# Hypothesis Testing

A basic fact about testing hypotheses is that a hypothesis may be rejected but that the hypothesis never can be unconditionally accepted until all possible evidence is evaluated.

In the case of sampled data, the information set cannot be complete. So if a test using such data does not reject a hypothesis, the conclusion is not necessarily that the hypothesis should be accepted.

The null hypothesis in an experiment is the hypothesis that the independent variable has no effect on the dependent variable. The null hypothesis is expressed as H0. This hypothesis is assumed to be true unless proven otherwise. The alternative to the null hypothesis is the hypothesis that the independent variable does have an effect on the dependent variable. This hypothesis is known as the alternative, research, or experimental hypothesis and is expressed as H1. This alternative hypothesis states that the relationship observed between the variables cannot be explained by chance alone.

There are two types of errors in evaluating hypotheses:

Type I error

This occurs when one rejects the null hypothesis and accepts the alternative, when in fact the null hypothesis is true.

Type II error

This occurs when one accepts the null hypothesis when in fact the null hypothesis is false.

Because their names are not very descriptive, these types of errors sometimes are confused. Some people jokingly define a Type III error to occur when one confuses Type I and Type II. To illustrate the difference, it is useful to consider a trial by jury in which the null hypothesis is that the defendant is innocent. If the jury convicts a truly innocent defendant, a Type I error has occurred. If, on the other hand, the jury declares a truly guilty defendant to be innocent, a Type II error has occurred.

Hypothesis testing involves the following steps:

• Formulate the null and alternative hypotheses.
• Choose the appropriate test.
• Choose a level of significance (alpha) – determine the rejection region.
• Gather the data and calculate the test statistic.
• Determine the probability of the observed value of the test statistic under the null hypothesis given the sampling distribution that applies to the chosen test.
• Compare the value of the test statistic to the rejection threshold.
• Based on the comparison, reject or do not reject the null hypothesis.
• Make the marketing research conclusion.

In order to analyze whether research results are statistically significant or simply by chance, a test of statistical significance can be run

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