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?
Inferential
statistical procedures are ways to make decisions about the population that have
a high probability of being correct.
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.
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 thetwo treatments are
really similar.
4
STEPS IN HYPOTHESIS TESTING
1.State
the hypotheses
Hom = a(null)
H1m ? 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 8-5(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
POWER
The power of a statistical test is the probability that the test will correctly reject a false null hypothesis.
Another related definition is that power is the probability of obtaining sample data in the critical region when the null hypothesis is false.
WAYS TO INCREASE POWER
1.Increase the alpha level (e.g. from .01 to .05).
Any factor that causes more of the treatment distribution to be in the critical region will increase power.
2.Changing from a two-tailed (non-directional) to a one-tailed test.
3.Increase the sample size (this reduces standard error).
4.Make sure that the treatment is strong enough (this may require pilot testing)
ASSUMPTIONS FOR HYPOTHESIS TESTS WITH Z-SCORES
1.Random sampling.
2. Independent observations.
Make sure there are no consistent, predictable relationships between observations. A random sample ensures that.
3.The value of s is unchanged by the treatment.
We assume that the samples we use have equal variances
4. The sampling distribution is normal.