It can be shown using statistical software that the P -value is 0. The graph depicts this visually. The P -value, 0. Therefore, our initial assumption that the null hypothesis is true must be incorrect. That is, since the P -value, 0.
That is, the two-tailed test requires taking into account the possibility that the test statistic could fall into either tail and hence the name "two-tailed" test. The test statistic is a single number that summarizes the sample information. An example of a test statistic is the Z statistic computed as follows:. When the sample size is small, we will use t statistics just as we did when constructing confidence intervals for small samples. As we present each scenario, alternative test statistics are provided along with conditions for their appropriate use.
The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic e. The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance.
Each is discussed below. Notice that the rejection regions are in the upper, lower and both tails of the curves, respectively. The decision rules are written below each figure. The complete table of critical values of Z for upper, lower and two-tailed tests can be found in the table of Z values to the right in "Other Resources. Critical values of t for upper, lower and two-tailed tests can be found in the table of t values in "Other Resources.
Here we compute the test statistic by substituting the observed sample data into the test statistic identified in Step 2. The final conclusion is made by comparing the test statistic which is a summary of the information observed in the sample to the decision rule. The final conclusion will be either to reject the null hypothesis because the sample data are very unlikely if the null hypothesis is true or not to reject the null hypothesis because the sample data are not very unlikely.
If the null hypothesis is rejected, then an exact significance level is computed to describe the likelihood of observing the sample data assuming that the null hypothesis is true.
The exact level of significance is called the p-value and it will be less than the chosen level of significance if we reject H 0. Statistical computing packages provide exact p-values as part of their standard output for hypothesis tests. In fact, when using a statistical computing package, the steps outlined about can be abbreviated. The hypotheses step 1 should always be set up in advance of any analysis and the significance criterion should also be determined e. Statistical computing packages will produce the test statistic usually reporting the test statistic as t and a p-value.
We now use the five-step procedure to test the research hypothesis that the mean weight in men in is more than pounds. The research hypothesis is that weights have increased, and therefore an upper tailed test is used. We now substitute the sample data into the formula for the test statistic identified in Step 2.
We reject H 0 because 2. Because we rejected the null hypothesis, we now approximate the p-value which is the likelihood of observing the sample data if the null hypothesis is true. An alternative definition of the p-value is the smallest level of significance where we can still reject H 0.
Because 2. Using the table of critical values for upper tailed tests, we can approximate the p-value. This is the p-value. A statistical computing package would produce a more precise p-value which would be in between 0. In all tests of hypothesis, there are two types of errors that can be committed. The first is called a Type I error and refers to the situation where we incorrectly reject H 0 when in fact it is true.
This is also called a false positive result as we incorrectly conclude that the research hypothesis is true when in fact it is not. In fact, you will likely have trouble keeping your job as a conversion rate optimization specialist if you frequently allow tests to reach statistical significance for an effect in the negative direction sequential testing with a futility boundary can help prevent that. When a two-sided hypothesis is used the respective p-value should also be two-sided or a two-tailed test as it is sometimes called.
If a confidence interval is used to support a two-sided claim it should also be two-sided. Like this glossary entry?
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