Given a 05 which of the following is true

These numbers can give a false sense of security. In the ideal world, we would be able to define a "perfectly" random sample, the most appropriate test and one definitive conclusion. We simply cannot. What we can do is try to optimise all stages of our research to minimise sources of uncertainty. When presenting P values some groups find it helpful to use the asterisk rating system as well as quoting the P value:. The asterisk system avoids the woolly term "significant".

Please note, however, that many statisticians do not like the asterisk rating system when it is used without showing P values. As a rule of thumb, if you can quote an exact P value then do. The probability of a type I error, if the null hypothesis is true, is equal to the significance level. The probability of a type II error is much more complicated to calculate. We can reduce the risk of a type I error by using a lower significance level. The best way to reduce the risk of a type II error is by increasing the sample size.

In theory, we could also increase the significance level, but doing so would increase the likelihood of a type I error at the same time. We discuss these ideas further in a later module. In the long run, a fair coin lands heads up half of the time. For this reason, a weighted coin is not fair. We conducted a simulation in which each sample consists of 40 flips of a fair coin.

Here is a simulated sampling distribution for the proportion of heads in 2, samples. Results ranged from 0. In general, if the null hypothesis is true, the significance level gives the probability of making a type I error. This is a problem! Moore in Basic Practice of Statistics 4th ed. Freeman, :. This is an example of a probable type I error. So the conclusion that this one type of cancer is related to cell phone use is probably just a result of random chance and not an indication of an association.

Click here to see a fun cartoon that illustrates this same idea. Telepathy is the ability to read minds. Researchers used Zener cards in the early s for experimental research into telepathy. This is repeated 40 times, and the proportion of correct responses is recorded.

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. When we run a test of hypothesis and decide to reject H 0 e.

The different conclusions are summarized in the table below. Note that we will never know whether the null hypothesis is really true or false i. Table - Conclusions in Test of Hypothesis. Most investigators are very comfortable with this and are confident when rejecting H 0 that the research hypothesis is true as it is the more likely scenario when we reject H 0.

When we run a test of hypothesis and decide not to reject H 0 e. When we do not reject H 0 , it may be very likely that we are committing a Type II error i. Therefore, when tests are run and the null hypothesis is not rejected we often make a weak concluding statement allowing for the possibility that we might be committing a Type II error.

If we do not reject H 0 , we conclude that we do not have significant evidence to show that H 1 is true. We do not conclude that H 0 is true. All Rights Reserved. Date last modified: November 6, Wayne W. Contents All Modules.

Z score Table t score Table. Step 1. Step 2. Select the appropriate test statistic. 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.