Inferential Statistical Procedures
There are a wide variety of statistical tests available to the modern health sciences researcher. These tests allow the researcher to compare the mean of a sample of observations that he or she has collected to the general population to determine if a SIGNIFICANT difference exists between the two. From this difference we INFER that our treatment or manipulation actually changed something, that is why we call these calculations inferential statistical procedures. Significance in inferential statistics does not mean IMPORTANT; it means "unlikely to be due to chance." This is of interest to the researcher if he or she has manipulated the sample in some way, to treat a disease or improve longevity, for example and is comparing the result to what is typical or expected. If the number of days it takes a person to recover after the new treatment is different from the number of days to recover using conventional methods, and that difference is large enough, it will be statistically significant. This result may indeed turn out to be important, but this is a different issue. If the significant difference was the result of bias, then the results are essentially meaningless.
STATISTICAL INFERENCE involves using procedures based on samples or bits of information used to make statements about some broader set of circumstances. What is a FACT? It is something we know through the direct evidence of our senses. When we do basically descriptive statistics, we are directly counting and measuring. It is a fact that the mean height of a particular class of sixth grade boys is (let's say) 4'11" and it's a fact that the standard deviation of the heights in that class is 2.5". We can verify this directly.
How does an INFERENCE differ from a fact? In making an inference we are assuming that something is true, we draw a conclusion based on evidence or signs that it has occurred or it is true, not on a direct observation. To differentiate with an example from "real life": I arrive at one of my live, real-time Introductory Psychology classes looking very grim. I am carrying a stack of tests with me. What kinds of conclusion are the students going to draw? Now, can they be absolutely sure about their conclusions? How about an alternative hypothesis? For example, on my way to school I rear-ended someone, ruined my little car and my insurance rates. Or maybe I just had a big fight with the man I am dating. It could be that the tests were very poor, or it could be that I am having a hard time in some other aspect of my life. There is no way to tell until we move from the inferential to the descriptive. And of course, I may not actually tell my students what is going on, if it isn't the test that is bumming me out. So, how can they really know for certain?
Inductive reasoning involves putting our evidence together to support a claim about a phenomenon. Inductive reasoning is evaluated in terms of its strength. One can provide a strong inductive argument and still be wrong (this is not true of what we call deductive reasoning, but that is a story for a different day).