Signal detection estimates of sensitivity
d′ and likelihood criterion
β were used to measure performance in the different conditions (Green & Swets,
1966/1974). These values are reported in
Table 1. We will first discuss the
d′ values, which are also summarized in
Figure 3.
In carrying out the hypothesis tests below, it would be appropriate to correct for multiple tests by a Bonferroni correction. However, for all of the tests in this experiment and the succeeding one, a Bonferroni correction would not change any conclusions as the reader can verify. Consequently, we simply present the p values (or bounds on the p values) for each test.
A
d′ value of 0 corresponds to chance performance, and a
d′ value of 3.5 corresponds to a practically perfect performance. The
d′ value in the FF condition was significantly different from 0 (
z = 14.838,
p < .0001, one tailed). The one-tailed test is justified as it is plausible to assume
d′ ≥ 0. The participants, when able to observe the entire face, could classify the pairs as siblings or not siblings markedly above chance level. The
d′ values are similar to those that we have found in earlier related work (Maloney & Dal Martello,
2006). The
d′ value in the LHM condition was also significantly different from 0 (
z = 6.486,
p < .0001, one tailed). When the lower half of the face was hidden, the observers could still discriminate well between sibling and nonsibling pairs. Performance in the FF and LHM conditions did not differ significantly (
z = 0.553,
p = .580, two tailed). The absence of information from the lower half of the face resulted in a small decrease in sensitivity that was not statistically significant.
The d′ value in the UHM condition was significantly different from 0 ( z = 5.440, p < .0001; one tailed): Participants can classify the pairs at a level above chance even if the upper half of the face is hidden. It appears that there are useful signals for kin recognition in the lower half of the face as well. Performance in the UHM condition ( d′ = 0.41) was significantly worse than either the FF condition ( z = −7.104, p < .0001) or the UHM condition ( z = −6.486, p < .0001). Although it was still possible for the observers to detect relatedness at a level above chance when just the bottom half of the face was visible, the performance in this condition deteriorated markedly when compared with the other two conditions.
We emphasize that, when we fail to reject a null hypothesis, it would not be correct to conclude that the null hypothesis is true or that we have evidence in favor of the null hypothesis. This is the common fallacy of “accepting the null hypothesis” (see Loftus,
1996). When, for example, we do not reject the null hypothesis that the
d′ value for the LHM condition was equal to that for the FF condition, we have not shown that the
d′ values are equal or that the lower half of the face adds nothing to performance in judging relatedness. We have simply shown that we cannot reliably measure the difference with our experimental design: The difference is correspondingly small, and the best information available for the magnitude of the difference is the estimates of
d′ in
Table 1 and the accompanying estimates of their standard deviations.
If the information available in the upper and lower halves of the face were statistically independent and if there were no additional sources of information available only in the FF condition (the “full-face signals” discussed in the
Introduction), then we would be able to predict the
d′ value for the full face from the
d′ values in the other two conditions (Green & Swets,
1966/1974):
where
d′
_{FF},
d′
_{UHM}, and
d′
_{LHM} are the
d′ values in the three corresponding conditions. If we form a prediction of
d′
_{FF} based on the values for the other two conditions in
Table 1, we find that this prediction,
$ d ^ F \u2062 F \u2032$
= 1.196, is remarkably close to the value observed,
d′
_{FF} = 1.187, and that the two values are not significantly different (
p > .05). Thus, although the
d′ value for the FF condition was not significantly different from that for the LHM condition, the small difference observed is consistent with the combination of statistically independent information from the two halves of the face.
In conclusion, there are useful cues to kinship available when either the upper or the lower half of the face is visible, but the upper half of the face contains almost as much useful information as the entire face. The results are also consistent with the claim that statistically independent information from the two halves of the face is combined in the FF condition and that the contribution of full-face signals in collateral kin recognition is negligible. We will return to this point in the
General discussion section.
The
β values reported in
Table 1 measure the bias of the response toward classifying as kin or not kin. The
β values for each condition are not significantly different from one another (
p > .05). That is, observers did not show any change in bias because of the presence or absence of the masks. Most important, they do not become more cautious (adopting a stricter criterion) when just half of a face is visible.
Note that the three conditions showed a common bias. We tested the β values against 1 and, in all conditions, the difference from 1 was significant ( p < .01) in all cases. The actual prior odds that the pairs are related are 1:1 (half of the pairs portray siblings), and the observers were given this information. Still, the observers were slightly biased in favor of classifying the pairs as related. That is, they err in the direction of misclassifying unrelated pairs as related (Type 1 error).