. For a research question, two rival hypotheses are formed. The null hypothesis states that there is no difference between the variables being compared or that any difference that does exist can be explained by chance. The alternative hypothesis states that an observed difference is likely to be genuine and not likely to have occurred by chance alone. Sometimes called a two-tailed test, a test of a nondirectional alternative hypothesis does not state the direction of the difference, it indicates only that a difference exists. In contrast, a directional alternative hypothesis specifies the direction of the tested relationship, stating that one variable is predicted to be larger or smaller than null value, but not both. Choosing a nondirectional or directional alternative hypothesis is a basic step in conducting a significance test and should be based on the research question and prior study in the area. The designation of a study's hypotheses should be made prior to analysis of data and should not change once analysis has been implemented.

For example, in a study examining the effectiveness of a learning strategies intervention, a treatment group and a control group of students are compared. The null hypothesis states that there is no difference in mean scores between the two groups. The nondirectional alternative hypothesis states that there is a difference between the mean scores of two groups but does not specify which group is expected to be larger or smaller. In contrast, a directional alternative hypothesis might state that the mean of the treatment group will be larger than the mean of the control group. The null and the nondirectional alternative hypothesis could be stated as follows:

A common application of nondirectional hypothesis testing involves conducting a t test and comparing the means of two groups. After calculating the t statistic, one can determine the critical value of t that designates the null hypothesis rejection region for a nondirectional or two-tailed test of significance. This critical value will depend on the degrees of freedom in the sample and the desired probability level, which is usually .05. The rejection region will be represented on both sides of the probability curve because a nondirectional hypothesis is sensitive to a larger or smaller effect.

Figure 1 shows a distribution in which at the 95% confidence level, the solid regions at the top and bottom of the distribution represent 2.5% accumulated probability in each tail. If the calculated value for t exceeds the critical value at either tail of the distribution, than the null hypothesis can be rejected. [Page 910]

Figure 1 Nondirectional t Test with df = 30

Note: Alpha = 0.05, critical value = 2.0423.

In contrast, the rejection region of a directional alternative hypothesis, or one-tailed test, would be represented on only one side of the distribution, because the hypothesis would choose a smaller or larger effect, but not both. In this instance, the critical value for t will be smaller because all 5% probability will be represented on one tail.

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