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Chapter 8:Introduction to Hypothesis Testing - Coggle Diagram
Chapter 8:Introduction to Hypothesis Testing
To differentiate between real, systematic patterns and random, chance occurrences, researchers rely on a statistical technique that is known as hypothesis testing.
A hypothesis test first determines the probability that the pattern could have been produced by chance alone.
If this probability is large enough, we conclude that the pattern can reasonably be explained by chance.
One of the fundamental techniques of inferential statistics.
Uses the limited information from a sample to reach a general conclusion about a population.
The hypothesis-testing procedure are as follows:
Before selecting sample, use the hypothesis to predict the characteristics that the sample should have.
Obtain a random sample from the population.
State a hypothesis about a population. Usually the hypothesis concerns the value of a population parameter.
Compare the obtained sample data with the prediction that was made from the hypothesis. If the sample mean is consistent with the prediction, we conclude that the hypothesis is reasonable. But if there is a big discrepancy between the data and the prediction, we decide that the hypothesis is wrong.
A hypothesis test helps researchers differentiate between real and random patterns in the data.
Hypothesis testing is a statistical procedure that allows researchers to use sample data to draw inferences about the population of interest.
The goal of the hypothesis test is to determine whether the treatment has any effect on the individuals in the population
The first and most important of the two hypotheses is called the null hypothesis.
States that there is no change, no effect, no difference—nothing happened, hence the name null.
Is identified by the symbol H0 (The H stands for hypothesis, and the zero subscript indicates that this is the zero-effect hypothesis.)
Null hypothesis states that the treatment has no effect
The alternative hypothesis states that there is a change, a difference, or a relationship for the general population. In the context of an experiment, predicts that the independent variable (treatment) does have an effect on the dependent variable.
Simply states that there will be some type of change.
Does not specify whether the effect will be increased or decreased tips.
The null hypothesis and the alternative hypothesis are mutually exclusive and exhaustive. They cannot both be true. The data will determine which one should be rejected
To formalize the decision process, we use the null hypothesis to predict the kind of sample mean that ought to be obtained.
The alpha (α) value is a small probability that is used to identify the low-probability samples.
The extremely unlikely values, as defined by the alpha level, make up what is called the critical region.
To determine the exact location for the boundaries that define the critical region, we use the alpha-level probability and the unit normal table.
There are two types of errors that can be committed.
A Type I error is defined as rejecting a true H0. This is a serious error because it results in falsely reporting a treatment effect. The risk of a Type I error is determined by the alpha level and therefore is under the experimenter’s control.
A Type II error is defined as the failure to reject a false H0. In this case, the experiment fails to detect an effect that actually occurred. The probability of a Type II error cannot be specified as a single value and depends in part on the size of the treatment effect. It is identified by the symbol that is (beta).
In addition to using a hypothesis test to evaluate the significance of a treatment effect, it is recommended that you also measure and report the effect size.
One measure of effect size is Cohen’s d, which is a standardized measure of the mean difference.
