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Introduction to Hypothesis Testing (As the size of the treatment effect…
Introduction to Hypothesis Testing
A hypothesis test is a statistical method that uses sample data to evaluate a hypothesis about a population.
A hypothesis test is typically used in the context of a research study
The goal of the hypothesis test is to determine whether the treatment has any effect on the individuals in the population
The Four Steps of a Hypothesis Test:
State the Hypothesis
Set the Criteria for a Decision
Collect Data and Compute Sample Statistics
Make a Decision
The alternative hypothesis states that there is a change, a difference, or a relationship for the general population.
The alpha level, or the level of significance, is a probability value that is used to define the concept of “very unlikely” in a hypothesis test.
The 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 null hypothesis states that in the general population there is no change, no difference, or no relationship.
The critical region is composed of the extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true. The boundaries for the critical region are determined by the alpha level. If sample data fall in the critical region, the null hypothesis is rejected.
Test Statistic: A statistic that summarizes the sample data in a hypothesis test. The test statistic is used to determine whether or not the data are in the critical region.
A Type I error occurs when a researcher rejects a null hypothesis that is actually true. In a typical research situation, a Type I error means the researcher concludes that a treatment does have an effect when in fact it has no effect.
A Type II error occurs when a researcher fails to reject a null hypothesis that is really false. In a typical research situation, a Type II error means that the hypothesis test has failed to detect a real treatment effect.
A result is said to be 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.
The final decision in a hypothesis test is determined by the value obtained for the z-score statistic. If the z-score is large enough to be in the critical region, we reject the null hypothesis and conclude that there is a significant treatment effect.
In a directional hypothesis test, or a one-tailed test, the statistical hypotheses specify either an increase or a decrease in the population mean. That is, they make a statement about the direction of the effect.
A measure of 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.
Cohen's d : A standard measure of effect size computed by dividing the sample mean difference by the sample standard deviation.
The 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.
As the size of the treatment effect increases, statistical power increases. Also, power is influenced by several factors that can be controlled by the experimenter:
Increasing the alpha level increases power.
A one-tailed test has greater power than a two-tailed test.
A large sample results in more power than a small sample.
