# P-value and Level of Significance

At times understanding statistical concepts can be really tricky. One such concept is P-value. (You can look at the definition on Google. I could not understand it. Some of you might not be able to understand it unless you study Statistics like Anubhav Dubey :P).

Thus, Chintu and Chutki are here to explain it in simple terms to you!

Chutki and Chintu often play cricket in their apartmentâ€™s park. Like all children, they have played shots that have led to some trouble in the past. (They are not as innocent as you think them to be :D)

One evening, one of their neighbors returns home after spending the day on a trip. He finds a huge crack on a window glass that faces the park. The neighbor thinks that the children are behind this event.

However, he decides to follow the maxim of innocent until proven guilty. Hence, in this case, the null hypothesis becomes that the children are innocent.

### P-value

Now, in a world where this hypothesis is true and children are innocent, the neighbor decides to think of other possible causes of the cracked glass. Probably, some jealous neighbor threw a stone that didnâ€™t break the glass but caused the crack; maybe, the glass cracked on its own. Ummm, black magic anyone?

So, the neighbor thinks of the number of times out of a hundred that all these causes could lead to the cracked glass. Suppose, he concludes that it is possible that out of 100, this event could happen 6 times due to causes other than the cricket ball hitting the window. Thus, the p-value is 6/100 or 0.06.

### Level of Significance

Now to make a decision, this neighbor has a predetermined number out of 100 in his mind based on his experiences to compare with this p-value. This number is referred to as the level of significance.

If the p-value is smaller than this predetermined number (level of significance), the neighbor would decide to pursue the matter with the parents of the children. Otherwise, he would let it go for the time being.

The level of significance is arbitrary. It can vary a lot depending upon the context and field in which it is being used. In physics, even 1 out of 100 is too high while in certain medical experiments, 10 out of 100 could be too low.

### Definitions

The p-value is the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct.

The significance level of an event (such as a statistical test) is the probability that the event could have occurred by chance. If the level is quite low, that is, the probability of occurring by chance is quite small, we say the event is significant.

Limitations of p-value

1. P-values do not measure the probability that the studied hypothesis is true or the probability that the data were produced by random chance alone.
2. A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.

Other Examples:

1. P-value explained using Pizza Delivery time by Admond Lee (Medium Article)
2. P-value explained using Puppies example by Cassie Kozyrkov (YouTube Video)

You can find some of the resources that helped us here.

You can read the other articles here.

For any query about the process or suggestion about topics that we can talk about in future, you can reach out to us on Linkedin.

Cheers and Best!