# p-value of a coefficient from a regression

#### oahz

##### New Member
The t-stat value follows a two-tail symmetric t-distribution with mean and median of zero?

Am I correct so far?

If so, then how can you get a p-value > .5 if the t-stat is greater than 0?

What does a p-value of .89 mean? Wouldn't that mean the t-stat is way negative and is to the other end of the tail?

#### hlsmith

##### Omega Contributor
Not following, may help if you provide your example. The p-value is the probability of getting a value (parameter) that extreme given that there really exist not relationship. Are you talking about your t-statics or p-values? T-statistic is the difference over the standard error, which is the number of standard deviations the groups differs from the other group. So typically if it is around 2 standard deviation different in either direction, we say the probability is low for that extreme of a difference under the pretenses that the two groups are equal.

#### Dason

Have you learned about two-sided tests?

#### evelyn13

##### New Member
Oahz, I think you are confusing the relationship between the t-statistic and p-value.
I think visuals can help understand distributions and p-values, so to build on hlsmith answer, here are a few links:

Here is a video series that may help also: https://www.khanacademy.org/math/pr...sis-testing/v/hypothesis-testing-and-p-values

#### oahz

##### New Member
I think might have figured it out. Tell me if I'm correct.

My question was, how is the p-value for an estimated coefficient derived?

If you get a positive t-stat of, say t, and t corresponds to a probability, say p*, of randomly getting t or a value greater than t from the t-distribution, then the p-value is equal to 2p*.

Conversely,

If you get a negative t-stat of, say t, and t corresponds to a probability, say p*, of randomly getting t or a value less than t from the t-distribution, then the p-value is equal to 2P*.

Am I correct?

#### hlsmith

##### Omega Contributor
Are you examining a simple linear regression model? If you tell us about the model we can provide more and better information.

#### oahz

##### New Member
It is linear, but it there could be multiple explanatory variables.

#### hlsmith

##### Omega Contributor
You are testing whether the variable has a slope equal to zero.

It is taking the slope value (coefficient) for the variable and dividing it by the standard error (sampling variation) and that provides the t-statics. Can be negative or positive, just like the slope. Now it interprets the value based on the degrees of freedom using the t-distribution. If the t-statistic is large or small enough then it would have a low probability of occurring given that the slope is really zero (null hypothesis).

#### oahz

##### New Member
You are testing whether the variable has a slope equal to zero.

It is taking the slope value (coefficient) for the variable and dividing it by the standard error (sampling variation) and that provides the t-statics. Can be negative or positive, just like the slope. Now it interprets the value based on the degrees of freedom using the t-distribution. If the t-statistic is large or small enough then it would have a low probability of occurring given that the slope is really zero (null hypothesis).
I understand that much.

My confusion is the p-value.

Just answer this one question: can you have p-value of greater than .5 if the t-statistic is greater than 0?