HYPOTHESIS TESTING

Hypothesis: The Independent Variable (IV) will cause a difference in behavior (DV) between the conditions.

The experiment is conducted and descriptive statistics are calculated.  Suppose a difference between the two means is observed.

IS THIS DIFFERENCE THE RESULT OF SAMPLES COMING FROM DIFFERENT POPULATION DISTRIBUTIONS OF VALUES?

(In other words, is this a real difference?)

Using inferential statistics, we determine the probability that the samples come from the same population distribution (i.e., there is no real effect).

This possibility is represented by the Null Hypothesis (Ho).  THIS IS THE POSSIBILITY THAT WE ACTUALLY TEST.

If the probability is less than .05, Ho is rejected.  We conclude that a real difference exists. I.e., that the samples come from different population distributions.  All other possibilities are represented by the Alternative Hypothesis (H1).  This is similar to the research hypothesis.

INFERENTIAL STATISTICAL PROCEDURES

Allow us to answer questions such as:

Based on our sample, what would we expect to find if we could perform this study on the entire population?

Since we can't always know what the population would contain, the best we can do is to place an intelligent bet.

Inferential statistical procedures are ways to make decisions about the population that have a high probability of being correct.

Relations between samples and populations are most often described in terms of probability.

In experimental work:

·        We formulate a particular hypothesis

·        Select a sample

·        Obtain data

HOW ARE THE DATA INTERPRETED?

How do we know if they support or reject the hypothesis?

Such questions involve considerations of probability.

The conclusions are expressed in probabilistic terms.

For example,

Two methods for the treatment of a disease are under consideration.  Two groups of 20 patients suffering from the disease are selected.

Method A is applied to one group.

Method B is applied to the other group.

After a period of treatment, 16 patients in group A and 10 patients in group B show marked improvement.

How can we evaluate this difference? Can we say that treatment A is, in general, superior to treatment B?

We usually assume that no difference exists between the two treatments.  Then, we estimate the probability of obtaining by random sampling a difference equal to or greater than the one observed.

If this probability is small, the effect is real, and we may need to reject the original assumption (that the two treatments are similar).

If this probability is large, then the effect is not real, but the result of chance, and the  two treatments are really similar.

4 STEPS IN HYPOTHESIS TESTING

1.        State the hypotheses

      Ho          m = a        (null)

      H1          m ≠ a        (alternative)

2.      Set the criteria for a decision.  We need to establish criteria about how much of a difference one should expect due to sampling error

Figure 8-3  (p. 236)
The set of potential samples is divided into those that are likely to be obtained and those that are very unlikely if the null hypothesis is true.

Figure 8-4  (p. 238)
The critical region (very unlikely outcomes) for a = .05.

Figure 8-5  (p. 245)
The locations of the critical region boundaries for three different levels of significance: a = .05, a = .01, and a = .001.

3.      Collect sample data

4.      Evaluate the Ho