2.7 Final conclusions
3.2.3 Testing hypotheses
Detailed statistical analyses were conducted to test the hypotheses. We describe briefly the procedures, however a reader not interested in statistical details may skip this part and read only the conclusions under each subsection.
3.2. Results 77
Hypothesis 5: Scalar implicature of “most” will be evaluated as true on a highly significant level.
χ2 tests for scalar implicatures of “most” in both groups (2a and 2b) showed a significant inequality of subjects’ scores (ranging between 0 and 10)4 for both
positive and negative premises. (2a – for “most”: χ2(10) = 135.450,p=.000and for “mostnot”: χ2(10) = 140.950, p=.000; 2b – for “most”: χ2 = 73.3, p=.000
and for “mostnot”: χ2 = 33.7,p=.000)
Conclusion 4. This result together with the analysis of histograms of frequency distribution for these variables displaying the clear negative skew in each of four cases (peaks at the value of 10) allows to conclude that hypothesis 5 can be sustained.
Hypothesis 6: Weak scalar implicature of “some” will be evaluated as true on a highly significant level.
χ2 tests for weak scalar implicature of “some” showed a significant inequality of subjects’ scores (0−10) for both positive and negative premises. For “some”:
χ2(10) = 275.583, p=.000 and for “somenot”: χ2(10) = 204.083, p=.000.
Conclusion 5. The above result together with the analysis of relevant histograms displaying the clear negative skew in both cases (peaks at 10) allows to conclude that hypothesis 6 can be sustained.
Hypothesis7: “Most” has stronger existential import than the univer- sal quantifier. Negative premises have weaker existential import than positive premises.
Mann-Whitney tests were conducted to check the between-subject effect, namely to compare so-called existential import of premises with “most” with so-called existential import of universal premises. Positive and negative premises were compared separately, namely we compared “most” with “all” with regard to so- called existential import, and separately “mostnot” with “no”. The analysis confirmed our predictions. Significantly more subjects evaluated conclusions with “some” as correct for premises with “most” (M dn = 6)5 than for premises with
“all” (M dn = 2): U = 870, z = −2.235, p = .013 (exact 1-tailed), effect size
r =−.227. The effect was even stronger for the comparison between “mostnot” and “no”. Significantly more subjects evaluated “somenot” conclusions as true for premises with “mostnot” (M dn= 6) than for premises with “no” (M dn = 1):
U = 478.5 z =−5.075 p=.000, effect size: r =−.515.
4Subjects’ scores for this variables ranged from0to10since there were as many as10tasks
of a given form to evaluate.
Further, we checked whether there is a significant within-subject difference with respect to negation, so we compared “most” with “mostnot” and “all” with “no” with regard to so-called existential import. We expected negation to weaken so-called existential import. Wilcoxon signed-rank test was conducted to check both within-subject effects. However, for the comparison between “most” and “mostnot”, we got slightly stranger so-called existential import for “mostnot” than for “most” and the result was not significant even for the 2-tailed hypothesis. Only the comparison between “all” and “no” confirmed the directorial hypothesis. Subjects evaluated “somenot” conclusions as correct inferences from premises with “no” (M dn = 1) with significantly lower frequency than “some” conclusions as correct inferences from premises with “all” (M dn = 2): z = −3.237, (T = 55.5), p < .0001 (exact 1-tailed), effect size: r=−.330.
Conclusion 6. On the basis of our analysis we conclude that, as far as pas- sive logical competence is concerned, premises with “most” are characterized with stronger so-called existential import than universal premises. Negation weakens existential import, but only in the case of universal quantifier, so “no” has weaker existential import than “all”, but “most”- and “mostnot”-premises do not differ in this respect. Thus hypothesis 7 is sustained.
Hypothesis8: The strong scalar implicature of “some” is less frequent than the weak implicature.
We expected the strong scalar implicature of “some” to be evaluated as a correct inference with much lower frequency than the weak implicature. Mann-Whitney tests were conducted to check the difference between the strong and the weak implicatures separately for positive and negative premises with “some”. Accord- ing to our predictions, significantly more subjects evaluated as a correct inference from positive premises with “some” the weak implicature (M dn = 10) than the strong implicature (M dn = 6): U = 319.5 , z = −6.478 , p < .0001, effect size:r = −.658. A similar result was obtained for premises with “somenot”: the weak implicature (M dn = 10) displayed significantly higher frequency than the strong implicature (M dn = 5): U = 283.5, z = −6.628, p < .0001, effect size:
r=−.673.
Additionally, we checked whether there is a within-subject difference with respect to negation in the premise. Wilcoxon signed-rank tests were conducted to compare frequency of the strong implicature of “some”- versus “somenot”- premises on the one hand, and frequency of the weak implicature of “some”- versus “somenot”-premises on the other. None of these tests were significant.
Conclusion 7. Based on the above analysis we conclude that, as far as passive logical competence is concerned, the weak implicature of “some” is characterized by a much stronger impact on reasoning (measured as the frequency of evaluating by people such inferences as correct) than the strong implicature, so hypothesis
3.2. Results 79 8 is sustained. Positive and negative premises with “some” do not differ in this respect.
Hypothesis 9: Particular and universal scalar implicatures of “most” are accepted as correct with different frequency.
Mann-Whitney tests were conducted to check how a form of a conclusion (uni- versal versus particular) influenced the frequency of accepting scalar implicatures of “most”. Universal and particular forms of implicature were compared sep- arately for positive and negative premises. There was no significant difference for the positive premise, but the result was significant for the negative premise. Significantly less subjects evaluated scalar implicature of “mostnot” as a true in- ference in the group in which it had the universal form “it is not the case, that no... ” (M dn = 8) than in the group where it had the particular form “some” (M dn = 10): U = 595, z = −2.090 , p = .036 (exact 2-tailed)6 r = −.233.
We explain this effect by the complicated form of this conclusion (negation used twice, or eventhree times – due to the double negation form of “no” in the Polish language).
Furthermore, the analysis was conducted to check the within-subject effect of negation, so we compared the frequency of “yes” responses to scalar implicature in the case of positive and negative premises with “most”. This was done separately in testsa (particular implicature) and b(universal implicature). “Yes” responses were expected to occur less frequently in the case of negative premises. This effect was significant only in group2b. Subjects’ frequency of evaluating as a true inference the universal implicature was lower in the case of a negative premise (M dn= 8, form “not the case that no...”) than in the case of a positive premise (M dn= 9, form: “not all”). The Wilcoxon signed-rank test’s result: z =−2.602, (T = 98),p=.004 (exact 1-tailed), r=−.291.
Conclusion 8. We cannot sustain hypothesis 9. The universal form of implicature had a significant impact on the (lower) frequency of evaluation this implicature as a correct inference only in the case of a negative premise, however it is doubtful that it was indeed universality of this form that played the role. Rather we believe that it was a complex form of the considered sentence (three negations) that lowered subjects’ willingness to evaluate it as true, especially that for the positive premise we did not observe any significant effect of the universal form. (What is even more, in the latter case the universal implicatures were even slightly more frequently evaluated as true than the particular ones.) Moreover, there was a significant difference between positive and negative premises with re- spect to subjects’ evaluating the universal implicature as correct, which was not observed for the particular implicature.
Hypothesis 10: All/M ost (N o/mostnot) inferences will be more frequent than All/Some (N o/Somenot) inferences, and similarly as frequent as M ost/Some (M ostnot/Somenot)inferences.
Since, to be correct, the inferences All/M ost and N o/M ostnot require the as- sumption of non-empty domains (due to classical definitions of these quantifiers), they can also be considered a case of existential import. We were interested in checking the difference between these inferences and the so-called existential import of the universal quantifier, thus All/Some and N o/Somenot inferences. We expected significantly higher frequency of inferencesAll/M ost(N o/M ostnot) evaluated as correct than of All/Some(N o/Somenot) inferences. Such an effect would confirm our theory that these inferences are dependent on scalar factors.
Mann-Whitney tests were conducted to check the between-group difference. We compared All/Some (N o/Somenot) inferences from test 1b with All/M ost
(N o/M ostnot) inferences from test2a and separately with the ones from test2b, which served here as a control group.
The comparisons were done separately for positive (“all”) and negative (“no”) premises. Our hypothesis was fully confirmed for the comparison between 1b
and 2a. In this case, significantly more subjects evaluated All/M ost inferences (M dn = 9) as correct than All/Some inferences (M dn = 2): U = 678.5,
z = −2.433 , p = .007, r = −.259, and significantly more subjects evaluated
N o/M ostnot inferences (M dn = 8) are correct than N o/Somenot inferences (M dn= 1): U = 533, z=−3.650, p=.000, r =−.389.
For the comparison between 1b and 2b the hypothesis was confirmed only for the premise with “no”, namely in this case significantly more subjects evalu- ated N o/M ostnot (M dn = 4.5) inferences as true than N o/Somenot inferences (M dn= 1): U = 724.5, z =−2.029,p=.021, effect size: r =−.216.
Subsequently, we compared reversed implicature with so-called existential im- port of “most”, thus with inferences: All/M ostwithM ost/Some. This was done by Mann-Whitney tests separately for negative and positive premises. Accord- ing to our predictions, there was no significant difference and based also on the mean percentages of evaluation such inferences as true we conclude that they have comparable frequency.
Conclusion 9. We conclude that, in general, sentences with “most” are ac- cepted as conclusions from universal premises more frequently than sentences with “some”. More precisely, N o/M ostnot inferences are evaluated as correct signifi- cantly more frequently than N o/Somenot inferences, however a similar effect for the positive premise was not clearly confirmed. Since, what is more, inferences M ost/Some and M ostnot/Somenot were evaluated as correct on an approxi- mately similar level as the considered All/Some (N o/M ostnot),hypothesis 10
3.2. Results 81