A probability value (p-value) is a number between 0 and 1 that describes the probability of observing a result as extreme as the one you actually observed, assuming that a certain hypothesis is true.

The p-value helps you understand how likely it is that your results were an extreme result or an outlier (a fluke).

To determine the p-value, You need a null hypothesis and an alternate hypothesis. The null hypothesis is like a baseline assumption, and the alternative is the one you will test.

For example, if I state “50% of Birds can fly”. That would be my null hypothesis, and the alternative hypothesis is “Not 50% of birds can fly.”

Imagine I gather data on 100 birds and only 52 of them can fly. Suppose I use a formula and determine the p value is 0.70.

This is a high p-value because my results were very close to the null hypothesis. The chance of the null hypothesis being wrong is low.

However, imagine the data showed 96 / 100 birds can fly, and suppose the calculated P value was 0.001.

This low P value indicates that the data is too different from the base assumption to ignore it as a fluke, there is a pattern of non conformity to the null hypothesis.

Usually this is when its safe to say the base assumption is wrong, because we observed entirely different results.

The p-value is calculated by finding the area of a shaded region under a probability distribution curve. The total area under the curb is assumed to be 1.

\[\int_{z_{obs}}^{\infty} f(x) \, dx\]

Z is the specific data point you observed converted into a standard deviation.

• A p-value of 0.05 is considered to be a significant amount. \(\alpha \le 0.05\)

• \(\alpha \le 0.01\) is a highly significant amount.

If the calculated value is below 0.05, the null hypothesis is rejected.

• “The p-value tells you the probability that the null hypothesis is true”
  • In hypothesis testing, we assume the the null hypothesis is always true.
• “Getting a significant p-value in one experiment suggests you will get a significant p-value in a repeat experiment”
  • P-values are only valid for the sample size they are calculated in. It can not reliably tell you anything about a different set of data.