# Statistics - (t-value|t-statistic)

### Table of Contents

## 1 - About

The (t-value|t-statistic) is a test statistic.

In NHST, it is essentially a ratio of what we observed relative to what we would expect just due to chance.

<MATH> \begin{array}{rrl} \text{t-statistic} & = & \frac{\text{What we observed}}{\text{What we get due to chance}} \\ \end{array} </MATH>

Each t-value has corresponding p-value depending on the sample size.

If I get:

- a t-value of one, I know that:
- I didn't find much of anything at all.
- It's not going to be statistically significant.
- P is not going to be less than 0.05
- (because) what I observed is exactly what I would expect just due to chance.

- a high t-value, it will result:
- in a low p-value and a statistically significant result.

- a t-value of a least two or more, it's what I want to show that I've observed the slope twice as large as what I would have expected due to chance.

In order to have a p-value of below 0.05 (which is quite significant), a t-statistic of about 2 is needed.
At 16, the t-statistic is huge, it's **very, very** significant.

## 2 - Articles Related

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## 3 - Formula

### 3.1 - Mean

See t-statistic

### 3.2 - Regression

See t-statistic