I have two different data sets. I try to find the zipf's law parameter that represent both of them. HOw do I know if the parameter values are statistically different. Do I use a t-test or f-test or something else

Data set 1: frequencies of terms present in a corpus.
Data set 2: frequencies of terms present in a sub corpus (of the corpus above)

y = c/(x^a)
y is the actual frequency of the terms
x ranges from 1:N (N is the total number of terms)

I get c1 and a1 for data set 1 and c2 and a2 for dataset 2 using regression.

How do I test if c1 and c2 (or a1 and a2) are significantly different

Answer 1

[Star Strider]

If you have already done the regression (ideally using nlinfit), you should have the confidence intervals (using nlparci) of the parameters for each dataset.

If the confidence intervals for the respective parameters do not overlap between dataset regressions and do not include zero, they are significant and statistically different and you can probably stop there. If they do overlap, you will likely need to do a paired t-test (using the square roots of the diagonals of the covariance matrices to calculate the standard deviations) to calculate the t-statistics to determine the probability that they are different.

That would be my approach. There may be others.

[Parth Mehta]

I cannot do a paired t-test because the two data sets are not of the same size. Is there any other alternative ?

[Star Strider]

I assumed they were the same size. The t-test for unequal sizes is appropriate then. (See: ‘Unequal sample sizes, equal variance’ or ‘Equal or Unequal sample sizes, unequal variances’ just below it. Also see Snedecor and Cochran, Statistical Methods, 8th Ed., p. 93-5.)

[Parth Mehta]

Thanks. That helped :)

[Star Strider]

My pleasure!