Can you reject the null hypothesis

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. An important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity.

Whatever information that is against the stated null hypothesis is captured in the alternative hypothesis H 1. For the above examples, the alternative hypothesis would be:. In other words, the alternative hypothesis is a direct contradiction of the null hypothesis. As an example related to financial markets, assume Alice sees that her investment strategy produces higher average returns than simply buying and holding a stock. In these cases, the two considerations trade off against each other so that a weak result can be statistically significant if the sample is large enough and a strong relationship can be statistically significant even if the sample is small.

Table The columns of the table represent the three levels of relationship strength: weak, medium, and strong. The rows represent four sample sizes that can be considered small, medium, large, and extra large in the context of psychological research.

Thus each cell in the table represents a combination of relationship strength and sample size. If it contains the word No , then it would not be statistically significant for either. There is one cell where the decision for d and r would be different and another where it might be different depending on some additional considerations, which are discussed in Section If you keep this lesson in mind, you will often know whether a result is statistically significant based on the descriptive statistics alone.

It is extremely useful to be able to develop this kind of intuitive judgment. One reason is that it allows you to develop expectations about how your formal null hypothesis tests are going to come out, which in turn allows you to detect problems in your analyses. For example, if your sample relationship is strong and your sample is medium, then you would expect to reject the null hypothesis.

If for some reason your formal null hypothesis test indicates otherwise, then you need to double-check your computations and interpretations. A second reason is that the ability to make this kind of intuitive judgment is an indication that you understand the basic logic of this approach in addition to being able to do the computations. A statistically significant result is not necessarily a strong one. Even a very weak result can be statistically significant if it is based on a large enough sample.

The differences between women and men in mathematical problem solving and leadership ability are statistically significant. But the word significant can cause people to interpret these differences as strong and important—perhaps even important enough to influence the college courses they take or even who they vote for.

This is why it is important to distinguish between the statistical significance of a result and the practical significance of that result. Practical significance refers to the importance or usefulness of the result in some real-world context. Many sex differences are statistically significant—and may even be interesting for purely scientific reasons—but they are not practically significant.

Yet this effect still might not be strong enough to justify the time, effort, and other costs of putting it into practice—especially if easier and cheaper treatments that work almost as well already exist.

Although statistically significant, this result would be said to lack practical or clinical significance. In the background is a child working at a desk. I remember reading a big study that conclusively disproved it years ago. We should get inside! Lightning only kills about 45 Americans a year, so the chances of dying are only one in 7,, A formal approach to deciding between two interpretations of a statistical relationship in a sample.

The idea that there is no relationship in the population and that the relationship in the sample reflects only sampling error. The idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population.

When the relationship found in the sample is likely to have occurred by chance, the null hypothesis is not rejected. The probability that, if the null hypothesis were true, the result found in the sample would occur. How low the p value must be before the sample result is considered unlikely in null hypothesis testing. Skip to content Chapter Inferential Statistics. Explain the purpose of null hypothesis testing, including the role of sampling error.

Describe the basic logic of null hypothesis testing. Describe the role of relationship strength and sample size in determining statistical significance and make reasonable judgments about statistical significance based on these two factors. 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.