Demystify p-value, α and Degree of Freedom in Statistics using Examples
Disclaimer : All characters and scenarios are imaginary. It has no relation with practical data.
Let’s create a scenario to understand the concepts better. One day I found my friend ‘L’ boasting about himself that he can run for 1.5 hours straight without a break ( but he always feels sick to walk a distance of 10 minutes for school ). Although he was well known athlete in our area but I decided to give it a check. What I found after after a little probing is :
Fig 1, shows minimum and maximum stamina an athlete can have. Point A denotes minimum and Point B denotes maximum number of minutes an athlete can run without a break as per recorded observations. Now check out Fig 2 below,
L’s claim that he is able to run for straight 1.5 hours i.e. Point C ( difficult to Trust ) and he feels tired while going to school i.e. Point D ( again difficult to Trust ). So it’s pretty obvious that his claims are False.
α: The RED regions on both Left and Right side which are beyond acceptance are denoted by α. So, if a claim is on that RED region then it can be True or it can be False but for our safekeeping, we will REJECT it ( it is also known as Type I Error ).
p-value: In out story Point C and Point D are p-values. It gives an indication on acceptability of the claim.
Degree of Freedom (d.f.): You are given an equation, X1 + X2 +X3 = 15 to find the values of X1, X2, X3. Then one way is to assign values to X1,X2,X3 randomly.
You can do that for any two variables of the equation but can’t do the same for 3rd variable. The 3rd variable must have a value such that [ value of 3rd variable + Σ( value of other two variables ) = 15 ].
So you were free to choose value of 2 variables i.e. d.f. = (n-1). In our case n=3.
Thank You for coming so far.
Hope you liked the article and feel free to question or correct me. 😇