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Group and individual performance on a single-stage task as a function of distribution of individual performance
JOURNAL
Group
OF EXPERIMENTAL
and
as a Function
SOCIAL
Individual
Performance
of Distribution HOMER
3, 266273
PSYCHOLOGY
H.
JOHNSON Loyola
on a Single-Stage
of Individual AND
University,
(1967)
JAMES
M.
Task
Performance1 TORCIVIA
Chicago
In a test of predict,ions from a single-stage model of group problem-solving which considers initial performance, 263 college students aolved a simple mathematical puzzle. They then solved the puzzle again individually or in one of four pair-groups: (a) two initially right subjects (RR), (b) one initially right and one initially wrong subject (RW), (c) two initially wrong subjects whose initial answers were the same (WWs), and (d) two subjects who had different wrong answers initially (WWd). Major results indicate that (1) neither WWs nor WWd pair-groups improved their performance relative to W subjects working independently; (2) performance of RR subjects did not decrease; and (3) the relative certainty of correctness of initial solution was an accurate predictor of performance in RW pair-groups.
One of the most frequently occurring models of group problem-solving is the “pooling of resources” model. It is assumed that each individual possessesresources that are unshared by the other members of the group, and that pooling of these resources within the group gives it superioritS over the perfor’mance of individuals working independently. This pooling model has been labeled the complementary model by Steiner (1966)) and is similar to Model B of Lorge and Solomon (1955). Laughlin and Johnson (1966) have attempted to refine the complementary model by taking into account the ability level of the group members. More specifically, these authors predicted that a person working with a partner of greater or comparable ability will improve his performance relative to a person of his ability working alone, while a person working with a partner of less ability will not improve his performance relative to a person of his ability working alone. An expeCmcnta1 test confirmed this hypothesis with one exception: groups consisting of two persons of low ability did not improve relative to low ability individuals working independently. Apparently at low ability levels there is considerable overlap or homogeneity of performance-relevant knowledge, which results in ’ This research was supported by a grant from the Loyola Research Committee the senior author. 266
to
GROUP
AND
INDIVIDUAL
PERFORMANCE
26i
each individual’s contributing little unique or nonshared information in the group. The t,ask cited above can be conceptualized as consisting of a series of independent stages, and the grcat’er the number of stages the group has correct,, or about which the group has valid information, the greater the group performance. Another frequently occurring problem-solving task is the single-stage task. Prediction of group performance on this type of task is not only important in its own right but also because accurate prediction for the single-stage task may lead to an accurate prediction for complementary tasks which consist of a collection of stages. For the single-stage task the group has the ability to solve the prohlem if at least one of its members possesses the minimum ability required to solve the problem; thus, the group is potentially as productive as its most competent member. For example, with a simple mathematical puzzle, individuals either have the right answer or one of several wrong answers, and any group having at least one member who ran solve the problem correctly has the potential ability to be correct. Bot,h Steiner’s (1966) disjunctive model of problem solving and Lorge :mcl Solomon’s (1955) Model A can be used to predict group perfor,mance for the single-stage task by taking into account t’he initial performance of the group members. Bot,h models would predict that pair-groups consisting of two initially “right” individuals would produce the correct solution to the problem and pair-groups consisting of two initially Yvrong” individuals would produce an incorrect solution. Although the hypotheses of the experiment presented in t.hie paper are in accord with these predictions, it must he noted that there are reasons why this latter prediction may not be supported. One might hypothesize a “group facilitation effect” by which the interaction and discussion in the “wrong” pair-groups would increase the chances of a right solution occurring. This might be especially prominent in pair-groups in which members initially disagree on the solution, each advocating a different wrong solution. Thomas and Fink (1961) offer some empirical support for this assumption in that they found some tendency for groups of size two (relative to larger groups) to arrive at the correct solution even though both members were initially wrong. Their (post hoc) rationale for this trend cent.ered around the fact that majority pressures cannot appear in a two-person group; thus minority opinions, such as the correct solution (or discussion of steps leading to t,he correct solution), cannot be overruled or terminated because of majority pressures. This evidence was based on a small N and did not reach st,atistical significance. Pair-groups may also be composed of an individual who was initially right and an individual who was initially wrong. Prediction of the group
263
JOHNSON
AND
TORCIVIA
product for this pair-group is somewhat equivocal. Lorge and Solomon assume that “truth wins” and thus this pair-group should produce the correct solution. However, this prediction is based on the assumption that the correct solution would be readiIy recognized as such if it appeared. Although this assumption is valid for some single-stage tasks it is probably more frequently not the case, and the interest in this paper is with tasks in which it is not the case. Steiner’s model predicts potential (not actual) productivity and would postulate that this pair-group has the potential to be correct; however, this potential need not be realized, because of coordination difficulties. One such coordination problem involves the differential weighting of group-members’ contributions, i.e., the contribution of one member (whether right or wrong) is weighted to a greater degree than that of the other member. It is hypothesized that (in this type of situation) the weighting is determined by t,he reIative confidence of each group member as to the correctness of his initial solution. More specifically, it is hypothesized that an accurate predictor of the number of correct solutions produced by right-wrong pair-groups is the number of pair-groups in which the initially right member is more certain of the correctness of his solution than the initially wrong member.’ To summarize the predictions of this study, it is hypothesized that (a) pair-groups consisting of two initially right individuals will produce the correct solution, (b) pair-groups consisting of two initially wrong individuals will produce a wrong solut’ion, and (c) for pair-groups consisting of an initially right and an initially wrong individual, an accurate predictor of the number of correct solutions produced is the number of pairgroups in which the initially right individual is more certain of his solution than the initially wrong individual. METHOD The method here was similar to that used by Laughlin and Johnson (1966). The subjects were 263 undergraduate students in introductory and social psychology courses at Loyola University. They were given a sheet of paper on which appeared the following problem as used by Maier and Solem (1952). ‘Thomas and Fink (1961) have suggested three models of group problem-solving. However, the application of these models is restricted to situations in which the group’s product is expressed as a distribution of individual answers, and in the research presented here the group’s product is a single solution to the problem for the group. However, all three models would support the hypotheses made in this paper for right-right and wrong-wrong pair-groups. Prediction of a single outcome for right-wrong pair-groups from the Thomas and Fink models is somewhat equivocal, although from the logic of the models it appears that their rational model (“truth wins”) would predict 100% correct solutions and their consensus model would predict 50% correct solutions.
GROUP
AND
INDIVIDUAL
269
PERFORMANCE
,4 man bought a horse for $60.00 and sold it for $70.00. Then he bought it back again for $80.00 and sold it for $90.00. How much money did he make in the horse business? The ring
correct answer is $20.00, with $10.00 and $30.00 being the most frequently occurwrong answers. Subjects were asked t,o indicate what they believed to be the correct answer and also to indicate how certain they were that the answer they had given was the correct answer. For this latter measure subjects checked a six-point scale ranging from extremely certain to extremely uncertain. Immediately after the subjects had solved the problem individually, they were assigned to one of six treatments. In two of the treatments subjects who had the right solution (R) or the wrong solution (W) on the initial administration of the problem were asked to solve the problem again on an individual basis. In the other four treatments subjects then worked in pairs. All four of the possible types of pairs were assembled: (a) two subjects, both of whom had solved the problem correctly (RR), (b) one subject who had the correct solution and one subject who had a wrong solution (RW), (c) two subjects, both of whom had the same wrong solution (WWs), and (d) two subjects having different wrong solutions (WWd). Pair-groups were instructed to discuss the problem and arrive at a mutually agreed-upon solution to the problem as well as a mutual estimate of certainty (on a single answer sheet). A fifteen-minute time limit was imposed, and three pair-groups (two RW and a WWd) failed to reach agreement within the allotted time. Their data were eliminated from the study analysis. RESULTS
Table 1 reports the number of pair-groups or individuals in each treatment as well as the percent having the correct solution on the second administration of the problem. It is readily observable from the table that R individuals and RR pairs showed little, if any, decrease in performance on the second administration. It is also apparent from Table 1 that the WW pairs showed little improvement relative to W individuals on the second administration of the problem, and this was true for both WWs and WWd pair-groups. TABLE
1
CORRECTNESS AND CERTAINTY SCORES FOR THE SIX TREATMENT GROUPS Group
Na
RR pairs RW pairs WWs pairs WWd pairs R individuals W individuals
21 36 20 26 26 34
a N refers to number individual treatments.
Mean initial certainty
of pair-groups
Mean certainty, second admin.
Ye Correct, second admin.
5.78 5.36 4.85
6.00 5.14 5.30
5.10
5.19
8%
5.58 5.29
5.62 5.47
96% 9%
in group
treatments
100%
72% 10%
and number
of individuals
in
270
.lOHNSON
AND
TORCIVIA
The performance of the RW pair-groups was significantly better than that of W individuals working independently on t,he second administration of the problem (x2 = 27.18, p < .OOl, df = I), and significantly lower than that of R individuals working independently (x’ = 4.40, p < .05, df = 1). It is noted that 72% of these mixed groups produced correct solutions whereas only 50% should have done so if the correct individual prevailed in only half of the groups (x2 = 7.12, p < .Ol, c1f = 1). Seventytwo per cent is also significantly less than the 100% correct responses that would be expected from a “truth wins” model. It was hypothesized that an accurate predictor of performance would be the number of times the correct person was initially more certain of the correctness of his solution than the wrong partner was of his response. For the 36 RW pair-groups, in 18 pairs R certainty was greater than W certainty and 17 of these groups emerged with the correct solution; in 11 pairs R certainty was equal to W certainty and 7 of these groups emerged with the correct solution. In 7 pairs the R certainty was less than W certainty and only 2 of these groups emerged with the correct solution. Based on the hypot.heses that (a) all pair-groups in which R certainty is greater than W certainty will emerge with the correct solution, (b) all pair-groups in which W certainty is greater than R certainty will emerge with an incorrect solution, and (c) half of the pair groups in which R and W certainty are equal will obtain the correct answer. it would be predicted that 23.5 of the 36 RW groups would emerge with correct solutions. This expected 23.5 (65%) is not significantly different from the obtained 26 (72%) correct solutions (x” = .77, n.s., df = 1). Certainty scores. Table 1 also reports the mean certainty scores for the six treatment groups on the first and second administrations of the problem. Although these means are not relevant to the hypotheses of this study, certain trends are worthy of note. It is to be noted that most individuals were quite certain as to the correctness of their solution (six is the highest certainty score possible) on the first, administration of the problem, and that correct individuals tended to he more certain than wrong individuals (x2 = 28.48, p < ,001, CEf= I ) . The change in certainty from first to second administration of the problem is somewhat limited by the fact that most individuals were quite certain initially that their solution was correct. Chi-square analysis revealed that the only two categories in which a trend to increase in certainty occurred were the RR (p < .lO) and WWs (p < .25). Perhaps these trends are to be expected because in both of these types of pairgroups the members were in initial agreement concerning the solution and simply reinforced each other’s conviction.
GROUP
AND
INDIVIDUAL
PERFORMANCE
271
DISCUSSION
The results of this experiment confirm the predictions of a single-stage model of group problem-solving that takes into account the initial performance of the group members. Pair-groups consisting of initially R individuals did not diminish in performance, and pair-groups consisting of initially W individuals did not improve in performance. Prediction of the performance of RW pairs by taking into account the initial certainty of each member was demonstrated to be fairly accurate. The finding that WWs and WWd pairs showed no improvement relative to W individuals empirically confirms the theoretical assumption of those mathematical models of group problem-solving which assume that the group performance is simply a combination of members’ resources (e.g.! Large and Solomon, 1955; Restle, 1962; Steiner, 1966). If both of the pair-group members have the wrong solution on a single-stage task, the combination of these (wrong) resources in the group leads the group to urrive at the wrong solution. The finding that WWd groups were not superior to WWs or W individuals has additional implications in that disagreement (or heterogeneity) of wrong solutions on a single-stage task apparently does not help the group performance. Another interesting question not previously considered is whether or uot certainty is also an accurate predictor of the wrong solution that arises out of WWd pairs. For this analysis, groups in which the two members were of equal certainty have to be eliminated. There were 18 WWd pair-groups in which the initial certainty of one member was higher than the other member, and in only 10 of these pair-groups was the solution with the higher certainty rhosen as the group eolution. Thus, although certainty was an accurate predictor for RW groups, it does not appear to be very accurate for WWd groups. Rather, for this latt.er pairgrow, an equal-chance model appears more accurate. Some recent evidence from the laboratory at Loyola provides a clue to reconciling the discrepancy between the RW and WWd groups as to the accuracy of certainty as a predictor. It appears that, to some extent, initially W individuals (relative to initially R individuals) have lessknowledge about this type of task, have considered fewer alternative rolutions, and have less of a basis for choosing one solution over another. This apparently leads them to be more willing to accept ot,her soiutions in a group situation, regardless of their initial certainty. If this assumption iu valid, then the certainty formula should tend to underestimate the performance in the RW groups (because there will be some yielding of initially highly certain W’s), and should also favor an equal-chance formula more than
272
JOHNSON
AND
TORCIVIA
the certainty formula for prediction of WWd groups. The data of this study tend to support these hypotheses. This latter finding suggests that certainty in itself may not be sufficient to derive rather precise prediction of the group product, and that an additional variable may be needed. This additional variable is somewhat difficult to define conceptually or operationally, but seems to resemble the concept of informational support for an opinion as used by Smith, Bruner, and White (1956). Informational support is defined as the amount of information a person is capable of bringing to bear in appraising an opinion. It is reasonable to assume that persons who are highly uncertain as to the correctness of their solution have little informational support for their solution; however, apparently, persons who are highly certain may or may not have much informational support for their solution. Continuing this line of reasoning, it is assumed that for people with low informational support, certainty of correctness of solution is not a predictor. These people may be easily influenced by new information regardless of their initial certainty. For people with high informational support certainty of solution may be the determining factor as to which solution is adopted by the group. Summarizing the theory and findings discussed in this paper, it is assumed that single-stage tasks fall into two major categories: (a) those tasks for which the correct solution would be readily recognized as such (or verifiable as such), if it appeared, and (b) those tasks for which the correct solution is not readily recognized nor verifiable. For the former category, it is assumed that a “truth wins” model is appropriate, and that any group which has at least one member who is able to solve the problem correctly will arrive at the correct solution. However, it is hypothesized that if a group does not have at least one member who is able to solve the problem correctly, the group will not arrive at the correct solution. For the latter category of single-stage tasks, it is assumed that pair-groups in which both members initially have the correct soIution will arrive at the correct solution, and pair-groups in which both members initially have wrong solutions will arrive at the wrong solution. For pair-groups consisting of an initially right and an initially wrong individual, our tentative hypothesis is that “highest certainty wins” if the individuals’ level of informational support about the task is high, but with low levels of informational support an equal-chance model is appropriate and groups will arrive at a wrong solution as frequently as they arrive at a correct solution. REFERENCES P. IL., AND JOHNSON, H. H. Individual complementary task as a function of initial mental Social P.yychology, 1966, 2, 407414.
LAUGHLIN,
versus ahilit,p
group level.
performance Journal of
on a Ezperi-
GROUP
AND
INDIVIDUAL
PERFORMANCE
273
I., AND SOLOMON, H. Two models of group behavior in the solution of Eurekaproblems. Psychometrika, 1955,20, 139-148. AM.4~~~, N. R. I?., AND SOLEM. A. It. The contribution of a discussion leader to the quality of group thinking: The effective use of minority opinions. Human Relations. 1952, 5, 277-288. HESTLE, F. Speed and accuracy of cognitive achievement in small groups. In J. Criswell, H. Solomon, and P. Suppes (Eds.), Mathematical methods in small group pror~s~s. Stanford, California: Stanford University Press, 1962. Pp. 250-262. SMITH, M. B., BRUNER, J. S., AND WHITE, R. W. Opinions and personality. New York: Riley, 1956. STEINER, I. D. Models for inferring relationships between group size and potential group productivity. Behavioral Science, 1966, 11, 273-283. TIIO;MAF, E. J., AND FINK, C. F. Models of group problem solving. Journal of Abmmal and Social Psychology, 1961. 63, 5343. I,ORGE,
type
(Recrived
November
15, 1966)
Group
OF EXPERIMENTAL
and
as a Function
SOCIAL
Individual
Performance
of Distribution HOMER
3, 266273
PSYCHOLOGY
H.
JOHNSON Loyola
on a Single-Stage
of Individual AND
University,
(1967)
JAMES
M.
Task
Performance1 TORCIVIA
Chicago
In a test of predict,ions from a single-stage model of group problem-solving which considers initial performance, 263 college students aolved a simple mathematical puzzle. They then solved the puzzle again individually or in one of four pair-groups: (a) two initially right subjects (RR), (b) one initially right and one initially wrong subject (RW), (c) two initially wrong subjects whose initial answers were the same (WWs), and (d) two subjects who had different wrong answers initially (WWd). Major results indicate that (1) neither WWs nor WWd pair-groups improved their performance relative to W subjects working independently; (2) performance of RR subjects did not decrease; and (3) the relative certainty of correctness of initial solution was an accurate predictor of performance in RW pair-groups.
One of the most frequently occurring models of group problem-solving is the “pooling of resources” model. It is assumed that each individual possessesresources that are unshared by the other members of the group, and that pooling of these resources within the group gives it superioritS over the perfor’mance of individuals working independently. This pooling model has been labeled the complementary model by Steiner (1966)) and is similar to Model B of Lorge and Solomon (1955). Laughlin and Johnson (1966) have attempted to refine the complementary model by taking into account the ability level of the group members. More specifically, these authors predicted that a person working with a partner of greater or comparable ability will improve his performance relative to a person of his ability working alone, while a person working with a partner of less ability will not improve his performance relative to a person of his ability working alone. An expeCmcnta1 test confirmed this hypothesis with one exception: groups consisting of two persons of low ability did not improve relative to low ability individuals working independently. Apparently at low ability levels there is considerable overlap or homogeneity of performance-relevant knowledge, which results in ’ This research was supported by a grant from the Loyola Research Committee the senior author. 266
to
GROUP
AND
INDIVIDUAL
PERFORMANCE
26i
each individual’s contributing little unique or nonshared information in the group. The t,ask cited above can be conceptualized as consisting of a series of independent stages, and the grcat’er the number of stages the group has correct,, or about which the group has valid information, the greater the group performance. Another frequently occurring problem-solving task is the single-stage task. Prediction of group performance on this type of task is not only important in its own right but also because accurate prediction for the single-stage task may lead to an accurate prediction for complementary tasks which consist of a collection of stages. For the single-stage task the group has the ability to solve the prohlem if at least one of its members possesses the minimum ability required to solve the problem; thus, the group is potentially as productive as its most competent member. For example, with a simple mathematical puzzle, individuals either have the right answer or one of several wrong answers, and any group having at least one member who ran solve the problem correctly has the potential ability to be correct. Bot,h Steiner’s (1966) disjunctive model of problem solving and Lorge :mcl Solomon’s (1955) Model A can be used to predict group perfor,mance for the single-stage task by taking into account t’he initial performance of the group members. Bot,h models would predict that pair-groups consisting of two initially “right” individuals would produce the correct solution to the problem and pair-groups consisting of two initially Yvrong” individuals would produce an incorrect solution. Although the hypotheses of the experiment presented in t.hie paper are in accord with these predictions, it must he noted that there are reasons why this latter prediction may not be supported. One might hypothesize a “group facilitation effect” by which the interaction and discussion in the “wrong” pair-groups would increase the chances of a right solution occurring. This might be especially prominent in pair-groups in which members initially disagree on the solution, each advocating a different wrong solution. Thomas and Fink (1961) offer some empirical support for this assumption in that they found some tendency for groups of size two (relative to larger groups) to arrive at the correct solution even though both members were initially wrong. Their (post hoc) rationale for this trend cent.ered around the fact that majority pressures cannot appear in a two-person group; thus minority opinions, such as the correct solution (or discussion of steps leading to t,he correct solution), cannot be overruled or terminated because of majority pressures. This evidence was based on a small N and did not reach st,atistical significance. Pair-groups may also be composed of an individual who was initially right and an individual who was initially wrong. Prediction of the group
263
JOHNSON
AND
TORCIVIA
product for this pair-group is somewhat equivocal. Lorge and Solomon assume that “truth wins” and thus this pair-group should produce the correct solution. However, this prediction is based on the assumption that the correct solution would be readiIy recognized as such if it appeared. Although this assumption is valid for some single-stage tasks it is probably more frequently not the case, and the interest in this paper is with tasks in which it is not the case. Steiner’s model predicts potential (not actual) productivity and would postulate that this pair-group has the potential to be correct; however, this potential need not be realized, because of coordination difficulties. One such coordination problem involves the differential weighting of group-members’ contributions, i.e., the contribution of one member (whether right or wrong) is weighted to a greater degree than that of the other member. It is hypothesized that (in this type of situation) the weighting is determined by t,he reIative confidence of each group member as to the correctness of his initial solution. More specifically, it is hypothesized that an accurate predictor of the number of correct solutions produced by right-wrong pair-groups is the number of pair-groups in which the initially right member is more certain of the correctness of his solution than the initially wrong member.’ To summarize the predictions of this study, it is hypothesized that (a) pair-groups consisting of two initially right individuals will produce the correct solution, (b) pair-groups consisting of two initially wrong individuals will produce a wrong solut’ion, and (c) for pair-groups consisting of an initially right and an initially wrong individual, an accurate predictor of the number of correct solutions produced is the number of pairgroups in which the initially right individual is more certain of his solution than the initially wrong individual. METHOD The method here was similar to that used by Laughlin and Johnson (1966). The subjects were 263 undergraduate students in introductory and social psychology courses at Loyola University. They were given a sheet of paper on which appeared the following problem as used by Maier and Solem (1952). ‘Thomas and Fink (1961) have suggested three models of group problem-solving. However, the application of these models is restricted to situations in which the group’s product is expressed as a distribution of individual answers, and in the research presented here the group’s product is a single solution to the problem for the group. However, all three models would support the hypotheses made in this paper for right-right and wrong-wrong pair-groups. Prediction of a single outcome for right-wrong pair-groups from the Thomas and Fink models is somewhat equivocal, although from the logic of the models it appears that their rational model (“truth wins”) would predict 100% correct solutions and their consensus model would predict 50% correct solutions.
GROUP
AND
INDIVIDUAL
269
PERFORMANCE
,4 man bought a horse for $60.00 and sold it for $70.00. Then he bought it back again for $80.00 and sold it for $90.00. How much money did he make in the horse business? The ring
correct answer is $20.00, with $10.00 and $30.00 being the most frequently occurwrong answers. Subjects were asked t,o indicate what they believed to be the correct answer and also to indicate how certain they were that the answer they had given was the correct answer. For this latter measure subjects checked a six-point scale ranging from extremely certain to extremely uncertain. Immediately after the subjects had solved the problem individually, they were assigned to one of six treatments. In two of the treatments subjects who had the right solution (R) or the wrong solution (W) on the initial administration of the problem were asked to solve the problem again on an individual basis. In the other four treatments subjects then worked in pairs. All four of the possible types of pairs were assembled: (a) two subjects, both of whom had solved the problem correctly (RR), (b) one subject who had the correct solution and one subject who had a wrong solution (RW), (c) two subjects, both of whom had the same wrong solution (WWs), and (d) two subjects having different wrong solutions (WWd). Pair-groups were instructed to discuss the problem and arrive at a mutually agreed-upon solution to the problem as well as a mutual estimate of certainty (on a single answer sheet). A fifteen-minute time limit was imposed, and three pair-groups (two RW and a WWd) failed to reach agreement within the allotted time. Their data were eliminated from the study analysis. RESULTS
Table 1 reports the number of pair-groups or individuals in each treatment as well as the percent having the correct solution on the second administration of the problem. It is readily observable from the table that R individuals and RR pairs showed little, if any, decrease in performance on the second administration. It is also apparent from Table 1 that the WW pairs showed little improvement relative to W individuals on the second administration of the problem, and this was true for both WWs and WWd pair-groups. TABLE
1
CORRECTNESS AND CERTAINTY SCORES FOR THE SIX TREATMENT GROUPS Group
Na
RR pairs RW pairs WWs pairs WWd pairs R individuals W individuals
21 36 20 26 26 34
a N refers to number individual treatments.
Mean initial certainty
of pair-groups
Mean certainty, second admin.
Ye Correct, second admin.
5.78 5.36 4.85
6.00 5.14 5.30
5.10
5.19
8%
5.58 5.29
5.62 5.47
96% 9%
in group
treatments
100%
72% 10%
and number
of individuals
in
270
.lOHNSON
AND
TORCIVIA
The performance of the RW pair-groups was significantly better than that of W individuals working independently on t,he second administration of the problem (x2 = 27.18, p < .OOl, df = I), and significantly lower than that of R individuals working independently (x’ = 4.40, p < .05, df = 1). It is noted that 72% of these mixed groups produced correct solutions whereas only 50% should have done so if the correct individual prevailed in only half of the groups (x2 = 7.12, p < .Ol, c1f = 1). Seventytwo per cent is also significantly less than the 100% correct responses that would be expected from a “truth wins” model. It was hypothesized that an accurate predictor of performance would be the number of times the correct person was initially more certain of the correctness of his solution than the wrong partner was of his response. For the 36 RW pair-groups, in 18 pairs R certainty was greater than W certainty and 17 of these groups emerged with the correct solution; in 11 pairs R certainty was equal to W certainty and 7 of these groups emerged with the correct solution. In 7 pairs the R certainty was less than W certainty and only 2 of these groups emerged with the correct solution. Based on the hypot.heses that (a) all pair-groups in which R certainty is greater than W certainty will emerge with the correct solution, (b) all pair-groups in which W certainty is greater than R certainty will emerge with an incorrect solution, and (c) half of the pair groups in which R and W certainty are equal will obtain the correct answer. it would be predicted that 23.5 of the 36 RW groups would emerge with correct solutions. This expected 23.5 (65%) is not significantly different from the obtained 26 (72%) correct solutions (x” = .77, n.s., df = 1). Certainty scores. Table 1 also reports the mean certainty scores for the six treatment groups on the first and second administrations of the problem. Although these means are not relevant to the hypotheses of this study, certain trends are worthy of note. It is to be noted that most individuals were quite certain as to the correctness of their solution (six is the highest certainty score possible) on the first, administration of the problem, and that correct individuals tended to he more certain than wrong individuals (x2 = 28.48, p < ,001, CEf= I ) . The change in certainty from first to second administration of the problem is somewhat limited by the fact that most individuals were quite certain initially that their solution was correct. Chi-square analysis revealed that the only two categories in which a trend to increase in certainty occurred were the RR (p < .lO) and WWs (p < .25). Perhaps these trends are to be expected because in both of these types of pairgroups the members were in initial agreement concerning the solution and simply reinforced each other’s conviction.
GROUP
AND
INDIVIDUAL
PERFORMANCE
271
DISCUSSION
The results of this experiment confirm the predictions of a single-stage model of group problem-solving that takes into account the initial performance of the group members. Pair-groups consisting of initially R individuals did not diminish in performance, and pair-groups consisting of initially W individuals did not improve in performance. Prediction of the performance of RW pairs by taking into account the initial certainty of each member was demonstrated to be fairly accurate. The finding that WWs and WWd pairs showed no improvement relative to W individuals empirically confirms the theoretical assumption of those mathematical models of group problem-solving which assume that the group performance is simply a combination of members’ resources (e.g.! Large and Solomon, 1955; Restle, 1962; Steiner, 1966). If both of the pair-group members have the wrong solution on a single-stage task, the combination of these (wrong) resources in the group leads the group to urrive at the wrong solution. The finding that WWd groups were not superior to WWs or W individuals has additional implications in that disagreement (or heterogeneity) of wrong solutions on a single-stage task apparently does not help the group performance. Another interesting question not previously considered is whether or uot certainty is also an accurate predictor of the wrong solution that arises out of WWd pairs. For this analysis, groups in which the two members were of equal certainty have to be eliminated. There were 18 WWd pair-groups in which the initial certainty of one member was higher than the other member, and in only 10 of these pair-groups was the solution with the higher certainty rhosen as the group eolution. Thus, although certainty was an accurate predictor for RW groups, it does not appear to be very accurate for WWd groups. Rather, for this latt.er pairgrow, an equal-chance model appears more accurate. Some recent evidence from the laboratory at Loyola provides a clue to reconciling the discrepancy between the RW and WWd groups as to the accuracy of certainty as a predictor. It appears that, to some extent, initially W individuals (relative to initially R individuals) have lessknowledge about this type of task, have considered fewer alternative rolutions, and have less of a basis for choosing one solution over another. This apparently leads them to be more willing to accept ot,her soiutions in a group situation, regardless of their initial certainty. If this assumption iu valid, then the certainty formula should tend to underestimate the performance in the RW groups (because there will be some yielding of initially highly certain W’s), and should also favor an equal-chance formula more than
272
JOHNSON
AND
TORCIVIA
the certainty formula for prediction of WWd groups. The data of this study tend to support these hypotheses. This latter finding suggests that certainty in itself may not be sufficient to derive rather precise prediction of the group product, and that an additional variable may be needed. This additional variable is somewhat difficult to define conceptually or operationally, but seems to resemble the concept of informational support for an opinion as used by Smith, Bruner, and White (1956). Informational support is defined as the amount of information a person is capable of bringing to bear in appraising an opinion. It is reasonable to assume that persons who are highly uncertain as to the correctness of their solution have little informational support for their solution; however, apparently, persons who are highly certain may or may not have much informational support for their solution. Continuing this line of reasoning, it is assumed that for people with low informational support, certainty of correctness of solution is not a predictor. These people may be easily influenced by new information regardless of their initial certainty. For people with high informational support certainty of solution may be the determining factor as to which solution is adopted by the group. Summarizing the theory and findings discussed in this paper, it is assumed that single-stage tasks fall into two major categories: (a) those tasks for which the correct solution would be readily recognized as such (or verifiable as such), if it appeared, and (b) those tasks for which the correct solution is not readily recognized nor verifiable. For the former category, it is assumed that a “truth wins” model is appropriate, and that any group which has at least one member who is able to solve the problem correctly will arrive at the correct solution. However, it is hypothesized that if a group does not have at least one member who is able to solve the problem correctly, the group will not arrive at the correct solution. For the latter category of single-stage tasks, it is assumed that pair-groups in which both members initially have the correct soIution will arrive at the correct solution, and pair-groups in which both members initially have wrong solutions will arrive at the wrong solution. For pair-groups consisting of an initially right and an initially wrong individual, our tentative hypothesis is that “highest certainty wins” if the individuals’ level of informational support about the task is high, but with low levels of informational support an equal-chance model is appropriate and groups will arrive at a wrong solution as frequently as they arrive at a correct solution. REFERENCES P. IL., AND JOHNSON, H. H. Individual complementary task as a function of initial mental Social P.yychology, 1966, 2, 407414.
LAUGHLIN,
versus ahilit,p
group level.
performance Journal of
on a Ezperi-
GROUP
AND
INDIVIDUAL
PERFORMANCE
273
I., AND SOLOMON, H. Two models of group behavior in the solution of Eurekaproblems. Psychometrika, 1955,20, 139-148. AM.4~~~, N. R. I?., AND SOLEM. A. It. The contribution of a discussion leader to the quality of group thinking: The effective use of minority opinions. Human Relations. 1952, 5, 277-288. HESTLE, F. Speed and accuracy of cognitive achievement in small groups. In J. Criswell, H. Solomon, and P. Suppes (Eds.), Mathematical methods in small group pror~s~s. Stanford, California: Stanford University Press, 1962. Pp. 250-262. SMITH, M. B., BRUNER, J. S., AND WHITE, R. W. Opinions and personality. New York: Riley, 1956. STEINER, I. D. Models for inferring relationships between group size and potential group productivity. Behavioral Science, 1966, 11, 273-283. TIIO;MAF, E. J., AND FINK, C. F. Models of group problem solving. Journal of Abmmal and Social Psychology, 1961. 63, 5343. I,ORGE,
type
(Recrived
November
15, 1966)