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
Trade Literature: Trade literature consists of documents that give information on the processes and materials involved in the manufacture of a product, various types of produc

An integer programming problem is identical to a linear programming problem except that one or more decision variables are constrained to take integer values. Such problems cannot

Question 1 Explain any five accessory industries Question 2 Explain the history of boots and shoes Question 3 Write short notes on following- Types of Gujarati emb

Discuss the methodology of operation research

Need Proposals are written for various reasons. They are prepared for different reasons which vary to the extent of details expected, but like research reports, the proposal a

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 grade Y paper i

a)Draw a network for the project. b)Determine the critical path. Activity Duration Activity Duration 1-2 15 5-10 22 1-3 13 6-9 33 1-4 1

Regression Line The line  of regression  is the  line  which give the best  estimate  to the  values  of one  variable  for any  specific  values  of other  variable. For t