degree of freedom

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the short presentation to get an idea of degree of freedom in statistic which is useful to understand the concept of degree of freedom for beginners.

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Degree of Freedom (df):

Degree of Freedom ( df ) Suresh G. Isave , Pune

Definitions :

6/18/2014 2 Definitions The number of independent variables is usually called the number of degree of freedom. S.K.Mangal (2012) sgisave@ymail.com

Definitions :

Definitions The number of degrees of freedom in a distribution is the umber of observations or values that are independent of each other, that cannot be deducted from each other. - Best, Kahn (2006) 6/18/2014 3 sgisave@ymail.com

Symbol :

Symbol df 6/18/2014 4 sgisave@ymail.com

Use :

Use df is used in statistical computation like t Distribution, Chi-Square Distribution, Standard Deviation etc. 6/18/2014 5 sgisave@ymail.com

Concept :

Concept Degree of freedom literally refers to the number of data values that are free to vary. In other words, if you know the mean, and all but one value, you can figure out the missing value.  All the values except one are free to vary.  One value is set once, the others are known.  6/18/2014 6 sgisave@ymail.com

Concept :

Concept T he concept is widely used in dealing with small sample statistics. The freedom means, freedom to vary. The df is associated with a given sample are determined by the number of observations that are free to vary. 6/18/2014 7 sgisave@ymail.com

Concept :

Concept When we want to predict about something and if there are only two prediction are possible. Only one prediction is independent whereas second can be guessed. The scope is only to predict one, hence degree of freedom is 1. 6/18/2014 8 sgisave@ymail.com

Concept :

Concept The degree of freedom is reduced from through the restrictions imposed upon the observations or variables. 6/18/2014 9 sgisave@ymail.com

Concept :

Concept General rule is one df is lost for each restrictions imposed. ( N-1 ) No. of degrees of freedom = No. of observation minus No. of constrains/restrictions 6/18/2014 10 sgisave@ymail.com

illustration:

illustration Suppose we have five scores 24, 20, 14, 12 and 10 and the mean is 16 and the deviation from the means are respectively, 8, 2, -2, -4, and -6. The sum of these deviation is Zero. If any mean is known and any four scores are known, fifth can be determined. If any four deviations are known the fifth one can be determined. 6/18/2014 11 sgisave@ymail.com

illustration:

illustration It means, out of five scores or deviations, only four are (N-1) free to vary but not one, otherwise the mean will vary. [restrictions/constrains – formula of mean or addition of all deviations = Zero] Here one degree of freedom is lost. One score or deviation can be vary. 6/18/2014 12 sgisave@ymail.com

illustration:

illustration Generally, one degree of freedom is lost when we use the mean of the scores for computing the variance of standard deviation. Originally there were Five degrees of freedom in the computation of the mean,( N=5), because all scores were independent. 6/18/2014 13 sgisave@ymail.com

illustration:

illustration But as we use the mean for computing variance and standard deviation, we lost one degree of freedom. (N-1) 6/18/2014 14 sgisave@ymail.com

illustration:

illustration Suppose there are four means M 1 , M 2, M 3 and M 4. For the computation of mean of these means –M, we require four independent observations i.e. M 1 , M 2 M 3 and M 4. O nce we get M, we lose one degree of freedom as the values of M 1 , M 2 M 3 and M 4. can be determined in the light of the value of M. 6/18/2014 15 sgisave@ymail.com

Conclusion :

In this way, when we employ the sample means as a prediction of population mean, one degree of freedom is reduced and N-1 degree of freedom is left for the prediction of variance and standard deviation of the population . 6/18/2014 16 Conclusion sgisave@ymail.com

Conclusion :

Conclusion However df is not N-1 always. In case of correlation, where deviation is computed from two means, the number of restrictions goes on two, consequently, the number of degree of freedom becomes N-2 6/18/2014 17 sgisave@ymail.com

Conclusion :

Conclusion In case of Chi square test and ANOVA, different formulae need to apply to compute df . However it is common that df = number of observation or values minus number of restrictions imposed on that data. 6/18/2014 18 sgisave@ymail.com

Bibliography :

Bibliography Best John B. & Kahn James V., Research in Education , Ninth edition, Prentice-Hall of India Private Limited, New Delhi- 110 001, 2006. Mangal S.K., Statistic in Psychology and Education , Second Edition, PHI Learning Private Learning, New Delhi- 110 001, 2012 6/18/2014 19 sgisave@ymail.com

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