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Statistical Hypothesis Testing

There are two general types of hypothesis testing procedures:

  1. A result is compared to a known population average. An example would be the rate of cancer in people exposed to a certain hazardous chemical in their line of work compared to the national average.
  2. Samples from two or more treatment populations are compared different dosage levels of a drug, or a drug, a non-pharmacological intervention, and no treatment.

In quantitative reasoning procedures, HYPOTHESIS TESTING is the comparison of sample results with some known or hypothesized population parameters.

TYPES OF HYPOTHESES: We all do hypothesis testing every day of our lives as we navigate through various situations where we have to make educated guesses about what is going on with people and situations at work and socially/interpersonally. Early I used the example of my introductory psychology students trying to spin hypotheses about why I was acting like such a grouch. The hypothesis testing that we do in research should be somewhat more rigorous and organized. First, we make a general statement about the relationship between the independent and dependent variables or the magnitude of the observation (the size of the effect of interest.) This is our conceptual hypothesis. Example: I am doing research to find out if doing 1 hour of moderate aerobic exercise 4 times a week as opposed to no regular aerobic exercise is related to longer lifespan among women over the age of 65. What is my independent variable? Exercise or no exercise. What is my dependent variable? Years of life. Try this one: You are doing a study of the effects of a vitamin supplement on energy levels of men who are recovering from heart bypass surgery. What is your independent variable? What is your dependent variable? We use our conceptual hypothesis as a basis for a statistical hypothesis. This is a mathematical statement that can be shown to be supported or not supported through statistical procedures. In my study, there should be a difference in the mean lifespan of the women who exercise and the women who don't. Specifically, the women who do exercise should having a higher mean lifespan than those who do not. What is the statistical hypothesis in your study (the vitamin supplement study?) It is customary for researchers to state first the hypothesis in terms of NO SIGNIFICANT RESULTS. It is a way of keeping one's hopes for exciting results in check so that experimenter expectations don't unduly influence the results. This is called the NULL hypothesis.

The Null Hypothesis

To put this into statistical language, the null hypothesis is that the mean of the treatment group has approximately the same value as the mean of the control group. This is how it looks in statistical language:
Directional hypothesis:
The direction of the relationship difference between the two populations is explicitly stated.It is part of the ethics of doing research.
So one needs to determine what the null and alternative hypotheses will be (conceptually and statistically) and then determine if the alternative will be stated directionally or non-directionally.
Whether one chooses a directional or non-directional expression will depend on the following:
- Is there strong evidence before beginning that the difference will be in a particular (positive or negative direction)? Just hoping it will be in a particular direction doesn't mean one should use a directional alternative hypothesis.
-If all that can be reasonably suspected is that the two population means will be different, it is more prudent to use a non-directional alternative hypothesis. It is tougher to obtain significant results under these conditions. This makes for more reliable results. 
Every time you and your friend get together and work on your latest exciting module, you go out for dinner together afterwards and discuss all the fascinating things that you have learned. You reject the null hypothesis, take the black eye, and find someone else with whom to review quantitative reasoning over dinner.

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Statistical Hypothesis Testing

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