Inferential Statistics

Now let’s continue with the logic of inferential statistics, what we started in class on June 7. It is always possible that chance is responsible for our findings. You might remember that if we take random samples, then they are going to differ because of chance. But if we’re taking them from the same population, the differences will be small.

So if I take random samples off of a list of social workers who are members of NASW, then compare them for certain attitudes, it is likely the attitudes will be different, but if we’re taking large samples, the differences will be small. These people are really from the same population.

But if my results are really different, if the attitudes vary greatly, then we might wonder if the samples came from different populations. The differences in the samples might be attributed to training, for example.

In the same way, if we find ANY large differences in samples that we’re comparing, the differences are less likely to be by chance. They are therefore significant. If we intervened in a sample in some way, perhaps by education or some other intervention, and the outcomes differ largely, we have reason to believe that what we did caused the change in the sample that got the intervention. Now we say that THAT sample no represents a different population, the population of people who have had the intervention.


That’s what most tests of significance are seeking to find. Is the sample from an entirely different population? And why. We hope it’s because of something we did.
The question tends to be, how big a difference does it take to say that the outcome isn’t by chance, rather is because of what we did? Or what we suspected?

If you’re testing a group to see if they went to work within the first six months of their child’s life, you might also check out what kinds of jobs they’re hoping to get, or how much education they have. A hypothesis might be that women who go back to work in the first six months have prospects of better jobs because they had more education.

If this is true, if your sample shows that there is this strong likelihood, then we say that these women come from a different population from the ones who did not go back to work, a better educated population.

If there’s only a small difference in the two groups, the one that went back to work and the one that didn’t, then we say that small difference was due to chance. The groups are too alike.

The test will tell us that there is only a .05 or less chance that the relationship we found is due to chance. Then we’ll say, must be a significant relationship, here.