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i am interested what does mean Harmonic F statistic in mathematical language?i have search about $F$ statistic and found a lot of explanation,for example like this

"**F Statistic

The F statistic is used in a test on the hypothesis that the ratio of a pair of mean squares is at least unity (i.e. the mean squares are identical). Ordinarily it is used to verify the significance of the regression and of the lack of fit. In a regression analysis, the F statistic is used in the ANOVA table to compare the variability accounted for by the regression model with the remaining variation due to error in the model (i.e. the model residuals). The null hypothesis of the test is that the coefficients of the regression model are zero; the alternative hypothesis is that at least on e of the coefficients is non-zero (thus providing some ability to estimate the response). Statistical software will usually directly report the p-value (i.e. level of significance) of the F statistic. In most analyses, a p-value of 0.05 or less is considered sufficient to reject the hypothesis that the coefficients are zero; in other words, when the p value is less than 0.10, the regression model may be worthy of further analysis. Note that a p-value of 0.10 may be used as the threshold for preliminary investigations (with limited data).**

but what about harmonic $F$ statistic?i know definition of harmonic mean,which is defined as

enter image description here

from this site

http://en.wikipedia.org/wiki/Harmonic_mean

so please help me to understand harmonic $F$ statistic,is there any weights introduced which are harmonicaly related to each other or what?thanks in advance

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  • $\begingroup$ What is the context in which you encountered the term? The large quote you give doesn't mention it. $\endgroup$ – Glen_b Apr 21 '14 at 23:55
  • $\begingroup$ as i remember it was signal processing,i forgot it $\endgroup$ – dato datuashvili Apr 22 '14 at 4:42
  • $\begingroup$ It may be that you were reading about the harmonic F-score, the harmonic mean of precision and recall. It is explicitly mentioned in the wikipedia article on the harmonic mean. $\endgroup$ – Glen_b Apr 22 '14 at 7:34
  • $\begingroup$ maybe thanks very much,if i would have some specific question,i will ask there,it was too early that why i can't recall why i posted it there $\endgroup$ – dato datuashvili Apr 22 '14 at 7:40

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