WEQATAL vs. QATAL statistics

Henry Churchyard churchh at usa.net
Sat Aug 12 15:04:58 EDT 2000

> From: Rolf Furuli <furuli at online.no>
>> Henry Churchyard wrote:
>>>> Henry Churchyard wrote:
>>>>> From: Rolf Furuli <furuli at online.no

[Rolf's data, condensed into 2x2 table:]

>>>>                  WEQATAL       QATAL
>>>>              .------------+-------------.
>>>>    PAST &    |            |             |
>>>>    PERFECT   |    412     |   10065     |
>>>>              +------------+-------------+
>>>>   Other      |            |    3470 ?   |
>>>>   Meanings   |   5675     |   or 3867 ? |
>>>>              `------------+-------------'

>> The exact definitions of semantic categories is somewhat outside my
>> main area of expertise (so it's not very useful to try to debate
>> these with me in detail) -- and it's not actually really the main
>> point at issue here, anyway.  I'm just seeing what happens when one
>> takes seriously the numbers you gave, and pointing out that
>> statistically they don't really support the conclusions you've
>> drawn from them (in the case of QATAL vs. WEQATAL).  I fed data
>> into the SAS statistical program and got output that the hypothesis
>> of "independence" (statistical non-correlation between meaning and
>> conjugation) is rejected at the p=.0001 level (which is one
>> five-hundredth of the p=.05 level which is usually accepted as
>> adequate -- therefore the hypothesis that there is no significant
>> difference in meaning between QATAL and WEQATAL is rejected five
>> hundred times more conclusively than is usually considered
>> necessary).  Also, "effect size" measures indicate a respectable
>> degree of observed correlation between meaning and conjugation (and
>> one which is solidly statistically significant, since the "ASE"'s,
>> or estimated standard deviations of the values, are less than a
>> tenth of the size of the values themselves).  So all in all, I'd
>> say that your own data has shown the existence of a significant and
>> significantly large meaning difference between QATAL and WEQATAL.
>> (It's not 100%, of course, but many statistical correlations can be
>> quite significant and solidly established without being 100%.)

>>       Statistic                     DF       Value      Prob
>>       ------------------------------------------------------
>>       Chi-Square                     1   7280.0923    <.0001

>>       Statistic                              Value       ASE
>>       ------------------------------------------------------
>>       Cramer's V                           -0.6030
>>       Pearson Correlation                  -0.6030    0.0050

>> (I'd be curious to see your data for YIQTOL vs. WEYIQTOL
>> vs. WAYYIQTOL by various meanings, in the form of a two dimensional
>> table, to see how they would calculate out.  But the data has to
>> fill a two-dimensional table to be able to do much calculating on
>> it: a list of the distribution of occurrences of WEYIQTOL by
>> meaning is not all that useful alone, in this context.)

> I agree with your last words that "a list of the distribution of
> occurrences of WEYIQTOL by meaning is not all that useful alone, in
> this context.".  Let us expand this somewhat and apply this to QATAL
> and WEQATAL as well.

Actually, I was speaking in a purely technical statistical sense: a
one-column list tabulating different semantic meanings for one
morphological category is a "one-dimensional nominal table" from the
statistical point of view, and there just isn't very much that can be
done to analyze such an unordered list.  However, if you provide data
on the occurrences of two or more different morphological categories,
cross-classified with respect to the same list of different meanings,
then the resulting two-column or multi-column table is a
two-dimensional table, and there are lots of statistical methods which
can be used to analyze two-dimensional tables, as seen in my post
where I gave the SAS output.  In any case, the basic question is
whether or not there are meaning differences between different
morphological form categories, which is a two-dimensional question.

So the one-dimensional tabulation you gave for occurrences of WEYIQTOL
("Ind.Fut 244 / Ind.Perf 9 / Ind.Pres 39 / Ind.Gnom 68 / Ind.Quest 21 /
Ind.Past 53 / Modal 426 / Final 195 / Purpose 75 / Modal Oth. 87")
isn't useful for much by itself, statistically -- but if you were to
provide a classification of the occurrences of WAYYIQTOL and plain
YIQTOL according to the same semantic categories, then it would be
possible to analyze the resulting two dimensional table.

> The basic premise behind your anaysis of these data seems to be that
> QATAL and WEQATAL in some sense are different *tenses* whose
> temporal uses are restricted.  But this is what is being discussed
> and therefore cannot be presumed.

Actually not.  The data you originally provided wasn't a full
2-dimensional table, since you didn't provide any breakdown of
occurrences of QATAL with respect to the "Modal", "Imperative",
"Final", "Cond. Prot", "Cond. Apod", "Gnomic", and "Other" categories;
and since there seemed to be 397 missing QATAL forms (I've been
assuming that these two facts are related, and that there are 397
QATAL forms distributed among these semantic categories, but you've
never seen fit to clarify this point):

>>>>> WEQATAL 6087              %               QATAL  13922    %
>>>>>         PAST      357     5,8             7450           53,5
>>>>>         PRESENT   192     3,15            2505           18
>>>>>         FUTURE    4100    67.35            965           6,9
>>>>>         PERFECT   55      0,9             2605           18,7
>>>>>         MODAL     147     2,41
>>>>>         IMPERATIVE 643    10,56
>>>>>         FINAL     31      0,5
>>>>>         COND,PROT 312     5,12
>>>>>         COND,APOD 123     2,02
>>>>>         GNOMIC    48      0,78
>>>>>         OTHER     79      1,29
>>>>>                   6087
>>>>                                  [Adds up to 13525, 397 forms missing?]

Since you didn't give a full two-dimensional table, I had to reduce
the data down (by collapsing semantic categories together) in order to
arrive at something that was a proper two-dimensional table, before I
could apply the statistical analysis.  Collapsing the data from
different semantic categories together can only weaken the evidence
for distinct semantic distributions of QATAL vs. WEQATAL forms
(i.e. it can never cause a spurious artifactual appearance of distinct
distributions), so such collapsing is always a statistically safe
thing to do, with respect to the particular statistical goals being
pursued here.  (If I were trying to find the particular bifurcation of
these semantic categories into two groups which would result in the
_highest_ distinctness between the distributions of QATAL and WEQATAL
forms across the two semantic groupings, then it would be circular to
consider only the grouping of "PAST & PERFECT vs. "Other Meanings",
but that's not at all what I've been trying to do here -- I've just
been showing that a particular collapsing of semantic categories into
two groups shows a significant correlation between morphology and
semantics, without attempting to compare this grouping with any other
possible grouping, or claiming any special status for the grouping).

To illustrate this, I've re-done the statistical analysis so that only
the absolute minimum number of semantic categories necessary to get
the data in the form of a proper two-dimensional table are collapsed:

PAST    QATAL   7450
OTHER   QATAL    397

Again, output must be viewed with non-proportional font:

                                                13:09 Saturday, August 12, 2000

                        The FREQ Procedure

                    Table of SEMANT by CONJUG

               SEMANT     CONJUG

               Percent  |
               Row Pct  |
               Col Pct  |QATAL   |WEQATAL |  Total
               FUTURE   |    965 |   4100 |   5065
                        |   4.82 |  20.49 |  25.31
                        |  19.05 |  80.95 |
                        |   6.93 |  67.36 |
               OTHER    |    397 |   1383 |   1780
                        |   1.98 |   6.91 |   8.90
                        |  22.30 |  77.70 |
                        |   2.85 |  22.72 |
               PAST     |   7450 |    357 |   7807
                        |  37.23 |   1.78 |  39.02
                        |  95.43 |   4.57 |
                        |  53.51 |   5.86 |
               PERFECT  |   2605 |     55 |   2660
                        |  13.02 |   0.27 |  13.29
                        |  97.93 |   2.07 |
                        |  18.71 |   0.90 |
               PRESENT  |   2505 |    192 |   2697
                        |  12.52 |   0.96 |  13.48
                        |  92.88 |   7.12 |
                        |  17.99 |   3.15 |
               Total       13922     6087    20009
                           69.58    30.42   100.00

             Statistics for Table of SEMANT by CONJUG

      Statistic                     DF       Value      Prob
      Chi-Square                     4  12154.8415    <.0001
      Likelihood Ratio Chi-Square    4  12943.9213    <.0001
      Mantel-Haenszel Chi-Square     1   8638.8062    <.0001
      Phi Coefficient                       0.7794          
      Contingency Coefficient               0.6147          
      Cramer's V                            0.7794          

                              Sample Size = 20009

Here the hypothesis of "independence" or statistical non-interaction
between morphology and semantics is still rejected at the p <.0001
level (or five hundred times more conclusively than the criterion of
p < .05 which is usually considered sufficient), and Cramer's V, the
nominal measure of "effect size" or association, has a significantly
higher absolute value -- 0.7794 -- than the 0.6030 which was seen in
the previous calculations (when semantic categories were lumped into
two broad groups).  The ordinal "effect size" / association measures
given in the SAS output listing in my previous post are not available
here (since all 2x2 tables are automatically ordinal, but a 4x2
nominal table such as the one here is not ordinal).

> Before we either presume that QATALs and WEQATALs *are* marked for
> tense, or reject the possibility that one and the same form of
> finite verbs can occur both with past, present and future reference,
> a serious discourse analysis of the material must be undertaken.

Actually, for the purposes of the statistical analysis above, the
nature of the semantic categories is irrelevant; we could re-label
them as "APPLE", "BANANA", "ORANGE", and "CUMQUAT", and the results of
the statistical calculations would come out exactly the same.  As long
as you have a reliable procedure for deciding which category a word
belongs to, and this procedure is consistent across QATAL and WEQATAL
forms, then that alone is sufficient in itself for the particular type
of statistical analysis I'm doing here (which therefore does not
depend on deep considerations and controversial philosophical
questions of tense/mood/aspect).

> Can the waw in the WEQATALs be explained as a simple conjunction?
> Can we explain why a conjunction is needed where the WEQATALs occur?
> And we must of course not forget the penultimate stress.  Although
> this stress is not consistently used, it is done so often that there
> can be no doubt that either those who wrote the text or some of
> those who at some point copied it, wanted to use this stress as a
> distinction.  But is this distinction just phonetic, or is it
> pragmatic, or is it semantic?

I'm not sure what the question "Is this stress distinction just
phonetic, or is it pragmatic, or is it semantic?" really means.  The
stress placement of final-syllable-stressed _w at qaatalTII_ is not "just
phonetic", since it is not allophonic or a matter of phonetic
implementation (i.e. is not sub-phonemic).  Therefore, it is
_phonological_ (which is a different thing than "phonetic").  This
phonological pattern is associated with a meaning difference in some
way (whether you would regard this as "semantic" or "pragmatic"), so
that stress positioning is therefore a matter of morphology as well as
phonology.  Here it is the _morphological distinction_ (rather than
the raw phonological stress patterns) whose meaning you can try to

Some of the apparent "inconsistency" in the _w at qaatalTII_ stress shift
(though admittedly not all) is actually due to the general Hebrew
phonological phenomenon of blocking of stress-shifts in "pausal"
(phrase-final) position; this purely phonological constraint affects
all relevant Hebrew stress-shifts (as discussed at length in my
dissertation).  This is hardly the only case in the languages of the
world where two morphological categories have identical phonological
realizations in certain cases (to pick a semi-random example, in Latin
the ablative singular ending of the 1st. declension is phonologically
identical to the dative singular ending of the 1st. declension, both
having the phonological shape _-o_).

> I would like to stress that I have not claimed that my statistics of
> QATAL and WEQATAL show that these forms are parts of one and the
> same semantic group (conjugation).  I have not even claimed that the
> material show that QATAL and WEQATAL are not aspects (which I
> believe that they are).  What I have claimed is that the statistics
> shows what they are not; they are not tenses, and they are not
> aspects in the English sense of the word.
But when you ask "Can the waw in the WEQATALs be explained as a simple
conjunction?", what you're suggesting is that WEQATAL should be purely
"compositional" in meaning, in which case the meaning of WEQATAL
should be a combination of the meaning of WE- (an ordinary conjunction
without inherent tense/mood/aspect meaning) together with the meaning
of plain QATAL.  This can be formulated as a hypothesis of the formal
statistical "independence" of a QATAL vs. WEQATAL variable with
respect to a semantic meaning variable.  It is this hypothesis (of the
posited identical relative semantic frequency distributions of QATAL
and WEQATAL) that I have shown above to be rejected five hundred times
more conclusively than is usually considered necessary statistically.
If you would provide data for WAYYIQTOL vs. WEYIQTOL vs. YIQTOL in a
form that could be put into a proper two-dimensional table, I'm pretty
sure that I could also show that the "null hypothesis" of independence
(or simple compositional semantics) would be conclusively rejected for
WAYYIQTOL vs. the other two; it would be an interesting empirical
question whether WEYIQTOL would be statistically independent from the
other two.  You may have the data that would pretty much conclusively
settle the question of whether or not WEYIQTOL is a distinct
morphological category, but I couldn't calculate this out until I'm
given your data in a form which can be put into a proper
two-dimensional table.

Henry Churchyard   churchh at usa.net   http://www.crossmyt.com/hc/

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