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The "p" in p-value stands for probability. More specifically, it is the probability of making a mistake. The p-value is a number that is generated by the computer based on the data the researcher has inputted. The p-value is a number that can range anywhere from 0 to 1. After the p-value is calculated by the computer it is compared to alpha or the level of significance which, in the social sciences, is generally set to 0.05. If I ran an experiment and my p-value was calculated to be 0.06 what would that mean?

Question

The "p" in p-value stands for probability. More specifically, it is the probability of making a mistake. The p-value is a number that is generated by the computer based on the data the researcher has inputted. The p-value is a number that can range anywhere from 0 to 1. After the p-value is calculated by the computer it is compared to alpha or the level of significance which, in the social sciences, is generally set to 0.05. If I ran an experiment and my p-value was calculated to be 0.06 what would that mean?

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Step 1

Explanation:

The p-value is the probability of obtaining a value (statistic) of the test result as extreme as, or more extreme than, the value that has been obtained, assuming H0 to be true. So, the p-value is not the probability of making a mistake. It is just a probability of getting a certain result when H0 is true.

The level of significance or α is the probability of rejecting H0 when, in fact, H0 is true. Rejecting H0 when it is true is an error or mistake. So, the level of significance is the probability of making a mistake, specifically termed as the probability of Type I error.

Researchers, naturally, want to minimize the probability of this mistake. So, they fix it at some convenient value (0.05 is a very widely used such value), so that this error probability cannot exceed that amount.

Even when H0 is true, there is a small chance that the test results are really extreme.

For example, in a family of people with average height of 5 ft 7 in, there may be a person who is 7 ft tall; it is quite unlikely, but that does not mean it is impossible; we cannot just conclude that the 7 ft tall person does not belong to the family.

If we get such extreme results from a test, we reject the null hypothesis. In view of this example, we conclude that the very tall person does not belong to the said family, which is actually a wrong conclusion or an error. The level of significance helps to control such errors.

A level of significance of 0.05 means that, for an extreme value, we will wrongly reject H0 in not more than 5% cases. In other words, you set a test result value (critical value) beforehand, such that, the probability of getting a test result more extreme than the critical value would be only 0.05 or 5%, which is quite low. If in your test, you do get a value more extreme than the critical value you have set, then you reject H0 while keeping in mind that there is a 5% chance that you are making the wrong decision.

Ideally, you would think that one should set a value such that there can never be any error, that is, one should set a value such...

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Math

Statistics

Hypothesis Testing

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