Statistics: P-Value Simply Explained

What’s the p-value, simply put?

The p-value tells us how likely it is to get the results like this if the null hypothesis is true. To get a better understanding of this, lets go through an example. Lets say that you have a bottle cap selling business. You send each customer a box of bottle caps, with some being very rare and others being normal but people have been complaining on your website that there are less rare bottle caps then promised! The website advertises for every 200 bottle caps you buy you will get 70 rare bottle caps or more! Logistically opening up every box to check would take way to much time so instead we are going to be using a statistical test!

The Statistical Test Process….

Lets start out by defining our null hypothesis. Our null hypothesis is the thing we are trying to provide evidence against. In our case that would be that there are at least 70 rare bottle caps for every 200. Our alternative hypothesis is what we are trying to prove so it that case that would be there are not at least 70 rare bottle caps for every 200, our significance level for this test will be 0.05. If the p value is lower than this then we will reject the null hypothesis.

Now we take a random sample of our bottle cap boxes. Now lets count all of the rare bottle caps in these boxes. If all of the amount of rare bottle caps were significantly lower than 70 with a mean of 20 for example then it would be obvious that it would be obvious that the boxes don’t have the required number of rare bottle caps. But lets say that in this case the average number of rare bottle caps in 68.7. Does this provide evidence to prove the alternative hypothesis or is this by luck?

Well then we can calculate the p value to be 0.18. This means that there is an 18% chance of getting this mean or lower if the null hypothesis is true. This p-value of 0.18 doesn’t provide enough evidence to reject the null hypothesis. The smaller the p-value is the less likely the result was from luck, since our p-value was greater than 0.05 then there are at least 70 rare bottle caps for every 200.

Review

1. We start off by saying the null hypothesis is true
2. We take a sample and get a statistic
3. We work out how likely it is to get a statistic like this is the null hypothesis is true(the p-value)
4. If our p-value is below the significance level then we reject the null. A small p-value means a significant result. The smaller the p-value is the more significant the result is.
5. If the p-value is large then the original idea is correct and we don’t reject the null.