QATAL C/RT [Statistics]

Henry Churchyard churchh at usa.net
Tue Aug 1 23:35:26 EDT 2000


> Date: Tue, 1 Aug 2000 18:08:03 +0200
> From: Rolf Furuli <furuli at online.no>
> Subject: LONG Re: QATAL C/RT [Statistics]

> Henry Churchyard wrote:

>>> From: Rolf Furuli <furuli at online.no
>>> Date: Tue, 25 Jul 2000 19:31:12 +0200

>>> 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?]


>> If you say that "PAST" and "PERFECT" meanings are the proper
>> province of QATAL, and the other meanings are the proper province
>> of WEQATAL, then at most ((13922-(7450+2605))/13922) or 28% of
>> QATAL forms have "unexpected" meanings, while only ((357+55)/6087)
>> or 7% of WEQATAL forms have "unexpected" meanings. [...]  So all in
>> all, I'm actually surprised by how strongly your statistics
>> distinguish WEQATAL from QATAL.  If you ran a statistical "level of
>> significance" test on the following table, it would probably come
>> out fairly strong:

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


> Statistics can be of course read in different ways, particularly if
> the premises are different. I take the English system of tense and
> aspect as a point of departure, because it can be clearly defined. I
> am not aware of a better explanation than the one given by Mari
> Broman Olsen, and I therefore use her model. As a background to my
> arguments, let me give a sketch of the English system based on
> Broman Olsen:


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).  In a lot of cases, social scientists would kill to get
2-by-2 tables with the weight of the data as strongly distributed
along a diagonal of the table as is the case with 412:10065::5675:3470
and 412:10065::5675:3867 (still not entirely sure which of these two
represents the actual data here).

I fed the following lines as input into the SAS statistical program,
and got the output appended below (must use a non-proportional font to
view):


OPTIONS LS = 80;
TITLE 'FURULI WEQATAL VS. QATAL:';
DATA;
INPUT SEMANT CONJUG COUNT;
LINES;
0 0 412
0 1 10065
1 0 5675
1 1 3867
PROC FREQ; WEIGHT COUNT;
TABLES SEMANT*CONJUG / MEASURES CHISQ;
OUTPUT OUT=freqdata MEASURES;
PROC PRINT DATA=freqdata;



                     FURULI WEQATAL VS. QATAL:
                                                21:31 Tuesday, August 1, 2000

                         The FREQ Procedure

                     Table of SEMANT by CONJUG

                SEMANT     CONJUG

                Frequency|
                Percent  |
                Row Pct  |
                Col Pct  |       0|       1|  Total
                ---------+--------+--------+
                       0 |    412 |  10065 |  10477
                         |   2.06 |  50.28 |  52.34
                         |   3.93 |  96.07 |
                         |   6.77 |  72.24 |
                ---------+--------+--------+
                       1 |   5675 |   3867 |   9542
                         |  28.35 |  19.32 |  47.66
                         |  59.47 |  40.53 |
                         |  93.23 |  27.76 |
                ---------+--------+--------+
                Total        6087    13932    20019
                            30.41    69.59   100.00


              Statistics for Table of SEMANT by CONJUG

       Statistic                     DF       Value      Prob
       ------------------------------------------------------
       Chi-Square                     1   7280.0923    <.0001
       Likelihood Ratio Chi-Square    1   8236.6477    <.0001
       Continuity Adj. Chi-Square     1   7277.4678    <.0001
       Mantel-Haenszel Chi-Square     1   7279.7287    <.0001
       Phi Coefficient                      -0.6030          
       Contingency Coefficient               0.5164          
       Cramer's V                           -0.6030          


                         The FREQ Procedure

              Statistics for Table of SEMANT by CONJUG

       Statistic                              Value       ASE
       ------------------------------------------------------
       Gamma                                -0.9457    0.0029
       Kendall's Tau-b                      -0.6030    0.0050
       Stuart's Tau-c                       -0.5542    0.0054

       Somers' D C|R                        -0.5554    0.0054
       Somers' D R|C                        -0.6548    0.0050

       Pearson Correlation                  -0.6030    0.0050
       Spearman Correlation                 -0.6030    0.0050

                        Sample Size = 20019


Here you see 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).

Finally, the three "nominal" measures of "effect size" or association
shown at the end of the first statistics listing, as well as the
"ordinal" measures of "effect size" or association shown in the second
statistics listing (available here since all 2x2 tables are by
definition ordinal tables), have values which are all in the 0.5-0.6
range (except for Gamma, which generally has a meaninglessly inflated
value in tables with very few rows and columns).  These "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%.

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:

              YIQTOL    WEYIQTOL    WAYYIQTOL
Meaning 1       
Meaning 2
Meaning 3
Meaning 4
  ...

(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.)

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



More information about the b-hebrew mailing list