I am currently doing collocational analysis in the Russian National Corpus, to be precise the Russian national news subcorpus, to see what is the most significant collocates of the lemma "gay".
In doing the analysis, I will be using the "logDice" association measure by Rychlý (2008), with this following formula:
$$ \text{logDice} = 14 + \text{log2} \frac{2(w_1 w_2)}{w_1 + w_2} $$
Where:
$w_1 w_2$ = the frequency of the word $x$ and $y$
$w_1$ = the frequency of the word $x$ (the lemma)
$w_2$ = the frequency of the word $y$ (the collocate)
This is the sample of data through which I will conduct a collocational analysis, gathered from the Russian National Corpus:
lex_1 lex_2 w1w2 w1 w2 dice
1 гей лесбиянка 256 3035 1000 11.935563044335458
2 гей бисексуал 56 3035 214 10.632396335625995
3 гей -пропаганда 33 3035 33 10.16087357953928
4 гей трансгендер 40 3035 1125 10.048756281418573
5 гей -активист 22 3035 25 9.758019438971836
6 гей пропаганда 109 3035 14989 9.585035580677008
The dice column stands for logDice value, as per stated in the Russian National Corpus. But, when I try to recalculate the logDice value (in the "recalculated_logDice" column), using Rychlý's formula, this is the result that I obtained:
lex_1 lex_2 w1w2 w1 w2 dice recalculated_logDice
1 гей лесбиянка 256 3035 1000 11.935563044335458 11.021647
2 гей бисексуал 56 3035 214 10.632396335625995 9.141575
3 гей -пропаганда 33 3035 33 10.16087357953928 8.461311
4 гей трансгендер 40 3035 1125 10.048756281418573 8.299560
5 гей -активист 22 3035 25 9.758019438971836 7.880116
6 гей пропаганда 109 3035 14989 9.585035580677008 7.630553
Basically, my calculation of logDice vs. the Russian News Corpus calculation is different. Therefore, I tried to do another calculation, this time using the natural log (in the "lnDice" column), which yielded this result:
lex_1 lex_2 w1w2 w1 w2 dice recalculated_logDice lnDice
1 гей лесбиянка 256 3035 1000 11.935563044335458 11.021647 11.935563
2 гей бисексуал 56 3035 214 10.632396335625995 9.141575 10.632396
3 гей -пропаганда 33 3035 33 10.16087357953928 8.461311 10.160874
4 гей трансгендер 40 3035 1125 10.048756281418573 8.299560 10.048756
5 гей -активист 22 3035 25 9.758019438971836 7.880116 9.758019
6 гей пропаганда 109 3035 14989 9.585035580677008 7.630553 9.585036
Which is basically the result retrieved from the Russian National Corpus.
My question is, can log2 be substituted with the natural log? Did I make a mistake in my calculation? I seem not able to find out why the Russian National Corpus uses the natural log in place of log2 in their calculation of logDice, given the logDice formula by Rychlý, 2008.