# Chi-squared and reduced Chi-squared

In my physics honours lab to check our "goodness of fit" we have to use the Chi-squared and reduced Chi-squared equations.

For the Lab we use the text Bevington Data analysis and error reduction. I'm having a problem on determining whether or not my chi-squared values are good because the book states that chi-squared should be close to zero while the reduced chi-squared should be close to 1.

this obviously doesn't make sense because you divide chi-squared by the number of degrees of freedom which is a positive integer number.

Can somebody please explain to me the meaning of both reduced and chi-squared numbers?

chiro
In my physics honours lab to check our "goodness of fit" we have to use the Chi-squared and reduced Chi-squared equations.

For the Lab we use the text Bevington Data analysis and error reduction. I'm having a problem on determining whether or not my chi-squared values are good because the book states that chi-squared should be close to zero while the reduced chi-squared should be close to 1.

this obviously doesn't make sense because you divide chi-squared by the number of degrees of freedom which is a positive integer number.

Can somebody please explain to me the meaning of both reduced and chi-squared numbers?

I am not sure about the reduced chi-squared, but since you are measuring variation between expected and observed, it makes sense intuitively that the variation should be minimized (and hence close to zero).

Can you give the definition of a reduced chi-square distribution and any sample statistics that you have to calculate?