Hi Jason Yes, I concur that the function "Levene" named in my package should really be called Brown-Forsthe.
I was vacillating between this correct naming versus following the nomenclature of scipy <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.levene.html>from which my implementation is numerically tested against. I looked at a couple of popular statistics software, and it seems that most differentiate between Levene and Brown-Forsythe * JMP <https://www.jmp.com/support/help/en/17.2/#page/jmp/unequal-variances-reports.shtml> * SPSS <https://www.ibm.com/docs/en/spss-statistics/28.0.0?topic=anova-one-way-options> * R <https://search.r-project.org/CRAN/refmans/ALSM/html/3_bftest.html> Therefore, perhaps I should not be following scipy and rename my function from Levene to BrownForsythe? I admit I am no statistician and would appreciate some professional guidance. On Monday, 30 October 2023 at 10:41:23 UTC+8 Jason E. Aten wrote: > 王富民awaw: Very nice. > > The Levene function, though, is confusingly named. The Levene test is > distinct from the Brown-Forsthe test, so mixing up the names > seems odd.[1] > > [1] quoting > https://www.statisticshowto.com/brown-forsythe-test/#:~:text=The%20Levene%20test%20uses%20deviations,a%20test%20that's%20more%20robust. > > below: (see the underlined sentence, underline and bold there is mine) > > How the Test Works > > Both the Levene and B-F tests transform dependent variables > <https://www.statisticshowto.com/dependent-variable-definition/> for use > in an ANOVA > <https://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/anova/>test. > > The only difference between the two tests is in how those transformed > variables are constructed. The Levene test uses deviations from group > means <https://www.statisticshowto.com/mean/>, which usually results in a > highly-skewed set of data; This violates the assumption of normality > <https://www.statisticshowto.com/assumption-of-normality-test/>.* The > Brown-Forsythe test attempts to correct for this skewness > <https://www.statisticshowto.com/probability-and-statistics/descriptive-statistics/skewness/>by > > using deviations from group medians > <https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/mean-median-mode/#median>.* > > The result is a test that’s more robust > <https://www.statisticshowto.com/robust-statistics/>. In other words, the > B-F test is less likely than the Levene test to incorrectly declare that > the assumption of equal variances has been violated. > > The test works as follows: > > - The median is calculated for each factor level group. > - The median value is subtracted from each dependent variable in the > group. > - An ANOVA > > <https://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/anova/> > is > run with the transformed variables. If a factor’s p-value > > <https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/p-value/> > is > less than the significance level > > <https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/what-is-an-alpha-level/> > (usually > 5%), the population variances are not equal. > > W or F statistic? > > The test statistic used in a regular ANOVA is an F-statistic > <https://www.statisticshowto.com/probability-and-statistics/f-statistic-value-test/>. > > The statistic used in an ANOVA with transformed variables is sometimes > called a W-Statistic — but it’s really just an F-Statistic with a > different name. It should not be confused with the coefficient of > concordance W-statistic > <https://www.statisticshowto.com/concordance-correlation-coefficient/>, > which is used to assess agreement between raters. > Cautions > > For the most part, the B-F test is thought to perform as well as or better > than other available tests for equal variances. However, Glass and Hopkins > (1996 p. 436) state that the Levene and B-F tests are “fatally flawed”; It > isn’t clear how robust they are when there is significant differences in > variances and unequal sample sizes. Hill et. al (2006) advise repeating the > test using a non-parametric > <https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/parametric-and-non-parametric-data/> > method. > > On Monday, October 30, 2023 at 1:08:19 AM UTC 王富民awaw wrote: > >> Hi Jan, Martin, and Jason >> >> Thanks for your tips and encouragement for rolling our sleeves. >> I have put together a small statistics library: >> >> stat package - github.com/fumin/stat - Go Packages >> <https://pkg.go.dev/github.com/fumin/stat> >> >> For my own needs, in addition to Brown-Forsythe, I also needed the Welch >> t-test and tools for multiple testing, so these are what's in the above >> package. >> >> On Monday, 30 October 2023 at 07:25:50 UTC+8 Jason E. Aten wrote: >> >>> For the ANOVA, I usually just call from Go into R for such things -- at >>> least until I >>> can validate if its the right thing to do/ meets the sensitivity/power >>> needs of the analysis. >>> >>> https://statsandr.com/blog/anova-in-r/ >>> >>> >>> https://github.com/glycerine/rmq#and-the-reverse-embedding-r-inside-your-golang-program >>> >>> >>> On Wednesday, October 25, 2023 at 6:48:56 AM UTC+1 Jan wrote: >>> >>>> So cool! >>>> On Monday, October 23, 2023 at 5:44:29 PM UTC+2 Martin Schnabel wrote: >>>> >>>>> Hi, >>>>> >>>>> I attempted to translate the linked JS implementation for fun. Maybe >>>>> someone can use it as a starting point and correct or verify its >>>>> correctness. >>>>> >>>>> https://go.dev/play/p/Wrw2yDRof0z >>>>> >>>>> Have fun! >>>>> >>>>> On 10/23/23 07:38, Jan wrote: >>>>> > hi, I did a quick search and I didn't find anything in Go. But >>>>> looking >>>>> > at the definition and at one implementation in JS >>>>> > < >>>>> https://github.com/lukem512/brown-forsythe-test/blob/master/src/brown-forsythe.js>, >>>>> >>>>> it sounds something relatively easy to write and share :) You can use >>>>> the >>>>> R implementation to create some test datasets. Maybe gonum/stat < >>>>> https://godocs.io/gonum.org/v1/gonum/stat> would be a potential home >>>>> for such a function ? What do you think ? >>>>> > >>>>> > cheers >>>>> > On Friday, October 20, 2023 at 10:54:55 AM UTC+2 王富民awaw wrote: >>>>> > >>>>> > Hi follow Gophers >>>>> > >>>>> > I wonder is there a canonical, verifiably correct Go package for >>>>> > statistics? >>>>> > In particular, Go code that does the Brown-Forsythe test of equal >>>>> > variance. >>>>> > Ideally in pure Go, but linking with CGo is OK. >>>>> > >>>>> > A search on Google and pkg.go.dev <http://pkg.go.dev> does not >>>>> > return helpful results. >>>>> > I wonder is there anything that the community could share? >>>>> > >>>>> > -- >>>>> > You received this message because you are subscribed to the Google >>>>> > Groups "golang-nuts" group. >>>>> > To unsubscribe from this group and stop receiving emails from it, >>>>> send >>>>> > an email to golang-nuts...@googlegroups.com >>>>> > <mailto:golang-nuts...@googlegroups.com>. >>>>> > To view this discussion on the web visit >>>>> > >>>>> https://groups.google.com/d/msgid/golang-nuts/7ee10c0f-8af6-4b31-baaf-ce2ccb9c0211n%40googlegroups.com >>>>> >>>>> < >>>>> https://groups.google.com/d/msgid/golang-nuts/7ee10c0f-8af6-4b31-baaf-ce2ccb9c0211n%40googlegroups.com?utm_medium=email&utm_source=footer>. >>>>> >>>>> >>>>> >>>> -- You received this message because you are subscribed to the Google Groups "golang-nuts" group. To unsubscribe from this group and stop receiving emails from it, send an email to golang-nuts+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/golang-nuts/dc170b8a-2ec0-40ca-945a-bef352d5af93n%40googlegroups.com.
