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Introduction to Hypothesis Testing - Coggle Diagram
Introduction to Hypothesis Testing
It involves a series of logical steps that use sample data to test hypotheses about a population, usually in the context of assessing possible treatment effects in an experiment.
Hypothesis testing is a statistical procedure that allows researchers to use sample data to draw inferences about the population of interest.
Second, we use the hypothesis to describe what values we should expect for the sample mean, if the hypothesis is really true.
Next, we obtain a random sample from the population.
First, we state a hypothesis about a population.
Finally, we compare the obtained sample data with the prediction that was made from the hypothesis.
The Four Steps of a Hypothesis Test
Make a Decision
In general, the final decision is made by comparing our treated sample with the distribution of sample means that would be obtained for untreated samples.
Collect Data and Compute Sample Statistics
the raw data from the sample are summarized with the appropriate statistics
The comparison is accomplished by computing a z-score that describes exactly where the sample mean is located relative to the hypothesized population mean from Ho
the data are collected after the researcher has stated the hypotheses and established the criteria for a decision.
Set the Criteria for a Decision
To find the boundaries that separate the high-probability samples from the low-probability samples, we must define exactly what is meant by “low” probability and “high” probability.
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 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.
State the Hypotheses and state two opposing hypotheses.
The alternative hypothesis states that there is a change, a difference, or a relationship for the general population.
The null hypothesis states that the treatment has no effect.
Z-Score Statistic
Test statistic simply indicates that the sample data are converted into a single, specific statistic that is used to test hypotheses.
Make a hypothesis about the value of
μ
. This is the null hypothesis.
Plug the hypothesized value into the formula along with the other values (ingredients).
If the formula produces a z-score near zero (which is where z-scores are supposed to be), we conclude that the hypothesis was correct. On the other hand, if the formula produces an extreme value (a very unlikely result), we conclude that the hypothesis was wrong.
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 there is evidence for a treatment effect when in fact the treatment has no effect.
A Type II error occurs when a researcher fails to reject a null hypothesis that is in fact false. In a typical research situation, a Type II error means that the hypothesis test has failed to detect a real treatment effect.
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.
In a directional hypothesis test, or a one-tailed test, the statistical hypotheses Ho( and )Hi 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.
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.