1 Curran, Barbara A., The Legal Needs of the Public: The Final Report of a National Survey (Chicago: American Bar Foundation, 1977).Google Scholar

2 For a discussion of the problems asked about and the precise wording in the questionnaire, see id. at 20-23, 287-336.Google Scholar

3 When a lawyer was used, there was further detailed probing into the nature of the client-lawyer relationship.Google Scholar

4 Cf. Curran, supra note 1, at 99-134.Google Scholar

5 For a brief description of the 29 specific problems along with information on incidence rates and lawyer use rates see id. at 161 table 4.27.Google Scholar

6 See, e.g., id. Google Scholar

7 See, e.g., id. Google Scholar

8 There were good reasons for not asking for that information. Id. at 44 n.26.Google Scholar

9 If each of these seven problem situations were assigned the relatively high average number of occurrences of 1.5, it would have increased the total number of problems encountered and cones quently the mean number of problems per respondent by no more than 6 percent.Google Scholar

10 See also Curran, supra note 1, at 100 table 4.1.Google Scholar

11 According to the Poisson distribution, the probability of 0, 1, 2,… occurrences is given by e^−λλ^k/KI, where K= 0, 1, 2,…., represents the number of occurrences, e (= 2.718…) is the basis of the natural logarithm, and h is the parameter that determines a specific distribution within the general type. The mean of the Poisson distribution is equal to h. For this reason, the calculations presented in the table were based upon h= 4.8 the mean number of occurrences for the sample.Google Scholar

12 The standard deviation is a measure of dispersion of the distribution around its mean: The smaller it is, the more concentrated are the points around the mean. The standard deviation of the Poisson distribution is √λ, which in the present case is √4.8 = 2.2.Google Scholar

13 See also Curran, supra note 1, at 100 table 4.2.Google Scholar

14 The percentages shown were calculated for K= 0 and the Poisson distributions corresponding to the observed means; h= 2.3, 4.5, 6.0, 6.0, 5.2, and 4.6.Google Scholar

15 The calculation wasGoogle Scholar

(0.100 × 332 + 0.011 × 439 + .002 × 371 + .002 × 391 ++ .006 × 270 + .010 × 254) ÷ 2,064 = .021.Google Scholar

16 The age 16, though arbitrary, represents an attempt at recognizing that adult respondents of age 18 and over as defined in the survey can and do accumulate problems before the age of 18. For almost all of the 29 problems, there are cases where the age of occurrence is before 18. Despite the arbitrariness of the age chosen, the model as developed is not sensitive to or dependent on this figure: to replace it with any neighboring figure would not alter the main conclusions derived from the model or significantly change the estimated number of problems from the model.Google Scholar

17 Various functions were tried in the model to describe the cumulative increase in the number of problems accumulated with age. The logarithm seems to fit best because of its moderate increase in the range of ages of interest. Thus, for example, the logarithm of 10, 30, 50, and 70 is 2.3, 3.4, 3.9, and 4.2, respectively. It also increases by a lesser amount between consecutive ages with the increase in age: the differences between 10 to 30, 30 to 50, and 50 to 70 are 1.1, 0.5, and 0.3, respectively. The model, however, does not assume this to be the actual increase in the number of problems with age but rather only the type of increase, since the coefficient a in the equation remains to be determined. The type of the functional increase is in turn confirmed by the goodness of fit of the model as a whole.Google Scholar

For the functional description of the behavior across generations, the third power gave a better fit than the first power (linear relationship). Higher (odd) powers would have increased the fit of the model only marginally.Google Scholar

For each age group the midpoint of the interval was used. Thus, for example, the midpoint of the 18-24 interval age group is 18 + (25 - 18) ÷ 2 = 21.5. The “middle” of the 65 and over age group is set at 70, despite its being “open” because the ages within the group are close to it (the sample mean is 71 and the sample median is 68).Google Scholar

18 Under the least squares criterion, the parameters to be determined from the data (in this case a, b, and c) are such as to minimize the sum of squared deviations between the observed figures and those given by the model.Google Scholar

19 R ² is a measure of goodness of fit of a model. It ranges from 0 to a maximum of 1. An R ¹ of .97 means that 97 percent of the variability encountered in the data can be explained by the model itself, whereas the remaining 3 percent is attributed to random variations in the data.Google Scholar

20 The more precise figure for 1973 is 2.34, compared with 2.32 for 1963, leading to the 1 percent increase stated.Google Scholar

21 Cf. Curran, supra note 1, at 99-134.Google Scholar

22 No direct comparison of the number of cases given in the table is meaningful. Even an attempt to compare these numbers for the first acquisition only (after correcting for the different lengths of the periods) would be misleading because of the different age composition of the population at different times.Google Scholar

23 Even for the real property problem, the number of cases is too small to permit a valid analysis of prior decades.Google Scholar

24 The survey was taken during the period between October 1973 and March 1974. Here as in all cases in this article, the information for the 1974 year of occurrence is also used.Google Scholar

25 Thus, e.g., in 1951-60 the mean age of 37.9 given in the total is a result of the following calculation (actually performed with a higher precision than shown):Google Scholar

33.8 × 133/270 + 38.3 × 75/270 + 46.0 × 62/270 = 37.9.Google Scholar

This is now corrected to beGoogle Scholar

33.8 × 153/396 + 38.3 × 88/396 + 46.0 × 155/396 = 39.6.Google Scholar

26 The number of cases is presented in parentheses. The absolute numbers cannot be directly compared. See note 22 supra. Google Scholar

27 The comparison is presented in terms of these three age groups only because out of the present population, the number that in the 1950s could have belonged to the older age groups is small. Also, these older groups would have participated much less in any changes that have occurred recently. For comparison, in the 1971-74 period there were 24 and 11 occurrences for the age groups of 55-64 and 65 and over, respectively, with a corresponding 3.6 and 4.2 mean number of acquisitions. In the 18-24 group there were 73 occurences, with 1.3 acquisitions on the average.Google Scholar

28 For 1951-60 the calculation isGoogle Scholar

1.5 × 140/288 + 2.0 × 88/288 + 2.4 × 60/288 = 1.8.Google Scholar

The calculations were actually performed with higher precision than is here presented.Google Scholar

29 Even though the correction in this case has only a minor effect, it is nevertheless essential here and elsewhere.Google Scholar

30 Even for the damage-theft problem, some irregularities resulting from the small numbers of occurrences appear in the 1951-60 period, indicating the limits on feasibility of the detailed analysis with existing data.Google Scholar

31 The 5.2 figure for the 1971-74 period is unduly affected by a few respondents with a very large number of “occurrences.” In this period of time there were three respondents who had 30, 75, and more than 95 “occurrences,” respectively. Their scores were reduced to 20. Even so, the 5.2 figure is still inflated. If the three respondents are excluded from the calculations, the mean number of occurrences is only 4.2.Google Scholar

32 For the purpose of graphic presentation, the representative point for the 1901-40 period is arbitrarily chosen as 1930, which is closer to the average year of occurrence in the period than the midpoint, since only the last occurrence is recorded. The other periods are represented by their midpoints of 1945, 1955, 1965, and 1972, respectively. The last is actually slightly to the right of the midpoint, which lies between 1971 and 1972.Google Scholar

33 The χ² test tests the hypothesis of no difference among the proportions corresponding to the different time periods. As such, it is not sensitive to trends. However, when such a hypothesis is not rejected by the test and the graphic pattern shows a persistent trend, the combination provides strong evidence of the existence of such a trend. Had a special test for trend been applied, it would have shown even stronger significance than the one presented. Such a test is not necessary. The χ¹ test was preferred since it presumes no trend. It is being used in all of the comparisons for all the problems in this part.Google Scholar

34 The P value is the level of probability at which the differences will be regarded as statistically significant. In this case χ²= 1.66 with 2 degrees of freedom will be significant at about the 46 percent level.Google Scholar

35 χ²= 30.97 with 4 degrees of freedom is significant at less than 0.1 percent level.Google Scholar

36 χ²= 3.83 with 2 degrees of freedom has a P value of 15 percent.Google Scholar

37 For the 4 periods, χ²= 21.24 with 3 degrees of freedom is significant at less than the 0.1 percent level. For the last 3 periods, χ³= 16.66 with 2 degrees of freedom is also significant at less than the 0.1 percent level, finally for the two last periods, χ²= 8.91 with 1 degree of freedom is significant at less than the 0.5 percent level.Google Scholar

38 χ²= 8.55 with 4 degrees of freedom, not significant at the 5 percent level when compared with χ²·os(4) = 9.49. The P value is approximately 8 percent. It is very plausible that the relatively small number of occurrences in most time periods prevented the detection of significant differences in this case. (The meaning of a negative result in the test of significance is that no such differences are detected with sufficient confidence, not that they may not exist. On the other hand, if a difference is found to be significant, then chances are high that such differences do exist in the population.)Google Scholar

39 For the last 4, 3, and 2 periods, χ²= 11.31, 9.16, and 7.09, with 3, 2, and 1 degrees of freedom, respectively. All are significant at the 1 percent level or very close to it.Google Scholar

40 See Curran, , supra note 1, at 100 table 4.2 (the coefficient of variation).Google Scholar

41 See id. at 101 table 4.3 (the coefficient of variation).Google Scholar