Why reject null hypothesis

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. Note that the P -value for a two-tailed test is always two times the P -value for either of the one-tailed tests.

Now that we have reviewed the critical value and P -value approach procedures for each of three possible hypotheses, let's look at three new examples — one of a right-tailed test, one of a left-tailed test, and one of a two-tailed test.

The good news is that, whenever possible, we will take advantage of the test statistics and P -values reported in statistical software, such as Minitab, to conduct our hypothesis tests in this course.

Breadcrumb Home reviews statistical concepts hypothesis testing p value approach. Specifically, the four steps involved in using the P -value approach to conducting any hypothesis test are: Specify the null and alternative hypotheses. If an alternative hypothesis has a direction and this is how you want to test it , the hypothesis is one-tailed. That is, it predicts direction of the effect. If the alternative hypothesis has stated that the effect was expected to be negative, this is also a one-tailed hypothesis.

Alternatively, a two-tailed prediction means that we do not make a choice over the direction that the effect of the experiment takes. Rather, it simply implies that the effect could be negative or positive. If Sarah had made a two-tailed prediction, the alternative hypothesis might have been:. In other words, we simply take out the word "positive", which implies the direction of our effect. In our example, making a two-tailed prediction may seem strange. After all, it would be logical to expect that "extra" tuition going to seminar classes as well as lectures would either have a positive effect on students' performance or no effect at all, but certainly not a negative effect.

However, this is just our opinion and hope and certainly does not mean that we will get the effect we expect. Generally speaking, making a one-tail prediction i. Notable exceptions to this rule are when there is only one possible way in which a change could occur.

That is, a protein might be "dormant" and the stimulus you are using can only possibly "wake it up" i. In addition, for some statistical tests, one-tailed tests are not possible.

If our statistical analysis shows that the significance level is below the cut-off value we have set e. Alternatively, if the significance level is above the cut-off value, we fail to reject the null hypothesis and cannot accept the alternative hypothesis. You should note that you cannot accept the null hypothesis, but only find evidence against it.

Hypothesis Testing cont Hypothesis Testing The null and alternative hypothesis In order to undertake hypothesis testing you need to express your research hypothesis as a null and alternative hypothesis. Alternative Hypothesis H A : Undertaking seminar class has a positive effect on students' performance. As such, we can state: Null Hypotheses H 0 : The mean exam mark for the "seminar" and "lecture-only" teaching methods is the same in the population.

Alternative Hypothesis H A : The mean exam mark for the "seminar" and "lecture-only" teaching methods is not the same in the population. A null hypothesis is a type of hypothesis used in statistics that proposes that there is no difference between certain characteristics of a population or data-generating process.

For example, a gambler may be interested in whether a game of chance is fair. If it is fair, then the expected earnings per play come to 0 for both players. If the game is not fair, then the expected earnings are positive for one player and negative for the other. To test whether the game is fair, the gambler collects earnings data from many repetitions of the game, calculates the average earnings from these data, then tests the null hypothesis that the expected earnings are not different from zero.

If the average earnings from the sample data are sufficiently far from zero, then the gambler will reject the null hypothesis and conclude the alternative hypothesis—namely, that the expected earnings per play are different from zero. If the average earnings from the sample data are near zero, then the gambler will not reject the null hypothesis, concluding instead that the difference between the average from the data and 0 is explainable by chance alone.

The null hypothesis, also known as the conjecture, assumes that any kind of difference between the chosen characteristics that you see in a set of data is due to chance. For example, if the expected earnings for the gambling game are truly equal to 0, then any difference between the average earnings in the data and 0 is due to chance. Statistical hypotheses are tested using a four-step process.

The first step is for the analyst to state the two hypotheses so that only one can be right. The next step is to formulate an analysis plan, which outlines how the data will be evaluated. The third step is to carry out the plan and physically analyze the sample data. The fourth and final step is to analyze the results and either reject the null hypothesis or claim that the observed differences are explainable by chance alone.

Analysts look to reject the null hypothesis because doing so is a strong conclusion. This requires strong evidence in the form of an observed difference that is too large to be explained solely by chance. Failing to reject the null hypothesis—that the results are explainable by chance alone—is a weak conclusion because it allows that factors other than chance may be at work but may not be strong enough to be detectable by the statistical test used.

Analysts look to reject the null hypothesis to rule out chance alone as an explanation for the phenomena of interest. Here is a simple example. A school principal claims that students in her school score an average of 7 out of 10 in exams.

The null hypothesis is that the population mean is 7. To test this null hypothesis, we record marks of say 30 students sample from the entire student population of the school say and calculate the mean of that sample. We can then compare the calculated sample mean to the hypothesized population mean of 7. The null hypothesis here—that the population mean is 7. Assume that a mutual fund has been in existence for 20 years.

We take a random sample of annual returns of the mutual fund for, say, five years sample and calculate the sample mean. For the above examples, null hypotheses are:. For the purposes of determining whether to reject the null hypothesis, the null hypothesis abbreviated H 0 is assumed, for the sake of argument, to be true. Then the likely range of possible values of the calculated statistic e. Then, if the sample average is outside of this range, the null hypothesis is rejected.