The null hypothesis and the research hypothesis

We don’t know, unfortunately, the population parameters of variables we wish to study. If we did, there would be no need to test samples. What we’re doing, when we measure samples, is trying to infer to the population from our sample’s results.
Tests of significance are simply called statistical tests.

Commonly used test statistics include the t, the F, and the chi-square. The distributions of these tests aren’t exactly normal, but there are tables, neverltheless, for determining the critical areas under their curves and the probablilities that are associated with them.

There are four components to a statistical test: a null hypothesis, a research hypothesis, a test statistic (decision maker) and a rejection region.
The null hypothesis is a hypothesis about the population (from which we’ve drawn our sample) that asserts that sampling error explains the results. Our results are from sampling error, not the intervention.

We have two groups, one with an intervention, and one without. We test both of the groups and then compare the results. If the differences are small then it is possible that the two groups are now representing different populations. Our intervention caused the difference, and it’s such a large, significant difference, that we have to reject the null hypothesis that the groups are from the same population. We’re testing to see if they’re independent of one another.

These tests are often called tests of independence.

You don’t need two groups. You can be testing one sample to see if variables are associated. In this case, we’re asking, are these two variables from the same population? If they are not associated, if there’s an insignificant association, a low r, for example, then we say that the variables are not independent, they are from the same sample. We don’t reject the null.

The null hypothesis is saying that the two variables are from the same population.
We do that test and that test is how we determine if we can accept the alternative hypothesis, that which we call the research hypothesis.

The null is that two variables are from the same population. If we accept this we’re saying the difference in the two v’s is due to chance.

The research hypothesis is that the two variables are from different populations.
When we reject a null we automatically accept the research hypothesis. The difference is not due to chance. Our theory about why the two variables are associated significantly is supported by the research.

The null hypothesis is that the mean of the first group is the same as the mean of the second group. So if the means differ significantly, we reject the mean and accept the research hypothesis that says that the two samples are from different populations.

What this distills down to is you doing a test, getting a result, and checking a table to see if that result is significant or not. Sometimes the result is the difference between two averages, you might be comparing the means of two different groups, using a t test for two variables, an F for three or more. Sometimes the result indicates how much two variables are associated with one another, how high or low the correlation, or r.

The table will say that the test statistic is < than or = to a particular number, and you will interpret the statistic based upon what you set your level of significance to be. So if you say that you want the odds of your results to be over 95% that you will have results that are significant, then the rejection statistic will be < or = to .05. that < or = finding is the likelihood that your results were due to chance.

So if the finding on the table is .11, then you would not reject the null. .11 is not in the rejection region of your curve.

But if it is .03, then you do reject the null. There is little likelihood that chance is responsible for your findings, only 3 times out of 100 will you get your result. It’s probably due to your intervention, or if you’re testing to see if there’s a relationship between variables, there’s reason to believe that they are associated, that it is not by chance, it is a real phenomenon in the world.