Degrees of freedom, Operation Research

Determining Degrees of Freedom

 

One of the prerequisites for using chi square test is that we should calculate the number of degrees of freedom for the contingency table. To understand degrees of freedom, let us look at this example. We know that 3 + 4 + 5 = 12, 2 + 6 + 4 = 12 and 6 + 1 + 5 = 12. If we express these equations in the manner shown below, what value will the blanks take so that we get a total of twelve in all the equations.

3 + 4 + ___ = 12, 2 + 6 + ___ = 12, 6 + 1 + ___ = 12

The possible values are 5, 4 and 5. Here the point to note is that after deciding what the first two numbers are going to be we lose the independence to assign the number at our discretion which the third value should take. It becomes mandatory that the number should be 5, 4 and 5 but no other number. In this case the number of degrees of freedom which we enjoy is two, as we have discretion to decide only the first two numbers.

For the contingency tables, it is calculated as follows:

Number of Degrees of Freedom = (Number of rows - 1)  (Number of columns - 1)

The number of rows and the number of columns in our example are 2 and 4. Therefore the number of degrees of freedom is given by

                   (2 - 1)(4 - 1) = 1 x 3 = 3

We use this value to look up the value of the chi square statistic. The value in the table is found at the intersection point of number of degrees of freedom (calculated from the contingency table) and the corresponding level of significance. This value denotes the area to the right end of the tail. In our problem, at α = 10% and 3 degrees of freedom the area under the right tail is 0.10 and the chi square statistic is 6.251. Since the sample chi square statistic does not fall in the acceptance region, we reject the null hypothesis.

 

Posted Date: 9/15/2012 6:02:15 AM | Location : United States







Related Discussions:- Degrees of freedom, Assignment Help, Ask Question on Degrees of freedom, Get Answer, Expert's Help, Degrees of freedom Discussions

Write discussion on Degrees of freedom
Your posts are moderated
Related Questions
INFORMATION RESOURCES - SELECTION PRINCIPLES: Selection of materials for a library requires sagacity, adroitness and attention to people's needs for everything from books and

Maximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = 2 X1, X2 = 0

#question. A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grad

#questiSix Operators are to be assigned to five jobs with the cost of assignment in Rs. given in the matrix below. Determine the optimal assignment. Which operator will have no ass

How do I set this problem up for Excel: A National Credit Union has $250,000 available to invest in a 12 month commitment. The money can be placed in Treasury notes yielding an 8%

Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = 2 X1, X2 = 0

NON PARAMETRIC TESTS All  practical  data follow normal distribution under  such situations can estimate the  parameters such  as mean  variance etc ,,, and use the  standard

I have looked at Hungarian algorithm to solve assignment problem, but it seems like it is limited to 1-to-1 assignment. I would like to know how to do 1-to-3 assignment.