# [Featured] P-value

hooodev·2023년 4월 18일
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## 머신러닝

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### In short…

Index which indicates the probability of the null hypothesis is valid. the higher the more likely the null hypothesis.

### How to get?

first we need test statistics through statistical test.

### What are statistical test and test statistics?

✅ test statistics is the index describing the difference between the variables and the null hypothesis. if the difference is big enough then we can assume there is meaningful relationship in between.

✅ It is an activity where we set null hypothesis and calculate the test statistics. so more inclusive concept.

✅ In null hypothesis, we assume that there are no relationships between the variables.

There are many methods depending on the types of variables. the most well known one is t-test. but in this chapter we will not dig into deeper into that.

### Ok so back to where we were… how we can get p-value using test statistics?

Refer the table which we can get p-value using test statistics.

### What does exactly p-value mean?

The p-value tells you how often you would expect to see a test statistic as extreme or more extreme than the one calculated by your statistical test if the null hypothesis of that test was true. So in short, how probable the null hypothesis is true?

### So how small p-value is enough for rejecting the null hypothesis?

This issue is called statistical significance. It depends on the field of the test. but usually we use the value 0.05. this threshold is called alpha value.

### Caution!

✅ p-value is usually higher in reality. especially when sample size is not big enough.

✅ p-value only tells about the null hypothesis. small p-value tells that the the null hypothesis is less probable. It doesn’t necessarily tell that the alternative hypothesis is valid enough.

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