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

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.

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

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:
• 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.

## Formula

### Regression

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