[SciPy-User] scipy.stats one-sided two-sided less, greater, signed ?

Sun Jun 12 06:20:40 EDT 2011

On Wed, Jun 8, 2011 at 12:56 PM, <josef.pktd at gmail.com> wrote:

> On Tue, Jun 7, 2011 at 10:37 PM, Bruce Southey <bsouthey at gmail.com> wrote:
> > On Tue, Jun 7, 2011 at 4:40 PM, Ralf Gommers
> > <ralf.gommers at googlemail.com> wrote:
> >>
> >>
> >> On Mon, Jun 6, 2011 at 9:34 PM, <josef.pktd at gmail.com> wrote:
> >>>
> >>> On Mon, Jun 6, 2011 at 2:34 PM, Bruce Southey <bsouthey at gmail.com>
> wrote:
> >>> > On 06/05/2011 02:43 PM, josef.pktd at gmail.com wrote:
> >>> >> What should be the policy on one-sided versus two-sided?
> >>> > Yes :-)
> >>> >
> >>> >> The main reason right now for looking at this is
> >>> >> http://projects.scipy.org/scipy/ticket/1394 which specifies a
> >>> >> "one-sided" alternative and provides both lower and upper tail.
> >>> > That refers to the Fisher's test rather than the more 'traditional'
> >>> > one-sided tests. Each value of the Fisher's test has special meanings
> >>> > about the value or probability of the 'first cell' under the null
> >>> > hypothesis.  So it is necessary to provide those three values.
> >>> >
> >>> >> I would prefer that we follow the alternative patterns similar to R
> >>> >>
> >>> >> currently only kstest has    alternative : 'two_sided' (default),
> >>> >> 'less' or 'greater'
> >>> >> but this should be added to other tests where it makes sense
> >>> > I think that these Kolmogorov-Smirnov  tests are not the traditional
> >>> > meaning either. It is a little mind-boggling to try to think about
> cdfs!
> >>> >
> >>> >> R fisher.exact
> >>> >> """alternative        indicates the alternative hypothesis and must
> be
> >>> >> one
> >>> >> of "two.sided", "greater" or "less". You can specify just the
> initial
> >>> >> letter. Only used in the 2 by 2 case."""
> >>> >>
> >>> >> mannwhitneyu reports a one-sided test without actually specifying
> >>> >> which alternative is used  (I thought I remembered other cases like
> >>> >> this but don't find any right now)
> >>> >>
> >>> >> related:
> >>> >> in many cases in the two-sided tests the test statistic has a sign
> >>> >> that indicates in which tail the test-statistic falls.
> >>> >> This is useful in ttests for example, because the one-sided tests
> can
> >>> >> be backed out from the two-sided tests. (With symmetric
> distributions
> >>> >> one-sided p-value is just half of the two-sided pvalue)
> >>> >>
> >>> >> In the discussion of https://github.com/scipy/scipy/pull/8  I
> argued
> >>> >> that this might mislead users to interpret a two-sided result as a
> >>> >> one-sided result. However, I doubt now that this is a strong
> argument
> >>> >> against not reporting the signed test statistic.
> >>> > (I do not follow pull requests so is there a relevant ticket?)
> >>> >
> >>> >> After going through scipy.stats.stats, it looks like we always
> report
> >>> >> the signed test statistic.
> >>> >>
> >>> >> The test statistic in ks_2samp is in all cases defined as a max
> value
> >>> >> and doesn't have a sign in R either, so adding a sign there would
> >>> >> break with the standard definition.
> >>> >> one-sided option for ks_2samp would just require to find the
> >>> >> distribution of the test statistics D+, D-
> >>> >>
> >>> >> ---
> >>> >>
> >>> >> So my proposal for the general pattern (with exceptions for special
> >>> >> reasons) would be
> >>> >>
> >>> >> * add/offer alternative : 'two_sided' (default), 'less' or 'greater'
> >>> >> http://projects.scipy.org/scipy/ticket/1394  for now,
> >>> >> and adjustments of existing tests in the future (adding the option
> can
> >>> >> be mostly done in a backwards compatible way and for symmetric
> >>> >> distributions like ttest it's just a convenience)
> >>> >> mannwhitneyu seems to be the only "weird" one
> >>
> >> This would actually make the fisher_exact implementation more
> consistent,
> >> since only one p-value is returned in all cases. I just don't like the R
> >> naming much; alternative="greater" does not convey to me that this is a
> >> one-sided test using the upper tail. How about:
> >>     test : {"two-tailed", "lower-tail", "upper-tail"}
> >> with two-tailed the default?
>
> I think matlab uses (in general) larger and smaller, the advantage of
> less/smaller and greater/larger is that it directly refers to the
> alternative hypothesis, while the meaning in terms of tails is not
> always clear (in kstest and I guess some others the test statistics is
> just reversed and uses the same tail in both cases)
>
> so greater smaller is mostly "future proof" across tests, while
> reference to the tail can only be used where this is an unambiguous
> statement. but see below
>
> I think I understand your terminology a bit better now, and consistency
across all tests is important. So I've updated the Fisher's exact patch to
use alternative={'two-sided', 'less', greater'} and sent a pull request:
https://github.com/scipy/scipy/pull/32

Cheers,
Ralf

>

>
> >>
> >> Ralf
> >>
> >>
> >>>
> >>> >>
> >>> >> * report signed test statistic for two-sided alternative (when a
> >>> >> signed test statistic exists):  which is the status quo in
> >>> >> stats.stats, but I didn't know that this is actually pretty
> consistent
> >>> >> across tests.
> >>> >>
> >>> >> Opinions ?
> >>> >>
> >>> >> Josef
> >>> >> _______________________________________________
> >>> >> SciPy-User mailing list
> >>> >> SciPy-User at scipy.org
> >>> >> http://mail.scipy.org/mailman/listinfo/scipy-user
> >>> > I think that there is some valid misunderstanding here (as I was in
> the
> >>> > same situation) regarding what is meant here. My understanding is
> that
> >>> > under a one-sided hypothesis, all the values of the null hypothesis
> only
> >>> > exist in one tail of the test distribution. In contrast the values of
> >>> > null distribution exist in both tails with a two-sided hypothesis.
> Yet
> >>> > that interpretation does not have the same meaning as the tails in
> the
> >>> > Fisher or Kolmogorov-Smirnov tests.
> >>>
> >>> The tests have a clear Null Hypothesis (equality) and Alternative
> >>> Hypothesis (not equal or directional, less or greater).
> >>> So the "alternative" should be clearly specified in the function
> >>> argument, as in R.
> >>>
> >>> Whether this corresponds to left and right tails of the distribution
> >>> is an "implementation detail" which holds for ttests but not for
> >>> kstest/ks_2samp.
> >>>
> >>> kstest/ks2sample   H0: cdf1 == cdf2  and H1:  cdf1 != cdf2 or H1:
> >>> cdf1 < cdf2 or H1:  cdf1 > cdf2
> >>> (looks similar to comparing two survival curves in Kaplan-Meier ?)
> >>>
> >>> fisher_exact (2 by 2)  H0: odds-ratio == 1 and H1: odds-ratio != 1 or
> >>> H1: odds-ratio < 1 or H1: odds-ratio > 1
> >>>
> >>> I know the kolmogorov-smirnov tests, but for fisher exact and
> >>> contingency tables I rely on R
> >>>
> >>> from R-help:
> >>> For 2 by 2 tables, the null of conditional independence is equivalent
> >>> to the hypothesis that the odds ratio equals one. <...> The
> >>> alternative for a one-sided test is based on the odds ratio, so
> >>> alternative = "greater" is a test of the odds ratio being bigger than
> >>> or.
> >>> Two-sided tests are based on the probabilities of the tables, and take
> >>> as ‘more extreme’ all tables with probabilities less than or equal to
> >>> that of the observed table, the p-value being the sum of such
> >>> probabilities.
> >>>
> >>> Josef
> >>>
> >>>
> >>> >
> >>> > I never paid much attention to the frequency based tests but it does
> not
> >>> > surprise if there are no one-sided tests. Most are rank-based so it
> is
> >>> > rather hard to do in a simply manner - actually I am not even sure
> how
> >>> > to use a permutation test.
> >>> >
> >>> > Bruce
> >>> >
> >>> >
> >>> >
> >>> > _______________________________________________
> >>> > SciPy-User mailing list
> >>> > SciPy-User at scipy.org
> >>> > http://mail.scipy.org/mailman/listinfo/scipy-user
> >>> >
> >>> _______________________________________________
> >>> SciPy-User mailing list
> >>> SciPy-User at scipy.org
> >>> http://mail.scipy.org/mailman/listinfo/scipy-user
> >>
> >>
> >> _______________________________________________
> >> SciPy-User mailing list
> >> SciPy-User at scipy.org
> >> http://mail.scipy.org/mailman/listinfo/scipy-user
> >>
> >>
> >
> > But that is NOT the correct interpretation  here!
> > I tried to explain to you that this is the not the usual idea
> > one-sided vs two-sided tests.
> > For example:
> > http://www.msu.edu/~fuw/teaching/Fu_ch10_2_categorical.ppt
> > "The test holds the marginal totals fixed and computes the
> > hypergeometric probability that n11 is at least as large as the
> > observed value"
>
> this still sounds like a less/greater test to me
>
>
> > "The output consists of three p-values:
> > Left: Use this when the alternative to independence is that there is
> > negative association between the variables.  That is, the observations
> > tend to lie in lower left and upper right.
> > Right: Use this when the alternative to independence is that there is
> > positive association between the variables. That is, the observations
> > tend to lie in upper left and lower right.
> > 2-Tail: Use this when there is no prior alternative.
> > "
> > There is also the book "Categorical data analysis: using the SAS
> > system  By Maura E. Stokes, Charles S. Davis, Gary G. Koch" that came
> > up via Google that also refers to the n11 cell.
> >
> > http://www.langsrud.com/fisher.htm
>
> I was trying to read the Agresti paper referenced there but it has too
> much detail to get through in 15 minutes :)
>
> > "The output consists of three p-values:
> >
> >    Left: Use this when the alternative to independence is that there
> > is negative association between the variables.
> >    That is, the observations tend to lie in lower left and upper right.
> >    Right: Use this when the alternative to independence is that there
> > is positive association between the variables.
> >    That is, the observations tend to lie in upper left and lower right.
> >    2-Tail: Use this when there is no prior alternative.
> >
> > NOTE: Decide to use Left, Right or 2-Tail before collecting (or
> > looking at) the data."
> >
> > But you will get a different p-value if you switch rows and columns
> > because of the dependence on the n11 cell. If you do that then the
> > p-values switch between left and right sides as these now refer to
> > different hypotheses regarding that first cell.
>
> switching row and columns doesn't change the p-value in R
> reversing columns changes the definition of less and greater, reverses them
>
> The problem with 2 by 2 contingency tables with given marginals, i.e.
> row and column totals, is that we only have one free entry. Any test
> on one entry, e.g. element 0,0, pins down all the other ones and
> (many) tests then become equivalent.
>
>
> http://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_freq_a0000000658.htm
> some math got lost
> """
> For <2 by 2> tables, one-sided -values for Fisher’s exact test are
> defined in terms of the frequency of the cell in the first row and
> first column of the table, the (1,1) cell. Denoting the observed (1,1)
> cell frequency by , the left-sided -value for Fisher’s exact test is
> the probability that the (1,1) cell frequency is less than or equal to
> . For the left-sided -value, the set includes those tables with a
> (1,1) cell frequency less than or equal to . A small left-sided -value
> supports the alternative hypothesis that the probability of an
> observation being in the first cell is actually less than expected
> under the null hypothesis of independent row and column variables.
>
> Similarly, for a right-sided alternative hypothesis, is the set of
> tables where the frequency of the (1,1) cell is greater than or equal
> to that in the observed table. A small right-sided -value supports the
> alternative that the probability of the first cell is actually greater
> than that expected under the null hypothesis.
>
> Because the (1,1) cell frequency completely determines the table when
> the marginal row and column sums are fixed, these one-sided
> alternatives can be stated equivalently in terms of other cell
> probabilities or ratios of cell probabilities. The left-sided
> alternative is equivalent to an odds ratio less than 1, where the odds
> ratio equals (). Additionally, the left-sided alternative is
> equivalent to the column 1 risk for row 1 being less than the column 1
> risk for row 2, . Similarly, the right-sided alternative is equivalent
> to the column 1 risk for row 1 being greater than the column 1 risk
> for row 2, . See Agresti (2007) for details.
> R C Tables
> """
>
> I'm not a user of Fisher's exact test (and I have a hard time keeping
> the different statements straight), so if left/right or lower/upper
> makes more sense to users, then I don't complain.
>
> To me they are all just independence tests with possible one-sided
> alternatives that one distribution dominates the other. (with the same
> pattern as ks_2samp or ttest_2samp)
>
> Josef
>
> >
> >
> > Bruce
> > _______________________________________________
> > SciPy-User mailing list
> > SciPy-User at scipy.org
> > http://mail.scipy.org/mailman/listinfo/scipy-user
> >
> _______________________________________________
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>
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