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.

Scenario 1

Minimum and Maximum stamina of an athlete

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.

Scenario 2

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. 😇



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