Alpha levels are controlled by the researcher and are related to . You get an alpha level by subtracting your confidence level from 100%. For example, if you want to be 98 percent confident in your research, the alpha level would be 2% (100% – 98%). When you run the hypothesis test, the test will give you a value for p. Compare that value to your chosen alpha level. For example, let’s say you chose an alpha level of 5% (0.05). If the results from the test give you:
The p value is just one piece of information you can use when deciding if your is true or not. You can use other values given by your test to help you decide. For example, if you run an, you’ll get a p value, an f-critical value and a .
In the above image, the results from the show a large p value (.244531, or 24.4531%), so you would not reject the null. However, there’s also another way you can decide: compare your f-value with your f-critical value. If the f-critical value is smaller than the f-value, you should reject the null hypothesis. In this particular test, the p value and the f-critical values are both very large so you do not have enough evidence to reject the null.
The null hypothesis can be thought of as a nullifiable hypothesis. That means you can nullify it, or reject it. What happens if you reject the null hypothesis? It gets replaced with the which is what you think might actually be true about a situation. For example, let’s say you think that a certain drug might be responsible for a spate of recent heart attacks. The drug company thinks the drug is safe. The null hypothesis is always the accepted hypothesis; in this example, the drug is on the market, people are using it, and it’s generally accepted to be safe. Therefore, the null hypothesis is that the drug is safe. The alternate hypothesis — the one you want to replace the null hypothesis, is that the drug isn’t safe. Rejecting the null hypothesis in this case means that you will have to prove that the drug is not safe.
Basically, you reject the null hypothesis when your test value falls into the . There are four main ways you’ll compute test values and either support or reject your null hypothesis. Which method you choose depends mainly on if you have a proportion or a .
Example question:The average wait time to see an E.R. doctor is said to be 150 minutes. You think the wait time is actually less. You take a of 30 people and find their average wait is 148 minutes with a standard deviation of 5 minutes. Assume the distribution is normal. Find the p value for this test.
In many statistical tests, you’ll want to either reject or support the . For elementary statistics students, the term can be a tricky term to grasp, partly because the name “null hypothesis” doesn’t make it clear about what the null hypothesis actually is!
Graphically, the p value is the area in the tail of a . It’s calculated when you run hypothesis test and is the area to the right of the test statistic (if you’re running a two-tailed test, it’s the area to the left and to the right).
If you have a , or are asked to find a p-value, follow these instructions to support or reject the null hypothesis. This method works if you are given an and if you are not given an alpha level. If you are given a , just subtract from 1 to get the alpha level. See: .
In general, there are three possible alternative hypotheses and rejection regions for the one-sample -test:For our two-tailed -test, the critical value is 1-/2, = 1.9673, where = 0.05 and = 326.
Find the . We’re dealing with a population, so the critical value is a .
Use the following formula to find the .
The absolute value of the test statistic for our example, 12.62059, is greater than the critical value of 1.9673, so we reject the null hypothesis and conclude that the two population meansare different at the 0.05 significance level.
NOTE: Excel can actually find the value of the CHI-SQUARE. To find this value first select an empty cell on the spread sheet then in the formula bar type "=CHIINV(D12,2)." D12 designates the p-Value found previously and 2 is the degrees of freedom (number of rows minus one). The CHI-SQUARE value in this case is 12.07121. If we refer to the CHI-SQUARE table we will see that the cut off is 4.60517 since 12.07121>4.60517 we reject the null. The following screen shot shows you how to the CHI-SQUARE value.
A researcher is interested in whether either people's hair color or their taste in music is a factor in cholesterol. Three people with each possible combination were tested for cholesterol. The results are shown below. Use a level of significance of 0 .05 to test researcher's hypothesis.
Find the by looking up your answer from step 3 in the . To get the p-value, subtract the area from 1. For example, if your area is .990 then your p-value is 1-.9950 = 0.005. Note: for a two-tailed test, you’ll need to halve this amount to get the p-value in one tail.
We have seen a method of testing for the difference between several means where three are two treatments. On the other hand, the example given showed only one value per cell. As we know, it is better to find a large sample, since the power of the test will be better. We can do this, but we must make sure that each cell is represented an equal number of times. This will only work if there is no interaction between the factors. Hence we will first test to see if there is an interaction. If there is an interaction, do not proceed. If there is not evidence for an interaction, then we can proceed as before. The next example illustrates this.