When we conduct t-test or ANOVA, then we compare the calculate value of 't' and ANOVA with the table value. For this purpose, we see the table value on two important criterion -(1) confidence interval and (2) degrees of freedom. My question is that what is degrees of freedom?
Hi Noushad
Suppose you had 5 numbers with one unknown and a total
1 3 4 3 ? Total=15
Then you can clearly work out the missing number, in this case 4. The same would be true if you were given the mean rather than the total.
1 3 4 3 ? Mean=5
In other words, if you are given a mean value, then one of the original numbers becomes redundant, as you can calculate it from the mean. In a t-test with a total sample size of n, you know the two means. Therefore the number of non-redundant numbers is n-2. THis is the degrees of freedom.
Adrian
I find this explanation quite useful:
http://courses.ncssm.edu/math/Stat_Inst/Worddocs/DFWalker.doc
Excellent and easy explanation by Robert Tomsik,
Degree of Freedom (df) = number of respondents - (minus) groups of comparison.
t-test have df always 2, whereas, ANOVA can have more than 2, as more than two categories can be compared there.
I know that's nitpicking, but Robert actually did not explain DF, he simply described the recipe how to calculate them fro one-factorial models based on the sample size and number of comparisons. Well, the word "comparisons" is a misnomer here that can be very misleading. Actually, DF is N - k, where k is not the number of comparisons but the number of estimates; it only coincidences in the t-test. In a single-factorial design with k groups there are k(k-1)/2 possible pairwise comparisons (e.g. 5*4/2=10 for k=5 groups), and there are always additional comparisons possible, e.g. each group mean against the average of the other groups etc. In simple one-factorial designs the DF is N minus the number of groups, since at least this many estimates ("group means", if you wish; this can be coded differently as well, but the total number of required estimates will remain the same) are part of the model. This rule will not hold when we move to more-factorial models, possibly with interactions and/or continuous covariables. Here the probability model of the test statistic ("F") is two-dimensional, with two different kinds of DF...
And yet another nitpick: Rahul, note that the one-sample t-test has only one estimate so DF = N-1. Your rule "t-test have df always 2" is correct only for the two-sample case. One may further add that this rule also only applies to models with assumed homoscedasticity. If this assumption is not resonable, the DF are typically adjusted by the Welch-Sattherwaite equation ("Welch t-test") what gives non-integer DF.
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