**One-Tailed and Two-Tailed Significance Tests**
One important concept in significance testing is whether you use a one-tailed or two-tailed test of significance. The answer is that it depends on your hypothesis. When your research hypothesis states the direction of the difference or relationship, then you use a one-tailed probability. For example, a one-tailed test would be used to test these null hypotheses: Females will not score significantly higher than males on an IQ test. Blue collar workers are will not buy significantly more product than white collar workers. Superman is not significantly stronger than the average person. In each case, the null hypothesis (indirectly) predicts the direction of the difference. A two-tailed test would be used to test these null hypotheses: There will be no significant difference in IQ scores between males and females. There will be no significant difference in the amount of product purchased between blue collar and white collar workers. There is no significant difference in strength between Superman and the average person. The one-tailed probability is exactly half the value of the two-tailed probability.
There is a raging controversy (for about the last hundred years) on whether or not it is ever appropriate to use a one-tailed test. The rationale is that if you already know the direction of the difference, why bother doing any statistical tests. While it is generally safest to use a two-tailed tests, there are situations where a one-tailed test seems more appropriate. The bottom line is that it is the choice of the researcher whether to use one-tailed or two-tailed research questions.
**Procedure Used to Test for Significance**
Whenever we perform a significance test, it involves comparing a test value that we have calculated to some critical value for the statistic. It doesn't matter what type of statistic we are calculating (e.g., a t-statistic, a chi-square statistic, an F-statistic, etc.), the procedure to test for significance is the same.
1. Decide on the *critical alpha level* you will use (i.e., the error rate you are willing to accept).
2. Conduct the research.
3. Calculate the statistic.
4. Compare the statistic to a *critical value* obtained from a table.
If your statistic is higher than the *critical value* from the table:
Your finding is significant.
You reject the null hypothesis.
The probability is small that the difference or relationship happened by chance, and __p__ is less than the critical alpha level (p < α ).
If your statistic is lower than the *critical value* from the table:
Your finding is not significant.
You fail to reject the null hypothesis.
The probability is high that the difference or relationship happened by chance, and __p__ is greater than the critical alpha level (p > α ).
Modern computer software can calculate exact probabilities for most test statistics. If you have an exact probability from computer software, simply compare it to your critical alpha level. If the exact probability is less than the critical alpha level, your finding is significant, and if the exact probability is greater than your critical alpha level, your finding is not significant. Using a table is not necessary when you have the exact probability for a statistic.
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