Degree of freedom

1. DEGREE OF FREEDOM

2. DEFINITION -
The degrees of freedom that are mathematical concepts to statistical calculation
represents the number of variables that have the freedom to vary in a
calculation.calculating degrees of freedom can help ensure the validity of chi square
test statistics, t-tests and highly f-tests, among other tests. These tests are often used
to compare data that has been detected with data that would be expected if a
particular hypothesis were true.

3. EXAMPLE -
• Mention that you have seven hats that you can wear for a week,and you decide to
wear each shirt only once a week. On Sunday, consider choosing 1of the 7
hats.wear any of the 7 hats.On the second day,the hats worn the first day can’t be
selected,and you should choose from the remaining hat’s.The pattern continues as
follows:
1st day:7 hats to choose from
2nd day:6 hats to choose from
3rd day: 5 hats to choose from
4th day:4 hats to choose from
5th day:3 hats to choose from
6th day:2 hats to choose from
7th day:1 hats to choose from

4. USE OF DEGREES OF FREEDOM -
• T-tests
• Chi square test
These tests are frequently used to compare observed data with data that would be
anticipated to be obtained as per particular hypothesis.

5. DEGREES OF FREEDOM FORMULA -
• Df= N-1 &
• Df=n1+ n2- 2( for two sample test)
Here,N= Actual sample size.

6. MATHEMATICAL EXAMPLE -