Hypothesis test
(INFERENTIAL PROCEDURE) Is a statistical method that uses sample data to evaluate a hypothesis about a population. (AFTER TREATMENT, THE INDIVIDUALS IN THE SAMPLE ARE MEASURED).
Null hypothesis (H0)
States that in general population there is no change, no difference, or no relationship. In the context of an experiment, H0 predicts that the independent variable (treatment) has no effect on the dependent variable (scores) for the population.
Alternative hypothesis H1
States that there is a change, a difference, or a relationship for the general population. In the context of an experiment, H1 predicts that the independent variable (treatment) does have an effect on the dependent variable.
Alpha level, or the level of significance
Is a probability value that is used to define the concept of "very unlikely" in a hypothesis.
Critical region
Is composed of the extreme sample (low probabilities if the null is true) values that are very unlikely to be obtained if the null hypothesis is true. The boundaries for the critical region are determined by the alpha level.
Type I error
WHENEVER A RESEARCHER REJECTS A TRUE NULL (H0); when a researcher rejects a true null hypothesis. In a typical research situation, means that the researcher concludes that a treatment does have an effect when, in fact, it has no effect.
Alpha level
For a hypothesis test is the probability that the test will lead to a Type I error. That is, the alpha level determines the probability of obtaining sample data in the critical region even though the null hypothesis is true. (the larger the alpha level fo
Type II error
WHENEVER A RESEARCHER FAILS TO REJECT A FALSE NULL (retain) HYPOTHESIS(H0); when a researcher fails to reject a false null hypothesis. . In a typical research situation, means that the hypothesis test has failed to detect a real treatment effect.
Significant, or statistically significant
If it is very unlikely to occur when the null hypothesis is true. That is, the result is sufficient to reject the null hypothesis. Thus, a treatment has a significant effect if the decision from the hypothesis test is to reject H0.
Directional hypothesis test, or a one-tailed test
The statistical hypothesis (H0 and H1) specify either an increase or a decrease in the population mean. That is, they make a statement about the direction of the effect.
Effect size
Is intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the sample (s) being used. (the larger the effect size, the greater the power)
Power
Of a statistical test is the probability that the test will correctly reject a false null hypothesis. That is, power is the probability that the test will identify a treatment effect if one really exists. (1-B)
Cohens d
measures the size of the mean difference in terms of the standard deviation. EFFECT SIZE
Not rejected (for p value)
> greater
Rejected (for p value)
< less
Beta
The probability of a type II error is represented by the symbol B, greek letter.
Relationship between alpha, size of critical region and risk of Type I error
when the alpha level increases, the critical region increases and type I error increases.
Factors of power
effect size (the larger the effect size, the greater the power), sample size (the larger the sample size, the greater the power), alpha level (the larger the alpha level for the test (.05 vs. .01) the greater the power), one tailed vs. two-tailed test (a
what is measured by the numerator of a z-score
actual difference between the sample (M) and the hypothesis (u).
what is measured by the denominator of a z-score
the average distance between M and u that would be expected if H0 was true.