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Accounting aggregation: User preferences and decision making
Accounting, Organizations and Society. VoL 4, No. 3, pp. 187-210. © Pergamon Press Ltd, 1979. Printed in Great Britain.
0361-3682/79/0701-018750200/0
ACCOUNTING AGGREGATION: USER PREFERENCES AND DECISION MAKING
DAVID W. HARVEY Tulane University
JOHN GRANT RHODE University o f San Francisco
and
KENNETH A. MERCHANT Harvard University
Abstract
This experiment tests the effects of alternative aggregationsof accounting data in a simulated portfolio task. Certain entropy-based aggregationcriteria were used to prepare differentially aggregated financial statements for use in the task. Subjects made allocations of initial endowments between hypothetical firms, disclosed confidence in their allocation decisions and reported on specific characteristics of the t'mancial statements. Differences in reported usefulness of statement sets furnished were found to be associated strongly with measured information content. The results also provide limited evidence that decisions and judgments of subjects were affected by the information content of the accounting aggregations provided.
The usefulness of the accounting product depends on the information content of particular data and how effectively that information is communicated to financial statement users. One important reporting decision, the extent of aggregation, involves summarization or condensation of data with resulting loss of detail. This decision is one of the factors affecting the usefulness of the accounting data. While information content may be lost by transmission of a reduced set of data, communication of the intended message may be enhanced by a beneficial clarification through summarization. Several accounting researchers have recognized the relevance of aggregation decisions, and the result of their interest is a growing body of knowledge in the literature (Lev, 1968, 1969, 1970; Bare field, 1972; Abdel-khalik, 1974; Ronen & Falk, 1973). This study attempts to provide
evidence of the effects of information aggregation on user perceptions, preferences and financial decisions. Earlier research on information was concerned with whether aggregation hindered or helped decision-making in a normative sense (Grilliches & Grunfeld, 1960; Orcutt, Watts & Edwards, 1968, 1969; Laub, 1972). In sum, these studies revealed that aggregation cannot provide more information than is present in the detailed data, and in many situations, information will be lost. While attempting to quantify the amount of information lost by aggregation, Lev (1968, 1969, 1970) adapted the Entropy Law from scientific information theory and suggested measures as general purpose surrogates for the value of the information lost. The major criticism of Lev's work has come from those who feel that the information must be situation- and user-dependent
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DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT
(Bernhardt & Copeland, 1970; Hofstedt, 1970; Horowitz & Horowitz, 1976), and there is some limited empirical evidence that the entropy measure is not useful as a general-purpose surrogate (Ronen & Falk, 1973; Abdel-khalik, 1974). For example, Stallman (1970) provided evidence that certain disaggregated disclosures are not necessarily useful or valuable. In the Stallman experiment financial analysts perceived no differences in the value of securities due to receiving data on divisional operations for two companies. The entropy measure, however, may have use as an indicator of lost information in certain specific situations as yet unexplored.
EXPERIMENTAL PURPOSE AND DESIGN This experiment was designed to test for relationships between the information content o f financial statements, as indicated by the Lev entropy measure, and decisions, judgments and preferences expressed by knowledgeable subjects in an investment situation. The independent variable in the study is information lost through aggregation based on maximum and minimum information financial statement aggregations. The experimental task required subjects to evaluate the investment quality o f c o m m o n shares of two fictitious domestic airlines, allegedly traded on the New York Stock Exchange. Financial statements used in the task were aggregated from the basic financial statements of American and United Airlines. The statements were modified to display uniform account titles and numbers of accounts. Scalar adjustments were made to reduce the likelihood that the source airline would be recognized and the airlines were renamed Alpha
and Beta. Selected financial comparisons are presented in Table 1. See Appendix I for the sample financial statements used. Financial statements were constructed from the basic data to yield low-information statements (LO) and high-information statements (HI) for each airline, a total of four different statements. The differences between the high and low information statements resulted from the choice o f data to aggregate, using Lev's entropy rules: (1) as the numerical inequality of two elements of a set increases, aggregating the elements becomes less undesirable and (2) as the total of the two elements decreases relative to the total of the related set, aggregating them becomes less undesirable (Lev, 1968). See Appendix II for a description of the entropy measurement procedure. It has been demonstrated that quantity of data presented to decision makers may have substantial effects on the communication of the information content of the financial statements (Schroeder, Driver & Streufert, 1967; Miller, 1972; Dermer, 1973; San Miguel, 1976). To control for these effects, the number of line items presented in the aggregated financial statements in each of the treatments was equalized at approximately onehalf that of the original presentations in the airlines' annual reports. The reduced number of presentations should make the instruments simple enough to avoid a state of information overload yet leave adequate information with which to make necessary judgments and decisions. The aggregations were made to preserve a number of traditional financial statement categories such that the statements did not appear so foreign that subjects would reject them. Table 2 presents a summary of the entropy-measure
TABLE 1. Selected financial comparisons between Alpha and Beta
Yearly common share price range Most recent common share price Range as percentage of current price Net income Preferred dividend Available for common Common shares Earnings per share Earnings yield - current price Earnings yield - high yearly price Earnings yield - low yearly price
Alpha
Beta
22-3/4 - 34-1/2 28-1/2 40 $33,638,000 0 $33,683,000 19,226,100 $1.7519 0.061 0.051 0.077
28-3/4 - 43-1/4 36 40 $33,400,000 $ 880,000 $32,520,000 14,739,247 $2.2063 0.061 0.05t 0.077
ACCOUNTING AGGREGATIONS: USER PREFERENCES AND DECISION MAKING information content o f the statements. Subjects in the study were security analysts and portfolio managers from a large midwestern metropolitan area. All subjects received a package containing ( 1 ) i n s t r u c t i o n s (see Appendix III), (2) a set of financial statements for each o f the two test companies from one o f four treatments described below, (3) a questionnaire o f twelve items, ten for use in the first part o f the study and two for use in the second (see Appendix IV), and (4) a sealed section containing another set o f financial statements for one o f the companies so that the subject would have both high information and low information statements from either Alpha
or Beta. This latter data set was used in the second part of the study, for questions 11 and 12 involving ascribed usefulness and preferences for different financial statements from the same company. Since data for each of the two experimental companies were aggregated in two different ways, packages containing a set of two financial statements could be assigned in four ways, as shown in Table 3. In addition, subjects could be provided with contrasting financial statements for either o f the two companies in the second part of the study. Consequently, a total o f eight possible treatment
TABLE 2. Information analysis Information content of Alpha airline statements Basic set
Minimum-loss aggregation
Maximum-loss aggregation
Information content
Information content
Loss through aggregation
Information content
Loss through aggregation
2.270300 2.863273
2.101380 2.618695
0.168920 0.244578
1.398993 1.892695
0.871307 0.970578
Revenue
1.714779
1.163709
0.551070
0.382890
1.331889
Expense & revenue reduction
2.907403
2.247677
0.657260
0.667762
2.239641
1.567691 0,814502
1.362607 0.609839
0.205084 0.204663
0.389616 0.106273
1.178075 0.708229
Balance sheet Assets
Liabilities O/E Income statement
Funds statements Sources Uses
Information content of Beta airline statements Basic set
Minimum-loss aggregation
Maximum-loss aggregation
Information content
Information content
Loss through aggregation
Information content
Loss through aggregation
Liabilities O/E
2.050736 2.879761
1.904188 2.613353
0.146548 0.266408
0.875564 1.807894
1.175172 1.071867
Income statement Revenue Expenses & revenue reduction
1.608390
1.047652
0.560708
0.126134
1.482226
2.845359
2.223848
0.621511
0.658506
2.186854
Funds statements Sources Uses
1.829491 0.423179
1.487316 0.331401
0.342175 0,091778
0.080965 0.106273
1.748526 0,316906
Balance sheet Assets
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DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT
combinations resulted•
HYPOTHESES Two related general expectations test the applicability of the Lev theoretical entropy model to the specific decision-making situation constructed in this experiment. TABLE 3. Experimental treatments Beta Airlines
Alpha Airlines
HI
LO
HI
1
2
LO
3
4
those alternatives. H5: Subjects' reports of confidences in their choices of alternative investments will be positively related to the information content of the alternative financial statements. Two additional hypotheses were tested which relate less directly to the general expectations but are significant to the study: H6: Subjects will consider high-information financial statements more nearly adequate to make the required decisions and judgments than the low-information statements. H7: Subjects will consider the financial statements in equal-information conditions more comparable than those with differing information levels.
ANALYSIS AND RESULTS First, with the quantity of data (number of line items of financial information) held constant to control for the psychological effects of data overload, it was expected that decision makers would prefer to work with financial statements with higher information content, as indicated by the entropy measure. This led to the following three operational hypotheses: HI: Subjects' reported usefulness of financial statements furnished will be positively related to the information content of the statements. H2: For each investment alternative, subjects will report a preference for financial statements in a high-information condition over financial statements in a lowinformation condition. H3: Subjects will find financial statements in the high-information condition easier to interpret than financial statements in the low-information condition• The second general expectation was that the information-content differences would be reflected in the actual decisions and judgments made, and that the alternatives about which additional information was provided would appear relatively attractive. The following hypotheses were used as the basis for tests in this area: H4: Subject judgments of investment desirability of alternatives will be positively related to the information content of the financial statements furnished describing
Experimental materials were sent to 298 potential participants at their work addresses and followed up by a reminder letter. Later, another full packet of experimental materials was sent to nonrespondents at their home addresses and followed up by a reminder letter. The final response rate was 26.5% (n --- 79). The number of respondents in each cell is presented in Table 4. Since nonrespondents were known because of questionnaire coding, follow-up mailings went only to subjects who had not responded. The identity of early and late respondents was not, however, preserved since responses were not dated on receipt. This did not appear to be of importance since all responses were received within a relatively short time period. There was no further follow-up of nonrespondents since the response rate compared favorably with other survey research studies involving security analysts (Buzby, 1974; Ortman, 1975). Chi-square (X2) tests were used to detect statistically significant differences among treatments for several nominal characteristics of respondents. Analysis of three classifications for primary duties reported - portfolio management (n = 28), security analysis (n = 23), and others (n = 28) - across 4 treatments in Table 3 yielded a X2 = 8.08 (d.f. = 6; p > 0.2). The organization level data combined into two classifications senior-level individuals and office managers in the first group (n = 57) and junior-level individuals in
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191
TABLE 4. Respondent distribution across treatments Alpha information
Beta information
Treatment
Cellfrequency
content
content
statements
Sealed
1 2 3 4 5 6 7 8
11 11 5 12 9 12 9 9
High High High High Low Low Low Low
High High Low Low High High Low Low
Alpha Beta Alpha Beta Alpha Beta Alpha Beta
Total 78 the second group (n = 19), × : = 1.71 ( d . f . = 3 , tions being the information level of the Alpha (A) p > 0.5). Moreover, when testing whether years of and Beta (B) t'mancial statements and the experience (~ = 14.8; S.D. = 10.4) differed among company (Alpha or Beta) for which the report was eight potential treatments the combinations by provided in the second part of the study (C). This ANOVA yielded an F = 1.79 (d.f. = 7.70; allowed an acceptable method of performing a p > 0.10). The four airlines specialists responding limited test of the sequential manipulation were spread over three treatment combinations. attempted through the mail. If subjects opened the Finally, a test for differences in response rates sealed package prior to answering the first ten across treatments gave no evidence of treatment questions, the main effect or interactions might effect (X2 = 4.67; d.f. = 7; p > 0.7). Consequently, tend toward significance. Table 5 presents a summary of the expected the results of these tests provide inadequate grounds to reject the hypothesis that respondent findings and relates the questions to the characteristics and response rates are not affected hypotheses tested. by treatments. After being shown financial statements for Reported Usefulness - Hypothesis 1. Questions 5 Alpha and Beta on one of the four treatments, and 6, 11 Hypothesis 1 stated that the reported usesubjects responded to questions one through ten (shown in Appendix IV). After completing these fulness would vary directly with the information questions, the subjects opened the sealed envelope content of the statements. Data from questions 5 containing financial statements to provide a and 6 were combined and coded on a seven-point complete set of high- and low-information scale from strong confidence in Alpha to strong statements for either Alpha or Beta and answered confidence in Beta, with no difference at midpoint. questions 11 and 12. The analysis of variance is presented in Table 6. Winer (1971) suggests that the appropriate analysis in the case of unequal cell frequencies Significant main effects are shown for the where the loss of observations in cells is not information content of the financial statements of related to experimental variables is the unweighted both Alpha and Beta together with the Alphameans ANOVA. A 2 X 2 X 2 analysis was chosen Beta report provided interaction (A X B X C). The as the primary statistical tool, the three manipula- results are consistent with the general expectation TABLE 5. Summary of expectations Significant effects Area of concern Reported usefulness Statement preference Interpretability Investment desirability Reported confidence Information adequacy Comparability Sequential manipulation
Hypothesis No. QuestionNo. 1 2 3 4 5 6 7 -
5, 6, & 11 7 & 12 10 3&4 1& 2 8 9 -
expected A, B A, B A, B A, B A, B A, B A ×B C not significant
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DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT
and strong e n o u g h to reject the null h y p o t h e s i s o f no difference in r e p o r t e d usefulness. Question 11 asked the subjects to indicate w h e t h e r the high- or l o w - i n f o r m a t i o n financial
Statement Preference - Hypothesis 2. Questions 7, 12 Similar to the r e p o r t e d usefulness hypothesis, it was e x p e c t e d that subjects w o u l d prefer to use the
TABLE 6. Usefulness ANOVA hypothesis 1 Source of variation
d.f.
Mean square
F
A : Alpha information level B: Beta information level C: Firm for second part A XB A × C B × C A ×BXC Within cell
1 1 1 1 1 1 1 70
39.5417 20.3427 1.1898 0.0119 0.1856 0.1856 4.6173 1.1255
35.1335 18.0748 1.0571 0.0106 0.1649 0.1649 4.1026
Total
77
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.41. TABLE 7. Preference ANOVA hypothesis 2 Source of variation
d.f.
Mean square
F
A: Alpha information level B: Beta information level C: Firm for second part A XB A XC B × C AXBX C Within cell
1 1 1 1 1 1 1 68
44.1416 26.0005 0.4901 4.1249 0.1943 0.0174 2.2643
19~4946 11.4828 0.2164 1.8217 0.0858 0.0077
Total
75
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) -- 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14.
statements o f the same c o m p a n y were perceived as m o r e useful and it was e x p e c t e d that t h e y w o u l d prefer the h i g h - i n f o r m a t i o n statements. The n o r m a l a p p r o x i m a t i o n to the binomial distribution was used to c o m p u t e a score c o r r e c t e d for c o n t i n u i t y to d e t e r m i n e the probability o f each response f r e q u e n c y o u t c o m e . In every case, the F-statistic was significant at the 0.01 level, indicating that the high-information statements were perceived as m o r e useful.
high-information statements. Table 7 presents the analysis o f variance w i t h the responses to q u e s t i o n 7 as the d e p e n d e n t variable. The statistically significant main effects for the Alpha and Beta statements' i n f o r m a t i o n level indicate a substantial preference for the high i n f o r m a t i o n statements. An F-test on the preferences expressed in q u e s t i o n 12 w h e n t w o sets o f statements were available for the same firm also revealed a difference significant at the 0.01 level in favor o f the high-information
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193
statements.
Allocation o f Resources - Hypothesis 4, Question 3 and 4
Interpretability - Hypothesis 3, Question 10
Two questions were related to subject expressions o f i n v e s t m e n t desirability. Question 3 asked for direct evaluation o f the desirability o f an investment in each c o m p a n y , and question 4 requested an allocation o f i n v e s t m e n t funds. It was
It was e x p e c t e d that the subjects w o u l d find the l o w - i n f o r m a t i o n statements m o r e difficult to interpret than those which presented more i n f o r m a t i o n . The results o f the analysis o f
TABLE 8. Interpretability ANOVA hypothesis 3 Source of variation
d.f.
Mean square
F
A : Alpha in formation level B: Beta information level C: Firm for second part A XB A XC B XC A XB X C Within cell
1 1 1 1 1 1 1 68
13.0688 7.0213 0.0299 0.0485 0.5125 0.3646 0.5761 0.7904
16.5338 8.8828 0.0378 0.0614 0.6484 0.4613 0.7288
Total
75
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14.
TABLE 9. Investment desirability (Question 3) ANOVA - hypothesis 4 Source of variation
d.f.
Mean square
A: Alpha information level B: Beta information level C: Firm for second part A XB A XC B× C A XB X C Within cell
1 1 1 1 1 1 1 68
44.4233 4.6384 20.7332 5.1697 0.3527 1.2856 2.2314 7.4685
Total
F 5.9481 0.6211 2.7761 0.6922 0.0472 0.1721 0.2988
75
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14.
variance, presented in Table 8, are consistent w i t h this e x p e c t a t i o n ; the main effect o f i n f o r m a t i o n level for each o f the c o m p a n y ' s statements is highly significant.
e x p e c t e d that these j u d g m e n t s w o u l d be biased in favor o f the investments a b o u t which m o r e i n f o r m a t i o n was provided. The analyses o f variance are presented in Tables
194
DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT was done for questions 5 and 6, and the analysis o f variance is s h o w n in Table 11. This analysis reveals a significant relationship b e t w e e n the Alpha i n f o r m a t i o n and r e p o r t e d confidence, but the result for the Beta disclosure is n o t statistically significant.
9 and 10. The i n f o r m a t i o n level o f the Alpha statements is s h o w n as strongly related to the j u d g e d i n v e s t m e n t desirability o f Alpha. However, the effect o f allocating funds for investment in Beta, while in the direction e x p e c t e d , is n o t statistically significant.
TABLE 10. Investment desirability ANOVA (Question 4) - hypothesis 4 Source of variation
d.f.
Mean square
F
A : Alpha information level B: Beta information level C: Firm for second part A XB A XC B XC A XB X C Within cell
1 1 1 1 1 1 1 68
4518.1172 25.6709 211.4400 430.6785 278.2222 557.1865 557.1865 660.0735
6.8449 0.0389 0.3203 0.6525 0.4215 0.8441 0.8441
Total
75
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05, 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14 TABLE 11. Confidence ANOVA hypothesis 5 Source of variation A : Information level B: Beta information level C: Firm for second part A XB A XC B XC A XB X C Within cell Total
d.f.
Mean square
F
1 1 1 1 1 1 1 71
36.7071 0.6674 5.2275 1.2388 0.3704 2.8704 1.4418
9.7316 0.1769 1.3859 0.3284 0.0982 0.7610 0.3823
78
F(0.01; 3, 60) -- 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. FI~ .10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14.
Reported Confidence - Hypothesis 5, Questions 1 and 2
Information Adequacy - Hypothesis 6, Question 8
It was also e x p e c t e d that the subjects' reports o f c o n f i d e n c e in their choices f r o m a m o n g alternative investments w o u l d vary directly w i t h the i n f o r m a t i o n c o n t e n t o f the financial s t a t e m e n t furnished to describe the alternatives. The responses to questions 1 and 2 were c o m b i n e d as
Question 8 e x p l o r e d the hypothesis that subjects w o u l d find the high-information statements m o r e nearly adequate for making the necessary decisions and j u d g m e n t s which d e p e n d on the i n f o r m a t i o n c o n t a i n e d in those statements. The result is presented in Table 12, and the a d e q u a c y relationship is statistically significant for
ACCOUNTING AGGREGATIONS: USER PREFERENCES AND DECISION MAKING
195
TABLE 12. Information adequacy ANOVA hypothesis 6 Source of variation
d.f.
Meansquare
F
A: Alpha information level B: Beta information level C: Firm for second part A XB A XC B XC A XB X C Within cell
1 1 1 1 1 1 1 71
11.2781 0.0332 0.8234 0.3873 0.2302 1.6111 0.0139 1.2081
9.3354 0.8560 0.6816 0.3206 0.1905 1.3336 0.0115
Total
78
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14. TABLE 13. Comparability ANOVA hypothesis 7 Source of variation
d.f.
Meansquare
F
A: Alpha informatmn level B: Beta information level C: Firm for second part AxB Ax C
1 1 1 1 1
1.47741 2.6382 0.0586 11.9595 0.0843
1.2219 2.1818 0.0484 9.8907 0.0698
B x C A X B x C
I I
0.0843 0.6771
0.0698 0.5600
Within eeH
71
1.2092
Toml
78
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14.
the Alpha statements but statements.
not
for
the
Beta
Comparability - Hypothesis 7, Question 9 Question 9 investigated the issue of whether subjects judged the statements aggregated by the same information loss rules as more or less comparable than statements aggregated by different information rules. The hypothesis was that similar statements are more easily compared; so a significant A X B interaction was expected. Table 13 presents the findings, and a highly significant A X B interaction is indicated. Data for each of the questions in part one of the study were also combined to yield eight dependent variable scores as described in Table 14.
These scores were subject to ANOVA and the data were treated as though measured at the interval-scale level or higher. A Pearson correlation coefficient was calculated for these data questions. All correlations were significant at the 0.001 level. The magnitude and direction of the correlations agrees with implicit and explicit hypotheses related to questions one through seven. Dependant variables six, seven and eight were also positively correlated with each other variable. Given the research design and the nature of the questions asked, it is not surprising to note the substantial correlation of dependent variables. For example, it is reasonable to expect that high confidence in Beta statements is negatively correlated with an investment in Alpha. An
196
DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT TABLE 14. Interpretation of scores on part 1 questions Dependent variable
Questionnake item(s)
1
l&2
2
3
3
4
4
5&6
5
7
6
8
7
9
8
10
a t t e m p t to isolate some independent dimensions among the dependent variables through factor analysis using varimax rotation revealed only one factor. That factor named "preference for financial information disclosure" perhaps best sums up the data analysis o f this experiment. SUMMARY AND CONCLUSIONS The data from this study generally support the stated research hypotheses since a definite difference exists when the low information and high information financial statements are contrasted. This indicates that the two aggregation rules used did affect information content. Moreover, these results had an effect on the subjects' decisions, confidence in their decisions and preferences for presentation o f data though the information content effect on Alpha was somewhat more pronounced than on Beta. Other studies (Abdel-kahlik, 1974; Ronen & Falk, 1973) have used the Lev measure in testing aggregation effects and have shown inconclusive results. While this study does not test the Lev entropy function directly, it does indicate that, in at least this specific instance, there is a relationship between the entropy-measured information content of financial statements and the
High score indicator Greater confidence in Beta financial statements Greater desirability of Alpha as an investment Greater investment allocation to Alpha Greater perceived usefulness of Beta financial statements Greater perceived usefulness of Alpha financial statements Lower perceived adequacy of financial data overall Lower perceived comparability of Alpha and Beta financial statements Aggregation doesn't make interpretation of Alpha financial statements more difficult than interpretation of Beta financial statements decision-makers' financial statement preferences, and the actual decisions made. Thus, this is a limited corroboration of the Lev measure in the direction of the effect, not a test of the specific functional relationship. Future tests are necessary to find circumstances where the Lev measure may be a reasonable surrogate for the information loss from aggregation. The evidence indicates that, at least for this investment analysis situation, decision-makers prefer high information financial statements to low information statements. Although these results may be generalizable to other situations, there is no guarantee that they will. Some other limitations of the study must be kept in mind: Most important, the experiment was kept simple. Only two o f Lev's aggregation rules were used in the aggregation, not the complete model. No conclusions can be drawn about other Lev hypotheses - such as if items show low variability over time, aggregation is less undesirable than if they are volatile (Lev, 1970) - because they were not tested. In addition, only maximum and minimum loss aggregations were prepared. Other rules could have been devised for testing, such as a random selection of candidates for aggregation subject to the rules for admissibility and perhaps traditional aggregation.
ACCOUNTING AGGREGATIONS: USER PREFERENCES AND DECISION MAKING The volume o f data provided here was probably not large enough to effect a data overload situation which could provide the substance for further experimentation. Research results demonstrate that the volume o f information processed is related to environmental load, one component of which is information complexity. In addition, mounting evidence suggests a more elaborate model relating preference for complex information to decision style (Driver & Mock, 1975). Further research on aggregation is needed in many areas. The entropy measure is presently the only available quantitative measure of information in accounting. Evidence should be gathered about the usefulness of the measure, in what situations it is a useful surrogate for the expected information loss caused by aggregation and whether it is the most precise measure of information that can be found. If the evidence looks promising, researchers may find ways to eliminate or reduce the mechanical problems o f applying the measure. Another difficulty lies in measuring the information content and effect of paragraph or context material which is often used instead of expanded financial statements. Failure to comprehend these effects greatly limits the usefulness o f a measure of information content or loss. There is a wide range o f behavioral variables which are potentially relevant in a search for the
197
optimal aggregation strategy. Information can only be useful to the extent it is communicated. Presenting data in different categories and using different titles in future studies may yield some interesting results. Limits to human information processing ability (data overload) in accounting related situations also needs further clarification. These suggested extensions have discussed only the effects of already prepared financial statements on users. It might also be valuable to examine the actual behavior of accountants as they prepare financial statements, to see, for example, to what extent they use a minimum information loss rule - or just what criteria they do use when aggregating accounting information. Financial statement presentation is not the only aggregation problem-related area in accounting. Aggregation decisions must be made in areas such as installation of charts of accounts and design of management information systems. Information can be lost in aggregation, and the accounting literature has just begun to yield limited insight into the nature of the aggregationinformation loss relationships. A knowledge of these relationships may develop such that aggregation rules can be proposed to replace, at least in part, the traditional and more subjective guides to aggregation presently in use. This study is, hopefully, a step in that direction.
BIBLIOGRAPHY Abdel-khalik, A. R., The Entropy Law, Accounting Data and Relevance to Decision-Making, The Accounting Review (April, 1974), pp. 271-283. Barefield, R.M., The Effects of Aggregation on Decision Making Success: A Laboratory Study, Journal o f Accounting Research (Autumn, 1972), pp. 229-242. Bernhardt, I. & Copeland, R. M., Some Problems in Applying an Information Theory Approach to Accounting Aggregation, Journal o f A ccounting Research (Spring, 1970), pp. 95 -98. Buzby, S. L., Selected Items of Information and Their Disclosure in Annual Reports, The Accounting Review (July, 1974), pp. 423-435. Dermer, J. D., Cognitive Characteristics and the Perceived Importance of Information, The Accounting Review (July, 1973), pp. 511-519. Driver, M.J. & Mock, T. J., Human Information Processing, Decision Style Theory and Accounting Information Systems, The Accounting Review (July, 1975), pp. 490-508. Grilliches, A. & Grunfeld, Y., Is Aggregation Necessarily Bad? Review o f Economics and Statistics (February, 1960), pp. 1-13. Hofstedt, T. R., Some Behavioral Implications of Aggregation in Accounting Reports. Unpublished Ph.D. dissertation, Stanford University, 1970. Horowitz, A. R. & Horowitz, I., The Real and Illusory Virtues of Entropy-Based Measures for Business and Economic Analysis, Decision Sciences (January, 1976), pp. 121-136. Laub, P. M., Some Aspects of the Aggregation Problem in Dividend Earnings Relationships, Journal o f the American Statistical Association (September, 1972), pp. 557 -559.
198
DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT Lev, B., The Aggregation Problem in Financial Statements: An Informational Approach, Journal of Accounting Research (Autumn, 1968), pp. 247-261. Lev, B., Accounting and Information Theory (Sarasota, Florida: American Accounting Association, 1969). Lev, B., The Informational Approach to Aggregation in Financial Statements: Extensions, Journal of Accounting Research (Spring, 1970), pp. 78-94. Miller, H., Environmental Complexity and Financial Reports, The Accounting Review (January, 1972), pp. 31-37. Orcutt, G. H., Watts, H. W. & Edwards, J. B., Should Aggregation Prior to Aggregation Be the Rule? Review o f Economics and Statistics (November, 1969), pp. 409-420. Orcutt, G.H., Data Aggregation and Information Loss, American Economic Review (September, 1968), pp. 773-787. Ortman, R. F., The Effects on Investment Analysis of Alternative Reporting Procedure for Diversified Firms, The Accounting Review (April, 1975), pp. 298-304. San Miguel, J. G., Human Information Processing and lts Relevance to Accounting: A Laboratory Study, Accounting Organizations and Society (1976), pp. 357-373. Schroeder, H. M., Driver, M. J. & Streufert, S., Human Information Processing (Ronald Press, 1971). Stallman, J.C., Toward Experimental Criteria for Judging Disclosure Improvement, Empirical Research in Accounting." Selected Studies, 1969, Journal o f Accounting Research (Supplement to volume 7), 1970, pp. 29-43.
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ACCOUNTING AGGREGATIONS: USER PREFERENCES AND DECISION MAKING A P P E N D I X II DESCRIPTION OF THE ENTROPY MEASUREMENT PROCEDURE To illustrate a simple entropy calculation, logarithms to any base may be used because, as monotonic transformations of each other, the calculations yield the same ranking of entropy losses. If base 2 is used, the units are called binary digits (bits). In this example, logarithms to base 10 are used. The formula for entropy (H) is: H = ~; - p log p, where p is the proportion of a given account's dollar value compared to the total for the section being considered, in this ease, total assets. Note in this example that the Buildings are shown net of depreciation because logarithms cannot be taken of negative numbers. Partial balance sheet Item
Assets
1 2 3
Current assets: Cash Accounts receivable Prepaid expenses
4 5
Fixed assets: Land Buildings - Net Total assets
p
-log p
- p log p
$ 10,000 40,000 20,000
0.10 0.40 0.20
1.0000 0.3979 0.6990
0.1000 0.1592 0.1398
15,000 15,000
0.15 0.15
0.8239 0.8239
0.1236 0.1236
$100,000
1.00
Total entropy
0.6462
Admissible pairs for aggregation are defined so that the subsections, Current Assets and Fixed Assets, are not violated. The entropy loss for the first admissible pair (Cash and Accounts Receivable) is calculated:
Cash and accounts receivable
$ 50,000
p
-log p
- p log p
0.50
0.3010
0.1505
Since all other items stay the same, the entropy loss from this aggregation is the old entropy minus the new entropy (0.1000 + 0.1592 - 0.1505 = 0.1087). Since the entropy loss is 0.1087, the entropy for this section of the balance sheet with Cash and Accounts Receivable aggregated is 0.6462 - 0.1087 = 0.5375. A table showing entropy loss for all admissible pairs is as follows: Admissible pairs 1, 1, 2, 4,
2 3 3 5
Entropy loss 0.1087 0.0829* 0.1659 0.1084
The first items to be aggregated under the minimum information loss criterion are (1, 3). If only one aggregation gave the desired volume of data, the procedure would stop here. If another aggregation was desired, the process would be repeated: Admissible pairs
Entropy loss
(1, 3), 2 4, 5
0.2314 0.0903*
The next items to be aggregated under the minimum information loss criterion are (4, 5).
207
208
DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT A P P E N D I X III INSTRUCTIONS TO SUBJECTS This is a financial analysis task. Your job is to help an investor decide how to allocate $20,000 between the common stocks of two companies. The investor, Mr. Robinson, is a single, professional man in his middle thirties. A confirmed bachelor, he has more than enough income from his practice to live comfortably and has as his primary investment objective long-term capital appreciation. Having decided to invest in the common stock of domestic airlines, he has narrowed the field to two companies, Alpha Airlines and Beta Airlines. Financial statements for each company are available for the prior year only. Though financial statements are not available for earlier years, it is known that the airlines have had similar records of development, growth and profitability. Their route structures are comparable, with no route changes anticipated for either company in the near future. Neither airline is a likely merger candidate. Assume that general economic and industry factors effect each company in the same way. Review the following financial statements of Alpha and Beta and answer the questions which come next. Examine the sealed material at the end only when directed to in the instructions. •
It is very important that you answer the questions in order.
•
Make whatever notes and calculations are useful on the face of the financial statements.
•
Feel free to separate the statements from the other material in this packet if it will aid your analysis.
A P P E N D I X IV TWELVE ITEM QUESTIONNAIRE 1. Given the financial statements for the two companies, which would you feel more confident in recommending to the investor described earlier? Alpha Beta No difference 2. Describe your preference. (Do not answer this question if you responded "No difference" in question 1 above.) Strong Moderate Weak 3. In view of the given investment objective (capital appreciation), rate each c o m p a n y on its desirability as an investment by circling the n u m b e r on the following scale best representing your evaluation. Alpha 1 2 Lowest
3
4
5
6
7
8
9
10 Highest
1
3
4
5
6
7
8
9
10
Beta 2
4. How should the investor allocate his $20,000 between Alpha and Beta? Alpha
%
Beta _ _ %
5. The term "Usefulness" may be used to mean the quality of facilitating decision-making. Employing this definition, which firm's set of statements was more useful to you in your analysis.
ACCOUNTING AGGREGATIONS: USER PREFERENCES AND DECISION MAKING Alpha's Beta's No difference 6. Describe the difference in usefulness. (Do not answer this question if you responded "No difference" in question 5 on the previous page.) Large Moderate Small 7. In the context of this decision setting, rate each company's financial statements on its usefulness by circling the number on the following scale best representing your evaluation. Alpha 1 2 Lowest
3
4
5
6
7
8
9
10 Highest
1
3
4
5
6
7
8
9
10
Beta 2
8. I find the financial statement data adequate for me to answer question 1 through 7 above. strongly agree
agree
neutral
disagree
strongly disagree
disagree
strongly disagree
9. The statements of Alpha and Beta are comparable. strongly agree
agree
neutral
10. The way data items are combined in the financial statements makes interpretation of Alpha statements more difficult than interpretation of Beta statements. strongly agree
agree
neutral
disagree
strongly disagree
I (Second Phase of the study.) 11. Defining "usefulness" as the quality of facilitating decision making, which set of Alpha statements would be more useful to you in the previous allocation decision if that task were to be repeated? Set used in task Set from sealed material
209
210
DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT 12. Now consider Alpha's income statements, balance sheets, and funds statements separately. First compare the income statement from the task material with the income statement from the sealed material. Indicate which of these two statements you would prefer if that task were to be repeated. Next compare the balance sheets. Indicate which of these you would prefer. Compare the funds statements and state your preference. Task Income Statement Balance Sheet Funds Statement
Sealed
0361-3682/79/0701-018750200/0
ACCOUNTING AGGREGATION: USER PREFERENCES AND DECISION MAKING
DAVID W. HARVEY Tulane University
JOHN GRANT RHODE University o f San Francisco
and
KENNETH A. MERCHANT Harvard University
Abstract
This experiment tests the effects of alternative aggregationsof accounting data in a simulated portfolio task. Certain entropy-based aggregationcriteria were used to prepare differentially aggregated financial statements for use in the task. Subjects made allocations of initial endowments between hypothetical firms, disclosed confidence in their allocation decisions and reported on specific characteristics of the t'mancial statements. Differences in reported usefulness of statement sets furnished were found to be associated strongly with measured information content. The results also provide limited evidence that decisions and judgments of subjects were affected by the information content of the accounting aggregations provided.
The usefulness of the accounting product depends on the information content of particular data and how effectively that information is communicated to financial statement users. One important reporting decision, the extent of aggregation, involves summarization or condensation of data with resulting loss of detail. This decision is one of the factors affecting the usefulness of the accounting data. While information content may be lost by transmission of a reduced set of data, communication of the intended message may be enhanced by a beneficial clarification through summarization. Several accounting researchers have recognized the relevance of aggregation decisions, and the result of their interest is a growing body of knowledge in the literature (Lev, 1968, 1969, 1970; Bare field, 1972; Abdel-khalik, 1974; Ronen & Falk, 1973). This study attempts to provide
evidence of the effects of information aggregation on user perceptions, preferences and financial decisions. Earlier research on information was concerned with whether aggregation hindered or helped decision-making in a normative sense (Grilliches & Grunfeld, 1960; Orcutt, Watts & Edwards, 1968, 1969; Laub, 1972). In sum, these studies revealed that aggregation cannot provide more information than is present in the detailed data, and in many situations, information will be lost. While attempting to quantify the amount of information lost by aggregation, Lev (1968, 1969, 1970) adapted the Entropy Law from scientific information theory and suggested measures as general purpose surrogates for the value of the information lost. The major criticism of Lev's work has come from those who feel that the information must be situation- and user-dependent
187
188
DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT
(Bernhardt & Copeland, 1970; Hofstedt, 1970; Horowitz & Horowitz, 1976), and there is some limited empirical evidence that the entropy measure is not useful as a general-purpose surrogate (Ronen & Falk, 1973; Abdel-khalik, 1974). For example, Stallman (1970) provided evidence that certain disaggregated disclosures are not necessarily useful or valuable. In the Stallman experiment financial analysts perceived no differences in the value of securities due to receiving data on divisional operations for two companies. The entropy measure, however, may have use as an indicator of lost information in certain specific situations as yet unexplored.
EXPERIMENTAL PURPOSE AND DESIGN This experiment was designed to test for relationships between the information content o f financial statements, as indicated by the Lev entropy measure, and decisions, judgments and preferences expressed by knowledgeable subjects in an investment situation. The independent variable in the study is information lost through aggregation based on maximum and minimum information financial statement aggregations. The experimental task required subjects to evaluate the investment quality o f c o m m o n shares of two fictitious domestic airlines, allegedly traded on the New York Stock Exchange. Financial statements used in the task were aggregated from the basic financial statements of American and United Airlines. The statements were modified to display uniform account titles and numbers of accounts. Scalar adjustments were made to reduce the likelihood that the source airline would be recognized and the airlines were renamed Alpha
and Beta. Selected financial comparisons are presented in Table 1. See Appendix I for the sample financial statements used. Financial statements were constructed from the basic data to yield low-information statements (LO) and high-information statements (HI) for each airline, a total of four different statements. The differences between the high and low information statements resulted from the choice o f data to aggregate, using Lev's entropy rules: (1) as the numerical inequality of two elements of a set increases, aggregating the elements becomes less undesirable and (2) as the total of the two elements decreases relative to the total of the related set, aggregating them becomes less undesirable (Lev, 1968). See Appendix II for a description of the entropy measurement procedure. It has been demonstrated that quantity of data presented to decision makers may have substantial effects on the communication of the information content of the financial statements (Schroeder, Driver & Streufert, 1967; Miller, 1972; Dermer, 1973; San Miguel, 1976). To control for these effects, the number of line items presented in the aggregated financial statements in each of the treatments was equalized at approximately onehalf that of the original presentations in the airlines' annual reports. The reduced number of presentations should make the instruments simple enough to avoid a state of information overload yet leave adequate information with which to make necessary judgments and decisions. The aggregations were made to preserve a number of traditional financial statement categories such that the statements did not appear so foreign that subjects would reject them. Table 2 presents a summary of the entropy-measure
TABLE 1. Selected financial comparisons between Alpha and Beta
Yearly common share price range Most recent common share price Range as percentage of current price Net income Preferred dividend Available for common Common shares Earnings per share Earnings yield - current price Earnings yield - high yearly price Earnings yield - low yearly price
Alpha
Beta
22-3/4 - 34-1/2 28-1/2 40 $33,638,000 0 $33,683,000 19,226,100 $1.7519 0.061 0.051 0.077
28-3/4 - 43-1/4 36 40 $33,400,000 $ 880,000 $32,520,000 14,739,247 $2.2063 0.061 0.05t 0.077
ACCOUNTING AGGREGATIONS: USER PREFERENCES AND DECISION MAKING information content o f the statements. Subjects in the study were security analysts and portfolio managers from a large midwestern metropolitan area. All subjects received a package containing ( 1 ) i n s t r u c t i o n s (see Appendix III), (2) a set of financial statements for each o f the two test companies from one o f four treatments described below, (3) a questionnaire o f twelve items, ten for use in the first part o f the study and two for use in the second (see Appendix IV), and (4) a sealed section containing another set o f financial statements for one o f the companies so that the subject would have both high information and low information statements from either Alpha
or Beta. This latter data set was used in the second part of the study, for questions 11 and 12 involving ascribed usefulness and preferences for different financial statements from the same company. Since data for each of the two experimental companies were aggregated in two different ways, packages containing a set of two financial statements could be assigned in four ways, as shown in Table 3. In addition, subjects could be provided with contrasting financial statements for either o f the two companies in the second part of the study. Consequently, a total o f eight possible treatment
TABLE 2. Information analysis Information content of Alpha airline statements Basic set
Minimum-loss aggregation
Maximum-loss aggregation
Information content
Information content
Loss through aggregation
Information content
Loss through aggregation
2.270300 2.863273
2.101380 2.618695
0.168920 0.244578
1.398993 1.892695
0.871307 0.970578
Revenue
1.714779
1.163709
0.551070
0.382890
1.331889
Expense & revenue reduction
2.907403
2.247677
0.657260
0.667762
2.239641
1.567691 0,814502
1.362607 0.609839
0.205084 0.204663
0.389616 0.106273
1.178075 0.708229
Balance sheet Assets
Liabilities O/E Income statement
Funds statements Sources Uses
Information content of Beta airline statements Basic set
Minimum-loss aggregation
Maximum-loss aggregation
Information content
Information content
Loss through aggregation
Information content
Loss through aggregation
Liabilities O/E
2.050736 2.879761
1.904188 2.613353
0.146548 0.266408
0.875564 1.807894
1.175172 1.071867
Income statement Revenue Expenses & revenue reduction
1.608390
1.047652
0.560708
0.126134
1.482226
2.845359
2.223848
0.621511
0.658506
2.186854
Funds statements Sources Uses
1.829491 0.423179
1.487316 0.331401
0.342175 0,091778
0.080965 0.106273
1.748526 0,316906
Balance sheet Assets
189
190
DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT
combinations resulted•
HYPOTHESES Two related general expectations test the applicability of the Lev theoretical entropy model to the specific decision-making situation constructed in this experiment. TABLE 3. Experimental treatments Beta Airlines
Alpha Airlines
HI
LO
HI
1
2
LO
3
4
those alternatives. H5: Subjects' reports of confidences in their choices of alternative investments will be positively related to the information content of the alternative financial statements. Two additional hypotheses were tested which relate less directly to the general expectations but are significant to the study: H6: Subjects will consider high-information financial statements more nearly adequate to make the required decisions and judgments than the low-information statements. H7: Subjects will consider the financial statements in equal-information conditions more comparable than those with differing information levels.
ANALYSIS AND RESULTS First, with the quantity of data (number of line items of financial information) held constant to control for the psychological effects of data overload, it was expected that decision makers would prefer to work with financial statements with higher information content, as indicated by the entropy measure. This led to the following three operational hypotheses: HI: Subjects' reported usefulness of financial statements furnished will be positively related to the information content of the statements. H2: For each investment alternative, subjects will report a preference for financial statements in a high-information condition over financial statements in a lowinformation condition. H3: Subjects will find financial statements in the high-information condition easier to interpret than financial statements in the low-information condition• The second general expectation was that the information-content differences would be reflected in the actual decisions and judgments made, and that the alternatives about which additional information was provided would appear relatively attractive. The following hypotheses were used as the basis for tests in this area: H4: Subject judgments of investment desirability of alternatives will be positively related to the information content of the financial statements furnished describing
Experimental materials were sent to 298 potential participants at their work addresses and followed up by a reminder letter. Later, another full packet of experimental materials was sent to nonrespondents at their home addresses and followed up by a reminder letter. The final response rate was 26.5% (n --- 79). The number of respondents in each cell is presented in Table 4. Since nonrespondents were known because of questionnaire coding, follow-up mailings went only to subjects who had not responded. The identity of early and late respondents was not, however, preserved since responses were not dated on receipt. This did not appear to be of importance since all responses were received within a relatively short time period. There was no further follow-up of nonrespondents since the response rate compared favorably with other survey research studies involving security analysts (Buzby, 1974; Ortman, 1975). Chi-square (X2) tests were used to detect statistically significant differences among treatments for several nominal characteristics of respondents. Analysis of three classifications for primary duties reported - portfolio management (n = 28), security analysis (n = 23), and others (n = 28) - across 4 treatments in Table 3 yielded a X2 = 8.08 (d.f. = 6; p > 0.2). The organization level data combined into two classifications senior-level individuals and office managers in the first group (n = 57) and junior-level individuals in
ACCOUNTINGAGGREGATIONS:USER PREFERENCES AND DECISIONMAKING
191
TABLE 4. Respondent distribution across treatments Alpha information
Beta information
Treatment
Cellfrequency
content
content
statements
Sealed
1 2 3 4 5 6 7 8
11 11 5 12 9 12 9 9
High High High High Low Low Low Low
High High Low Low High High Low Low
Alpha Beta Alpha Beta Alpha Beta Alpha Beta
Total 78 the second group (n = 19), × : = 1.71 ( d . f . = 3 , tions being the information level of the Alpha (A) p > 0.5). Moreover, when testing whether years of and Beta (B) t'mancial statements and the experience (~ = 14.8; S.D. = 10.4) differed among company (Alpha or Beta) for which the report was eight potential treatments the combinations by provided in the second part of the study (C). This ANOVA yielded an F = 1.79 (d.f. = 7.70; allowed an acceptable method of performing a p > 0.10). The four airlines specialists responding limited test of the sequential manipulation were spread over three treatment combinations. attempted through the mail. If subjects opened the Finally, a test for differences in response rates sealed package prior to answering the first ten across treatments gave no evidence of treatment questions, the main effect or interactions might effect (X2 = 4.67; d.f. = 7; p > 0.7). Consequently, tend toward significance. Table 5 presents a summary of the expected the results of these tests provide inadequate grounds to reject the hypothesis that respondent findings and relates the questions to the characteristics and response rates are not affected hypotheses tested. by treatments. After being shown financial statements for Reported Usefulness - Hypothesis 1. Questions 5 Alpha and Beta on one of the four treatments, and 6, 11 Hypothesis 1 stated that the reported usesubjects responded to questions one through ten (shown in Appendix IV). After completing these fulness would vary directly with the information questions, the subjects opened the sealed envelope content of the statements. Data from questions 5 containing financial statements to provide a and 6 were combined and coded on a seven-point complete set of high- and low-information scale from strong confidence in Alpha to strong statements for either Alpha or Beta and answered confidence in Beta, with no difference at midpoint. questions 11 and 12. The analysis of variance is presented in Table 6. Winer (1971) suggests that the appropriate analysis in the case of unequal cell frequencies Significant main effects are shown for the where the loss of observations in cells is not information content of the financial statements of related to experimental variables is the unweighted both Alpha and Beta together with the Alphameans ANOVA. A 2 X 2 X 2 analysis was chosen Beta report provided interaction (A X B X C). The as the primary statistical tool, the three manipula- results are consistent with the general expectation TABLE 5. Summary of expectations Significant effects Area of concern Reported usefulness Statement preference Interpretability Investment desirability Reported confidence Information adequacy Comparability Sequential manipulation
Hypothesis No. QuestionNo. 1 2 3 4 5 6 7 -
5, 6, & 11 7 & 12 10 3&4 1& 2 8 9 -
expected A, B A, B A, B A, B A, B A, B A ×B C not significant
192
DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT
and strong e n o u g h to reject the null h y p o t h e s i s o f no difference in r e p o r t e d usefulness. Question 11 asked the subjects to indicate w h e t h e r the high- or l o w - i n f o r m a t i o n financial
Statement Preference - Hypothesis 2. Questions 7, 12 Similar to the r e p o r t e d usefulness hypothesis, it was e x p e c t e d that subjects w o u l d prefer to use the
TABLE 6. Usefulness ANOVA hypothesis 1 Source of variation
d.f.
Mean square
F
A : Alpha information level B: Beta information level C: Firm for second part A XB A × C B × C A ×BXC Within cell
1 1 1 1 1 1 1 70
39.5417 20.3427 1.1898 0.0119 0.1856 0.1856 4.6173 1.1255
35.1335 18.0748 1.0571 0.0106 0.1649 0.1649 4.1026
Total
77
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.41. TABLE 7. Preference ANOVA hypothesis 2 Source of variation
d.f.
Mean square
F
A: Alpha information level B: Beta information level C: Firm for second part A XB A XC B × C AXBX C Within cell
1 1 1 1 1 1 1 68
44.1416 26.0005 0.4901 4.1249 0.1943 0.0174 2.2643
19~4946 11.4828 0.2164 1.8217 0.0858 0.0077
Total
75
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) -- 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14.
statements o f the same c o m p a n y were perceived as m o r e useful and it was e x p e c t e d that t h e y w o u l d prefer the h i g h - i n f o r m a t i o n statements. The n o r m a l a p p r o x i m a t i o n to the binomial distribution was used to c o m p u t e a score c o r r e c t e d for c o n t i n u i t y to d e t e r m i n e the probability o f each response f r e q u e n c y o u t c o m e . In every case, the F-statistic was significant at the 0.01 level, indicating that the high-information statements were perceived as m o r e useful.
high-information statements. Table 7 presents the analysis o f variance w i t h the responses to q u e s t i o n 7 as the d e p e n d e n t variable. The statistically significant main effects for the Alpha and Beta statements' i n f o r m a t i o n level indicate a substantial preference for the high i n f o r m a t i o n statements. An F-test on the preferences expressed in q u e s t i o n 12 w h e n t w o sets o f statements were available for the same firm also revealed a difference significant at the 0.01 level in favor o f the high-information
ACCOUNTING AGGREGATIONS: USER PREFERENCES AND DECISION MAKING
193
statements.
Allocation o f Resources - Hypothesis 4, Question 3 and 4
Interpretability - Hypothesis 3, Question 10
Two questions were related to subject expressions o f i n v e s t m e n t desirability. Question 3 asked for direct evaluation o f the desirability o f an investment in each c o m p a n y , and question 4 requested an allocation o f i n v e s t m e n t funds. It was
It was e x p e c t e d that the subjects w o u l d find the l o w - i n f o r m a t i o n statements m o r e difficult to interpret than those which presented more i n f o r m a t i o n . The results o f the analysis o f
TABLE 8. Interpretability ANOVA hypothesis 3 Source of variation
d.f.
Mean square
F
A : Alpha in formation level B: Beta information level C: Firm for second part A XB A XC B XC A XB X C Within cell
1 1 1 1 1 1 1 68
13.0688 7.0213 0.0299 0.0485 0.5125 0.3646 0.5761 0.7904
16.5338 8.8828 0.0378 0.0614 0.6484 0.4613 0.7288
Total
75
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14.
TABLE 9. Investment desirability (Question 3) ANOVA - hypothesis 4 Source of variation
d.f.
Mean square
A: Alpha information level B: Beta information level C: Firm for second part A XB A XC B× C A XB X C Within cell
1 1 1 1 1 1 1 68
44.4233 4.6384 20.7332 5.1697 0.3527 1.2856 2.2314 7.4685
Total
F 5.9481 0.6211 2.7761 0.6922 0.0472 0.1721 0.2988
75
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14.
variance, presented in Table 8, are consistent w i t h this e x p e c t a t i o n ; the main effect o f i n f o r m a t i o n level for each o f the c o m p a n y ' s statements is highly significant.
e x p e c t e d that these j u d g m e n t s w o u l d be biased in favor o f the investments a b o u t which m o r e i n f o r m a t i o n was provided. The analyses o f variance are presented in Tables
194
DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT was done for questions 5 and 6, and the analysis o f variance is s h o w n in Table 11. This analysis reveals a significant relationship b e t w e e n the Alpha i n f o r m a t i o n and r e p o r t e d confidence, but the result for the Beta disclosure is n o t statistically significant.
9 and 10. The i n f o r m a t i o n level o f the Alpha statements is s h o w n as strongly related to the j u d g e d i n v e s t m e n t desirability o f Alpha. However, the effect o f allocating funds for investment in Beta, while in the direction e x p e c t e d , is n o t statistically significant.
TABLE 10. Investment desirability ANOVA (Question 4) - hypothesis 4 Source of variation
d.f.
Mean square
F
A : Alpha information level B: Beta information level C: Firm for second part A XB A XC B XC A XB X C Within cell
1 1 1 1 1 1 1 68
4518.1172 25.6709 211.4400 430.6785 278.2222 557.1865 557.1865 660.0735
6.8449 0.0389 0.3203 0.6525 0.4215 0.8441 0.8441
Total
75
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05, 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14 TABLE 11. Confidence ANOVA hypothesis 5 Source of variation A : Information level B: Beta information level C: Firm for second part A XB A XC B XC A XB X C Within cell Total
d.f.
Mean square
F
1 1 1 1 1 1 1 71
36.7071 0.6674 5.2275 1.2388 0.3704 2.8704 1.4418
9.7316 0.1769 1.3859 0.3284 0.0982 0.7610 0.3823
78
F(0.01; 3, 60) -- 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. FI~ .10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14.
Reported Confidence - Hypothesis 5, Questions 1 and 2
Information Adequacy - Hypothesis 6, Question 8
It was also e x p e c t e d that the subjects' reports o f c o n f i d e n c e in their choices f r o m a m o n g alternative investments w o u l d vary directly w i t h the i n f o r m a t i o n c o n t e n t o f the financial s t a t e m e n t furnished to describe the alternatives. The responses to questions 1 and 2 were c o m b i n e d as
Question 8 e x p l o r e d the hypothesis that subjects w o u l d find the high-information statements m o r e nearly adequate for making the necessary decisions and j u d g m e n t s which d e p e n d on the i n f o r m a t i o n c o n t a i n e d in those statements. The result is presented in Table 12, and the a d e q u a c y relationship is statistically significant for
ACCOUNTING AGGREGATIONS: USER PREFERENCES AND DECISION MAKING
195
TABLE 12. Information adequacy ANOVA hypothesis 6 Source of variation
d.f.
Meansquare
F
A: Alpha information level B: Beta information level C: Firm for second part A XB A XC B XC A XB X C Within cell
1 1 1 1 1 1 1 71
11.2781 0.0332 0.8234 0.3873 0.2302 1.6111 0.0139 1.2081
9.3354 0.8560 0.6816 0.3206 0.1905 1.3336 0.0115
Total
78
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14. TABLE 13. Comparability ANOVA hypothesis 7 Source of variation
d.f.
Meansquare
F
A: Alpha informatmn level B: Beta information level C: Firm for second part AxB Ax C
1 1 1 1 1
1.47741 2.6382 0.0586 11.9595 0.0843
1.2219 2.1818 0.0484 9.8907 0.0698
B x C A X B x C
I I
0.0843 0.6771
0.0698 0.5600
Within eeH
71
1.2092
Toml
78
F(0.01; 3, 60) = 4.13. F(0.025; 3, 60) = 3.46. F(0.05; 3, 60) = 2.76. F(0.10; 3, 60) = 2.18. F(0.25; 3, 60) = 1.14.
the Alpha statements but statements.
not
for
the
Beta
Comparability - Hypothesis 7, Question 9 Question 9 investigated the issue of whether subjects judged the statements aggregated by the same information loss rules as more or less comparable than statements aggregated by different information rules. The hypothesis was that similar statements are more easily compared; so a significant A X B interaction was expected. Table 13 presents the findings, and a highly significant A X B interaction is indicated. Data for each of the questions in part one of the study were also combined to yield eight dependent variable scores as described in Table 14.
These scores were subject to ANOVA and the data were treated as though measured at the interval-scale level or higher. A Pearson correlation coefficient was calculated for these data questions. All correlations were significant at the 0.001 level. The magnitude and direction of the correlations agrees with implicit and explicit hypotheses related to questions one through seven. Dependant variables six, seven and eight were also positively correlated with each other variable. Given the research design and the nature of the questions asked, it is not surprising to note the substantial correlation of dependent variables. For example, it is reasonable to expect that high confidence in Beta statements is negatively correlated with an investment in Alpha. An
196
DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT TABLE 14. Interpretation of scores on part 1 questions Dependent variable
Questionnake item(s)
1
l&2
2
3
3
4
4
5&6
5
7
6
8
7
9
8
10
a t t e m p t to isolate some independent dimensions among the dependent variables through factor analysis using varimax rotation revealed only one factor. That factor named "preference for financial information disclosure" perhaps best sums up the data analysis o f this experiment. SUMMARY AND CONCLUSIONS The data from this study generally support the stated research hypotheses since a definite difference exists when the low information and high information financial statements are contrasted. This indicates that the two aggregation rules used did affect information content. Moreover, these results had an effect on the subjects' decisions, confidence in their decisions and preferences for presentation o f data though the information content effect on Alpha was somewhat more pronounced than on Beta. Other studies (Abdel-kahlik, 1974; Ronen & Falk, 1973) have used the Lev measure in testing aggregation effects and have shown inconclusive results. While this study does not test the Lev entropy function directly, it does indicate that, in at least this specific instance, there is a relationship between the entropy-measured information content of financial statements and the
High score indicator Greater confidence in Beta financial statements Greater desirability of Alpha as an investment Greater investment allocation to Alpha Greater perceived usefulness of Beta financial statements Greater perceived usefulness of Alpha financial statements Lower perceived adequacy of financial data overall Lower perceived comparability of Alpha and Beta financial statements Aggregation doesn't make interpretation of Alpha financial statements more difficult than interpretation of Beta financial statements decision-makers' financial statement preferences, and the actual decisions made. Thus, this is a limited corroboration of the Lev measure in the direction of the effect, not a test of the specific functional relationship. Future tests are necessary to find circumstances where the Lev measure may be a reasonable surrogate for the information loss from aggregation. The evidence indicates that, at least for this investment analysis situation, decision-makers prefer high information financial statements to low information statements. Although these results may be generalizable to other situations, there is no guarantee that they will. Some other limitations of the study must be kept in mind: Most important, the experiment was kept simple. Only two o f Lev's aggregation rules were used in the aggregation, not the complete model. No conclusions can be drawn about other Lev hypotheses - such as if items show low variability over time, aggregation is less undesirable than if they are volatile (Lev, 1970) - because they were not tested. In addition, only maximum and minimum loss aggregations were prepared. Other rules could have been devised for testing, such as a random selection of candidates for aggregation subject to the rules for admissibility and perhaps traditional aggregation.
ACCOUNTING AGGREGATIONS: USER PREFERENCES AND DECISION MAKING The volume o f data provided here was probably not large enough to effect a data overload situation which could provide the substance for further experimentation. Research results demonstrate that the volume o f information processed is related to environmental load, one component of which is information complexity. In addition, mounting evidence suggests a more elaborate model relating preference for complex information to decision style (Driver & Mock, 1975). Further research on aggregation is needed in many areas. The entropy measure is presently the only available quantitative measure of information in accounting. Evidence should be gathered about the usefulness of the measure, in what situations it is a useful surrogate for the expected information loss caused by aggregation and whether it is the most precise measure of information that can be found. If the evidence looks promising, researchers may find ways to eliminate or reduce the mechanical problems o f applying the measure. Another difficulty lies in measuring the information content and effect of paragraph or context material which is often used instead of expanded financial statements. Failure to comprehend these effects greatly limits the usefulness o f a measure of information content or loss. There is a wide range o f behavioral variables which are potentially relevant in a search for the
197
optimal aggregation strategy. Information can only be useful to the extent it is communicated. Presenting data in different categories and using different titles in future studies may yield some interesting results. Limits to human information processing ability (data overload) in accounting related situations also needs further clarification. These suggested extensions have discussed only the effects of already prepared financial statements on users. It might also be valuable to examine the actual behavior of accountants as they prepare financial statements, to see, for example, to what extent they use a minimum information loss rule - or just what criteria they do use when aggregating accounting information. Financial statement presentation is not the only aggregation problem-related area in accounting. Aggregation decisions must be made in areas such as installation of charts of accounts and design of management information systems. Information can be lost in aggregation, and the accounting literature has just begun to yield limited insight into the nature of the aggregationinformation loss relationships. A knowledge of these relationships may develop such that aggregation rules can be proposed to replace, at least in part, the traditional and more subjective guides to aggregation presently in use. This study is, hopefully, a step in that direction.
BIBLIOGRAPHY Abdel-khalik, A. R., The Entropy Law, Accounting Data and Relevance to Decision-Making, The Accounting Review (April, 1974), pp. 271-283. Barefield, R.M., The Effects of Aggregation on Decision Making Success: A Laboratory Study, Journal o f Accounting Research (Autumn, 1972), pp. 229-242. Bernhardt, I. & Copeland, R. M., Some Problems in Applying an Information Theory Approach to Accounting Aggregation, Journal o f A ccounting Research (Spring, 1970), pp. 95 -98. Buzby, S. L., Selected Items of Information and Their Disclosure in Annual Reports, The Accounting Review (July, 1974), pp. 423-435. Dermer, J. D., Cognitive Characteristics and the Perceived Importance of Information, The Accounting Review (July, 1973), pp. 511-519. Driver, M.J. & Mock, T. J., Human Information Processing, Decision Style Theory and Accounting Information Systems, The Accounting Review (July, 1975), pp. 490-508. Grilliches, A. & Grunfeld, Y., Is Aggregation Necessarily Bad? Review o f Economics and Statistics (February, 1960), pp. 1-13. Hofstedt, T. R., Some Behavioral Implications of Aggregation in Accounting Reports. Unpublished Ph.D. dissertation, Stanford University, 1970. Horowitz, A. R. & Horowitz, I., The Real and Illusory Virtues of Entropy-Based Measures for Business and Economic Analysis, Decision Sciences (January, 1976), pp. 121-136. Laub, P. M., Some Aspects of the Aggregation Problem in Dividend Earnings Relationships, Journal o f the American Statistical Association (September, 1972), pp. 557 -559.
198
DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT Lev, B., The Aggregation Problem in Financial Statements: An Informational Approach, Journal of Accounting Research (Autumn, 1968), pp. 247-261. Lev, B., Accounting and Information Theory (Sarasota, Florida: American Accounting Association, 1969). Lev, B., The Informational Approach to Aggregation in Financial Statements: Extensions, Journal of Accounting Research (Spring, 1970), pp. 78-94. Miller, H., Environmental Complexity and Financial Reports, The Accounting Review (January, 1972), pp. 31-37. Orcutt, G. H., Watts, H. W. & Edwards, J. B., Should Aggregation Prior to Aggregation Be the Rule? Review o f Economics and Statistics (November, 1969), pp. 409-420. Orcutt, G.H., Data Aggregation and Information Loss, American Economic Review (September, 1968), pp. 773-787. Ortman, R. F., The Effects on Investment Analysis of Alternative Reporting Procedure for Diversified Firms, The Accounting Review (April, 1975), pp. 298-304. San Miguel, J. G., Human Information Processing and lts Relevance to Accounting: A Laboratory Study, Accounting Organizations and Society (1976), pp. 357-373. Schroeder, H. M., Driver, M. J. & Streufert, S., Human Information Processing (Ronald Press, 1971). Stallman, J.C., Toward Experimental Criteria for Judging Disclosure Improvement, Empirical Research in Accounting." Selected Studies, 1969, Journal o f Accounting Research (Supplement to volume 7), 1970, pp. 29-43.
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ACCOUNTING AGGREGATIONS: USER PREFERENCES AND DECISION MAKING A P P E N D I X II DESCRIPTION OF THE ENTROPY MEASUREMENT PROCEDURE To illustrate a simple entropy calculation, logarithms to any base may be used because, as monotonic transformations of each other, the calculations yield the same ranking of entropy losses. If base 2 is used, the units are called binary digits (bits). In this example, logarithms to base 10 are used. The formula for entropy (H) is: H = ~; - p log p, where p is the proportion of a given account's dollar value compared to the total for the section being considered, in this ease, total assets. Note in this example that the Buildings are shown net of depreciation because logarithms cannot be taken of negative numbers. Partial balance sheet Item
Assets
1 2 3
Current assets: Cash Accounts receivable Prepaid expenses
4 5
Fixed assets: Land Buildings - Net Total assets
p
-log p
- p log p
$ 10,000 40,000 20,000
0.10 0.40 0.20
1.0000 0.3979 0.6990
0.1000 0.1592 0.1398
15,000 15,000
0.15 0.15
0.8239 0.8239
0.1236 0.1236
$100,000
1.00
Total entropy
0.6462
Admissible pairs for aggregation are defined so that the subsections, Current Assets and Fixed Assets, are not violated. The entropy loss for the first admissible pair (Cash and Accounts Receivable) is calculated:
Cash and accounts receivable
$ 50,000
p
-log p
- p log p
0.50
0.3010
0.1505
Since all other items stay the same, the entropy loss from this aggregation is the old entropy minus the new entropy (0.1000 + 0.1592 - 0.1505 = 0.1087). Since the entropy loss is 0.1087, the entropy for this section of the balance sheet with Cash and Accounts Receivable aggregated is 0.6462 - 0.1087 = 0.5375. A table showing entropy loss for all admissible pairs is as follows: Admissible pairs 1, 1, 2, 4,
2 3 3 5
Entropy loss 0.1087 0.0829* 0.1659 0.1084
The first items to be aggregated under the minimum information loss criterion are (1, 3). If only one aggregation gave the desired volume of data, the procedure would stop here. If another aggregation was desired, the process would be repeated: Admissible pairs
Entropy loss
(1, 3), 2 4, 5
0.2314 0.0903*
The next items to be aggregated under the minimum information loss criterion are (4, 5).
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DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT A P P E N D I X III INSTRUCTIONS TO SUBJECTS This is a financial analysis task. Your job is to help an investor decide how to allocate $20,000 between the common stocks of two companies. The investor, Mr. Robinson, is a single, professional man in his middle thirties. A confirmed bachelor, he has more than enough income from his practice to live comfortably and has as his primary investment objective long-term capital appreciation. Having decided to invest in the common stock of domestic airlines, he has narrowed the field to two companies, Alpha Airlines and Beta Airlines. Financial statements for each company are available for the prior year only. Though financial statements are not available for earlier years, it is known that the airlines have had similar records of development, growth and profitability. Their route structures are comparable, with no route changes anticipated for either company in the near future. Neither airline is a likely merger candidate. Assume that general economic and industry factors effect each company in the same way. Review the following financial statements of Alpha and Beta and answer the questions which come next. Examine the sealed material at the end only when directed to in the instructions. •
It is very important that you answer the questions in order.
•
Make whatever notes and calculations are useful on the face of the financial statements.
•
Feel free to separate the statements from the other material in this packet if it will aid your analysis.
A P P E N D I X IV TWELVE ITEM QUESTIONNAIRE 1. Given the financial statements for the two companies, which would you feel more confident in recommending to the investor described earlier? Alpha Beta No difference 2. Describe your preference. (Do not answer this question if you responded "No difference" in question 1 above.) Strong Moderate Weak 3. In view of the given investment objective (capital appreciation), rate each c o m p a n y on its desirability as an investment by circling the n u m b e r on the following scale best representing your evaluation. Alpha 1 2 Lowest
3
4
5
6
7
8
9
10 Highest
1
3
4
5
6
7
8
9
10
Beta 2
4. How should the investor allocate his $20,000 between Alpha and Beta? Alpha
%
Beta _ _ %
5. The term "Usefulness" may be used to mean the quality of facilitating decision-making. Employing this definition, which firm's set of statements was more useful to you in your analysis.
ACCOUNTING AGGREGATIONS: USER PREFERENCES AND DECISION MAKING Alpha's Beta's No difference 6. Describe the difference in usefulness. (Do not answer this question if you responded "No difference" in question 5 on the previous page.) Large Moderate Small 7. In the context of this decision setting, rate each company's financial statements on its usefulness by circling the number on the following scale best representing your evaluation. Alpha 1 2 Lowest
3
4
5
6
7
8
9
10 Highest
1
3
4
5
6
7
8
9
10
Beta 2
8. I find the financial statement data adequate for me to answer question 1 through 7 above. strongly agree
agree
neutral
disagree
strongly disagree
disagree
strongly disagree
9. The statements of Alpha and Beta are comparable. strongly agree
agree
neutral
10. The way data items are combined in the financial statements makes interpretation of Alpha statements more difficult than interpretation of Beta statements. strongly agree
agree
neutral
disagree
strongly disagree
I (Second Phase of the study.) 11. Defining "usefulness" as the quality of facilitating decision making, which set of Alpha statements would be more useful to you in the previous allocation decision if that task were to be repeated? Set used in task Set from sealed material
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DAVID W. HARVEY, JOHN GRANT RHODE and KENNETH A. MERCHANT 12. Now consider Alpha's income statements, balance sheets, and funds statements separately. First compare the income statement from the task material with the income statement from the sealed material. Indicate which of these two statements you would prefer if that task were to be repeated. Next compare the balance sheets. Indicate which of these you would prefer. Compare the funds statements and state your preference. Task Income Statement Balance Sheet Funds Statement
Sealed