comparison to their negative leadership expectations and not in comparison to their actual expressed influence.
In most of the previous studies, this gender difference in the perceiver effect was not measured and controlled. If a study included more men than women, and if women also tended to see more leadership than men, then it would falsely appear that men would be seen more as leaders than women because of the hidden gender difference in the perceiver effect.
One last issue should be addressed. When we study a fixed effect, such as Pgender, we might ask how much of the variance in the perceiver effect gender explains. To answer this question, we conducted the run twice – once with gender variables in the model and once without them – and each time we determined the perceiver variance. Conducting such an analysis, we found that the variance due to the perceiver declined by 12.8% when we included gender variables in the model. Thus, we conclude that gender variables, mainly Pgender, explain 12.8% of the variance in the perceiver effect. Because the perceiver effect itself explains approximately 12.2% of the total variance (seeTable 1), gender explains only 1.6% of the total variance, at least when only the perceiver effect is considered. Including the fixed effects of gender in the model reduced the perceiver variance while having little or no effect on the target or relationship variance. This result bolsters the conclusion that the effect of gender in this study is at the level of the perceiver.
The strategy illustrated here could also be applied to the study of variables that predict the target effect. If such research were carried out, we would have a much better understanding of the percentage of variance that traits explain in the random effect of target than we currently have. That is, because error variance is measured in SRM analyses, a much larger proportion of variance would almost certainly be explained than is possible when using conventional methods.
status, but did find appreciable levels of understanding of how others view their status.
Kwan, John, Kenny, Bond, and Robins (2004) proposed applying the SRM to the study of self-perception.Kenny and West (2008)have extended the Kwan et al. (2004) approach and have developed a detailed, and relatively complicated, SRM approach to the comparison between self-perceptions and the self-perceptions of other members in the group. In this section, we apply their approach to the study of leadership.
Kenny and West (2008) propose four ways in which self- and other perception of leadership can differ:
Self-enhancement: Do people, on average, see themselves more as leaders than the other members of the group see them and more than they see others as leaders?
Assumed similarity (the weighting of perceiver effect): If a person tends to see others in the group as a leader, does the person also see himself or herself as a leader?
Self–other agreement (the weighting of the target effect): If a person tends to be seen by others in the group as a leader, does the person see himself or herself as a leader?
Relationship variance: Is there more relationship variance in self-ratings (i.e., self-enhancement) than in the ratings of others (i.e., other enhancement)?
We detail these four differences next:
First, the equality of the means of self-ratings and the ratings of others may produce differences. If the self on average sees himself or herself as more of a leader than do the members of the group and more of a leader than he or she sees others, then self-enhancement would be present. Also possible is self-effacement: People see themselves as less of a leader than they see others as a leader and less than others see them as a leader. This difference refers to the average across all perceivers and targets; later, we discuss individual differences.
Second, the weight of the perceiver effect in self-ratings, a parameter denoted as k inKenny and West (2008), may lead to differences. If k is 1, then the idiosyncratic tendency of people to see others as leaders (the perceiver effect) is reflected equally for perceptions of the self. That is, self-ratings operate in the same way as self-ratings of others. If k is less than 1 but greater than zero, there is some assumed similarity, but self is seen somewhat differently than others. While possible, we do not usually find much evidence for k to be greater than 1. It is also possible for k to be
zero (i.e., no assumed similarity) and even for k to be negative (i.e., a contrast effect).
Third, the weight of the target effect in self-ratings, a parameter denoted as q inKenny and West (2008), may produce differences. If q is 1, then the tendency of others to see a person as a leader is the same for the perception of self. That is, the target effect is equally well reflected in self-ratings as in ratings of others. If q is less than 1 but greater than zero, some self–other agreement is present, but self is seen somewhat differently than others. If q is greater than 1, then self has some sort of special insight: Self agrees more with a member in the group than two members agree with each other. It is possible for k to be zero (i.e., no self–other agreement) or even negative.
Although negative or zero values for k seem implausible for traditional measures of leadership, they may be more plausible for certain types of transformational leaders. Certain sorts of leaders (e.g., Gandhi) may feel that they are not leaders at all, but see themselves as followers instead.
Fourth, there are differences in relationship variances, denoted as s2g, for self and others. This is perhaps the most difficult comparison to understand.
Kwan et al. (2004) conceptualized relationship variance as individual differences in enhancement. Thus, for self, it would represent individual differences in self-enhancement. For example, persons who experience high self-efficacy (Foti & Hauenstein, 2007) may have larger scores in relational self-perceptions. If someone has a positive relationship effect for self, then that person would think he or she is better than others – even better than members of the group see the person. Following the reasoning of Kwan et al. (2004), perhaps this measure of the individual difference in self-enhancement might moderate leader effectiveness (Atwater & Yammarino, 1992). For other perception, we can interpret the relationship effect as other enhancement. That is, the relationship effect represents the biased perception of a perceiver of a given target. Thus, the variances in both of the relationship effects quantify the biases of the perceivers. The question in terms of the comparison of self and other is whether there is more or less variance in the two types of judgments.Kenny and West (2008)argue that, because self-perception is generally considered to be more biased than the perception of others, we might expect more relationship variance in self-perception than in other self-perception. To be clear, relationship variance reflects differences in bias, rather than the overall level of bias.
Another useful aspect of the approach taken byKenny and West (2008)is that we can evaluate for the first time whether self-ratings operate in the same way as do the ratings of others. In such a situation, we would find that the means and relationship variances were the same in the two types of
ratings and that k ¼ q ¼ 1. For instance,Kenny and West (2008)found that for ratings of emotions in groups of strangers, the model for self- and other ratings was the same.
The estimation of the model is complex and uses SEM, a method detailed later in this chapter. The parameters k and q can be viewed as factor loadings; that is, self-ratings load on perceiver and target factors. For instance, Jack’s self-rating of his leadership loads on Jack’s perceiver and target factors.
Example
TheDabbs and Ruback (1984)study included 20 same-gendered groups of size 5. To reduce the complexity of the analysis, we did not separate error from relationship; rather, we simply summed the indicators to form the measure. We consider both task-oriented leadership (the sum of ‘‘atten-tion,’’ ‘‘leadership,’’ and ‘‘contribution’’) and socioemotional leadership (sum of ‘‘encourages participation’’ and ‘‘shows interest’’).Table 4presents the parameters in ratings of self and others for the two types of leadership.
Of key importance is the test that both k (assumed similarity) and q (self–
other agreement) equal 1. Both assumed similarity parameters were less than 1 for self-ratings. Consistent with the prior analyses undertaken by Kenny (1994), we found that the k paths were greater than 0 but less than 1.
However, for q (self–other agreement), the pattern was different for the two types of leadership. For task-oriented leadership, the pattern was the typical one of q being less than 1: Members agree more with one another than they
Table 4. Comparison of Ratings of Self and Others.
Effect Task Oriented Socioemotional
Others Self Others Self
ma 15.307 15.140 10.260 10.680
kb 1.000c 0.656 1.000c 0.934
qd 1.000c 0.706 1.000c 1.357
s2ge 5.785 6.152 4.094 1.455
aMean rating.
bAssumed similarity parameter.
cFixed to 1.
dSelf–other agreement parameter.
eVariance in enhancement.
do with the self. Conversely, for socioemotional leadership, q is greater than 1: The self is a better informant concerning socioemotional leadership than are the other group members.
In addition, we examined whether the self-mean and dyadic means were different. As can be seen in Table 4, they were not. Although mean differences were found, they were rather small. These results are consistent with the results of Anderson et al. (2006), who found little or no self-enhancement for perceptions of status.
We also examined whether relationship variance differed for the percep-tion of self and others. We did find a large difference for socioemopercep-tional leadership. Contrary to our expectations, less relationship variance was found in self-ratings than in the ratings of others. Another explanation for the task and socioemotional differences in self-enhancement is that socioemotional leadership is more closely linked to group belongingness than to more observable task activities. In essence, members refrain from making judgments that decrease social acceptance so as to maintain their belongingness in a group (Anderson et al., 2006).
Generally, for both types of leadership, the parameter estimates are not all dramatically different in the two types of ratings, self and other. There is little or no self-enhancement or effacement, and both k and q are close to 1.
Although some differences in relationship variance are apparent, they arise only with socioemotional leadership. The bottom line is that it would not be especially problematic to include self-ratings in the measurement of the target and perceiver effects.