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Hypothesis tests

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QXL Stat Tools Tab > Hypothesis tests

Hypothesis

A hypothesis test allows us to draw conclusions about the population by using a sample. The first step of hypothesis testing is to formulate a hypothesis. There are two types of statistical hypotheses.

  • Null hypothesis, denoted by H0. It states that relationships that appear in observations result purely from random chance.

  • Alternative hypothesis, denoted by H1. It states that relationships that appear in observations result from some non-random cause.

Example #1

If we were interested in whether one supermarket is more or less expensive than another, the hypothesis would be:

H₀: Prices are the same.

H₁: Prices in two supermarkets are different.

Errors

The best way to find if a statistical hypothesis is true is to examine the entire population. However, the population is almost always impossible to obtain, which makes using a sample desirable.

Using a sample comes with error. Two types of errors can be made when running a hypothesis test.

  • Type I error. Occurs when we decide to reject a null hypothesis when it is true.

  • Type II error. Occurs when we fail to reject a null hypothesis when it is false.

Example #2

When someone is accused of a crime, we put them on trial to determine their innocence or guilt. In this classic case, the two possibilities are the defendant is not guilty (innocent of the crime) or the defendant is guilty. The hypothesis would be:

H₀: Defendant is not guilty.

H₁: Defendant is guilty.

A Type I error is when the person is truly innocent but the jury finds them guilty. A Type II error is when a person is truly guilty but the jury finds him/her innocent. The generally accepted position of society is that a Type I Error or putting an innocent person in jail is far worse than a Type II error or letting a guilty person go free.

To minimize the risk of making a Type I error, we set a point (Decision criteria) at which we can reject the null hypothesis. This point is also known as significance level or alpha level, and it is denoted by α. The default significance level in Quantum XL is 0.05, but it can be changed in the options dialog of each hypothesis test.

Result

The result of a hypothesis test is given by a p-Value, a probability of making a mistake if we accept the alternative hypothesis. If the p-Value is less than the decision criteria, we can reject the null hypothesis.

Example #3

The result of hypothesis test in Example #1 is p-Value = 0.038. Since it is less than the decision criteria (0.05), we can reject null hypothesis and conclude that prices in two supermarkets are different.

Tests

You can let Quantum XL run the most appropriate test for your data (AutoTest), ask Quantum XL to help you decide which test to run (Advisor Wizard), or run one of the following supported hypothesis tests: