# Statistics: p-value for T-test

## Introduction

The p-value helps you determine whether the results of a test can explain the data. In a statistical test (such as a t-test which you can find explained here), the p-value lets you determine the probability that you can disprove the null hypothesis. The *null hypothesis* is the one you are trying to disprove. If you can reject the null hypothesis, you can accept the *alternative hypothesis*.

## Uses

P-values appear in the output of the function “T-TEST” as well as when using the T-test Tool. Refer to the tutorial T-Tests to see how to do this.

Once you have your results, look at the P(T<=t) values. Most of the time you will look at the two-tailed test which splits the 5% of uncertainty (alpha value) between the upper and lower confidence intervals, whereas the one-tail has the entirety of the 5% of uncertainty within a single interval (either upper or lower side of the distribution). However, you can also see the results from a one-tailed test listed in the results. If the p-value is less than 0.05, then that means that the results are significant, and you can reject the null hypothesis that there is no difference between groups. In other words, there is a difference between the averages of the two groups.

## Practice

Using this data set and answer the questions below. Answers to this lesson can be found TBD.

- Is there a statistical difference between the GDP of countries which have a HCI > than 0.5 and those that have a HCI <0.5? Note: you will have to first separate HCI into two categories before testing this assumption.
- What is the resultant two-tailed p-value? How does this
- What would it mean if the p-value were 0.001?

## Conclusion

P-values are a useful additional piece of information that lets researchers know the statistical significance of a result from a t-test. For instance, if you have two different results, one with a p-value of .04 and one with a p-value of .06, the .04 will be considered statistically significant while the .06 will not. Beyond this simplified example, you could compare a .04 p-value to a .001 p-value. Both are statistically significant, but the .001 provides an even stronger case against the null hypothesis than the .04.