Question

Search concept of Degrees of Freedom in statistics to explain what it is. Make sure to provide a couple of examples as to how it is applied. Short Paragraph.

Answer 1

Defination

In statistics, the degrees of freedom (DF) indicate the number of independent values that can vary in an analysis without breaking any constrain

1)

Degrees of freedom are the number of independent values that a statistical analysis can estimate. You can also think of it as the number of values that are free to vary as you estimate parameters

2)

Degrees of freedom is a combination of how much data you have and how many parameters you need to estimate.

For example

1)

In order to get the df for the estimate, you have to subtract 1 from the number of items. Let’s say you were finding the mean weight loss for a low-carb diet. You could use 4 people, giving 3 degrees of freedom (4 – 1 = 3), or you could use one hundred people with df = 99.

2)

If there is a data set of 4, (N=4).

Call the data set X and create a list with the values for each data.

For this example data, set X includes: 15, 30, 25, 10

This data set has a mean, or average of 20. Calculate the mean by adding the values and dividing by N:

(15+30+25+10)/4= 20

Using the formula, the degrees of freedom would be calculated as df = N-1:

In this example, it looks like, df = 4-1 = 3

This indicates that, in this data set, three numbers have the freedom to vary as long as the mean remains 20.