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sScpe <10 }Y; 10-20 N,; >20 N}Y. h2 -NV1998t^ؚNeP^[gIleN\pele~v\NN ^txQ~v\Nvt^R^(7usYTN)N'`+Rkvk t^ R ^'`+RkT#t^100101102103104105106107108109T100-104105-109100-109Ile38.6124.4914.578.944.923.132.141.610.850.7610026.1921.022249\pele30.0024.7115.888.829.412.354.122.351.760.5910017.0518.75179^txQ44.6425.4014.297.724.072.251.040.410.140.0410024.5319.345556 h3 -NV1998t^ؚNeP^[gvSO^|pe SϑR{|peϑSO^|pea1. N,R50.93952. S^R30.98863. {R50.99104. V_R50.98505. R60.89236. _{1uVT{ FO NVT{v320.98277. cknxVT{NYN,R0S^R0{R0V_R0RI{_{1uVT{v 23 0.95308. N;mRR20.80869. SO;mRRb20.845210. e8^u;mtR60.8790e8^u;mtR (V)c60.84e8^u;mtR (Rb'Y)d180.89la. bN(u NbvCronbach s alpha el{SO^|pe Rtt(alpha)=1-[(MSwithin/MSrespondents)-(MSrespondents-MSwithin)/MSrespondents], ُ̑MS/fGWfWv~ϑ EMBED Equation.3 125 poor. Mayers Index: <10 good, 10-20 so-so, >20 poor. Table 2. Age Distribution (Males and Females Combined) and Sex Ratio of Han and Minority Chinese Centenarians Interviewed in the 1998 survey, as Compared to Swedish Centenarians Age DistributionSex RatioTotal #Age100101102103104105106107108109Total100-104105-109100-109Han 38.6124.4914.578.944.923.132.141.610.850.7610026.1921.022249Minority 30.0024.7115.888.829.412.354.122.351.760.5910017.0518.75179Swedish44.6425.4014.297.724.072.251.040.410.140.0410024.5319.345556 The reliability coefficients of the 10 categories of variables are rather good (see Table 3). For example, the ADL reliability coefficient is 0.88 in our 1998 survey, while it was 0.87 in the Duke Older American Resources and Services Program survey (Fillenbaum, 1988) and 0.89 in the Canadian 1991-92 elderly survey (Penning and Strain, 1994). Another way of measuring reliability is to conduct factor analysis to see whether interviewees answers to questions of the same category are consistent (Anita et al., 1992). If they are, the answers to questions of the same category should be classified in one component and the values of the coefficients should be close to each other. Our factor analysis demonstrates clearly that the consistency and reliability of the answers are rather good (see Table 4). Table 3 Reliability Coefficients Category of Variables# of questionsRCa1. Orientation50.93952. Registration30.98863. Calculation 50.99104. Recall50.98505. Language60.89236. Unable to answer those questions which are supposed to be answered by interviewees320.98277. Correctly answer those questions concerning orientation, registration, attention, calculation, recall and language which are supposed to be answered by interviewees 230.95308. Upper extremities20.80869. Capacity of body movementb20.845210. ADL60.8790ADL (U.S.A.)c60.84ADL (Canada)d180.89Notes: a. RC = Reliability Coefficient. We used Cronbachs alpha to compute RC as follows: Rtt(alpha)=1-[(MSwithin/MSrespondents)-((MSrespondents-MSwithin)/MSrespondents)] where MS is Mean Squares. See: Anita L. Stewart, et al. 1992: 82. b. Include standing up from a chair and picking up a book from the floor. c. See: G.G. Fillenbaum, 1988: 24. d. See: Margaret J. Penning et al. 1994: s204. Table 4 Factor Analysis - Pattern Matrix Component12345ADLADLbathing0.00740.73100.05430.08140.0207ADLdressing0.04700.84620.00410.0177-0.0379ADLgoing to toilet0.04400.8976-0.0122-0.0077-0.0647ADLtransfer0.04230.8848-0.0252-0.0267-0.0822ADLcontinence-0.08520.6556-0.00440.00690.1572ADLfeeding0.04450.7755-0.0101-0.0598-0.1194OrientationOrientation-10.5404-0.1105-0.0794-0.01070.3286Orientation-20.5038-0.1198-0.2840-0.02220.1183Orientation-30.5294-0.0423-0.2580-0.05270.1578Orientation-40.5532-0.0641-0.2203-0.08190.1284Orientation-50.4696-0.0841-0.2412-0.06830.1430RegistrationRegistration-10.4459-0.05250.0982-0.59790.0690Registration-20.2313-0.0218-0.0908-0.43770.1418Registration-30.2478-0.0262-0.0598-0.45690.1229CalculationCalcualtion-10.2234-0.0250-0.6851-0.01410.0824Calcualtion-20.0818-0.0104-0.8403-0.0375-0.0352Calcualtion-30.0418-0.0121-0.8998-0.0122-0.0289Calcualtion-4-0.0108-0.0065-0.8905-0.0301-0.0368Calcualtion-50.0153-0.0036-0.8968-0.0237-0.0232RecallRecall-1-0.0551-0.0331-0.0814-0.8117-0.0051Recall-2-0.1241-0.0261-0.1139-0.78180.0326Recall-3-0.1460-0.0201-0.0829-0.82370.0137LanguageLanguage-a10.1786-0.03960.02960.05490.7972Language-a20.1615-0.03390.01130.06370.8015Language-b0.4459-0.05250.0982-0.59790.0690Language-c1-0.0450-0.0084-0.0291-0.08350.8385Language-c2-0.0962-0.0145-0.0512-0.08520.8645Language-c3-0.1002-0.0564-0.0401-0.09320.8353Notes: 1. All of the estimates of the coefficients of the same category items are consistent except the estimates for the language-b item, which are not consistent with other language items because the language-b item is not properly designed. It asked the interviewee to repeat a sentence Grow melons and beans in front of the house and in back of the house, and it turned out that this sentence was simply too difficult for the oldest old persons to understand and repeat. 2. SPSS Software (SPSS 9.0 version, 1998) was used to conduct the principal component analysis. The rotation method used was Oblimin with Kaiser normalization. The rates of logically inconsistent answers seem reasonably low (see Table 5). The rates of Dont know and Missing answers are also relatively small (see Table 6). The above-mentioned indicators have led us to believe that the data quality of our 1998 survey is generally good. However, we also realize that some problems exist in the data set. This is expected given its nature as the first large survey of oldest old people conducted in a developing country. For example, the proportion of oldest old living in institutions might be over-estimated. We noticed that the proportions of those living in institutions based on the 1998 survey had substantially increased as compared with the corresponding figures based on the 1990 census. This increase might be due to two main factors. First, because of rapid economic development and increased governmental and societal attentions to social service for the elderly since 1990, there was a real increase in institutional facilities between 1990 and 1998. Second, as discussed earlier, for each centenarian in the randomly selected half of the counties and cities, we instructed our survey teams to try to interview one close-by octogenarian and one close-by nonagenarian of pre-specified age and sex. If the centenarians resided in or close to an institution, it was likely that the matched octogenarians and nonagenarians were selected from the institution. Therefore, the institutionalized oldest old might be over-sampled. Another example is that we found that a substantially higher proportion of the oldest old, especially centenarians, were unable to answer more of the personality-related questions than other types of questions. This is because some illiterate oldest old, especially centenarians, could not understand the questions about personality, which ask oldest old to provide a comparison of themselves to a typical person with a specified disposition (e.g. always look on the bright side of things). We expect that further evaluation, accompanied by subsequent in-depth analysis, will provide information that will permit a more critical examination of the data quality. Table 5 Percentage of Oldest Old with Inconsistent Responses Items of inconsistent response#%1. Age at beginning smoking is greater than age at stopping smoking20.022. Didnt smoke in the past, but gave age of beginning (or stopping) smoking110.123. Didnt drink alcohol in the past, but gave age of beginning (or stopping) drinking350.394. Age of beginning exercising is greater than age of stopping exercising30.035. Didnt exercise in the past, but gave age of beginning (stopping) exercising360.406. Age of beginning doing physical labor is greater than age of stopping doing it10.017. Didnt do physical labor in the past, but gave age of beginning (or stopping) doing it 931.048. Age difference between mothers age and the interviewees age at time of mothers death is less than 12 years290.329. Age difference between fathers age and the interviewees age at time of fathers death is less than 12 years 260.2910. Reported no sibling, but gave sibling information or vice versa.70.0811. Age difference between interviewee and his or her eldest child is less than 12 years 420.4712. Reported bedridden, but able to stand up from a chair 1141.2813. Fully dependent (ADL) but able to turn around and stand up from a chair without help2562.8614. Unable to stand up from a chair but doing housework and field work everyday210.2315. Unable to turn around by self but doing housework and fieldwork everyday1281.4316. Reported bedridden but doing housework and field work everyday120.1317. Some items reported by proxy, but interviewer chose no one helped the interviewee to answer any question (this inconsistency might be caused by the interviewers misunderstanding the question Did anyone help the interviewee to answer any question? addressed to the interviewer. They might have misunderstood it as referring only to those questions that must be answered by interviewee.)118113.21 Oldest old with at least one of the inconsistencies listed above (not including the proxy inconsistency, as described in the above item 17) 756 8.46 Table 6 Percentage of Dont know and Missing Answers among all Questions Asked in the Chinese 1998 Healthy Longevity Survey Males (%)Females (%)AgeDont knowMissingTotalDont knowMissingTotal80-891.181.642.821.331.242.5790-991.511.072.581.850.872.72100+1.710.952.662.200.983.18 Chapter 5 Weighting method Our 1998 healthy longevity survey tried to interview all centenarians who voluntarily agreed to participate in the survey, in the randomly selected half of the counties and cities of the 22 provinces. For each centenarian, one nearby octogenarian (aged 80-89) and one nearby nonagenarian (aged 90-99) with pre-designed age and sex were matched and interviewed. We tried to have approximately equal numbers of male and female octogenarians and nonagenarians at each age from 80 to 99. We did not follow the procedure of proportional sampling, in order to avoid the errors of random fluctuation due to too small sample size at more advanced ages, especially for males. Consequently, appropriate weights should be used to compute the overall average for the oldest old persons age 80+ and the averages of the age groups (e.g. 80-89 and 90-99). The age (x), sex (s), and rural-urban residence (r) specific weight w(x,s,r) is computed as: w(x,s,r) = [ N(x,s,r) / (x(s(r N(x,s,r) ] / [ n(x,s,r) / (x(s(r n(x,s,r) ] = [N(x,s,r) / n(x,s,r) ] * [(x(s(r n(x,s,r) / (x(s(r N(x,s,r) ] N(x,s,r) is number of persons of age x, sex s, and residence r, derived from projected 1998 oldest old population based on the 1990 census 100% data tabulations for the 22 provinces where the 1998 survey was conducted, and the estimated age-sex-specific survival probabilities between 1990 and 1998. We have no age-specific data about rural-urban migration between 1990 and 1998. We, therefore, used the overall proportion of urban population age 80+ (0.378) derived from our 1998 survey, which is the same as our expert estimate of the urbanization level in the 22 provinces in 1998, to adjust the projected 1998 rural-urban distribution. The n(x,s,r) is number of persons of age x, sex s, and residence r, derived from the 1998 healthy longevity survey. The weight is actually the multiplication of the ratio of [N(x,s,r) / n(x,s,r) ] and the factor [(x(s(r n(x,s,r) / (x(s(r N(x,s,r) ]. The factor is the overall sampling ratio. No weights are needed when we compute the average of the centenarians age 100-105, since the survey attempted to interview all centenarians in the sampled areas. We did not include the very few cases of super-centenarians of age 106 and above due to possibility of questionable quality of their age reporting. The weight w(x,s,r) is actually the ratio of age distribution of the entire population age 80+ in 1998 to the age distribution of the 1998 sample. The weights for the over-sampled extremely old persons (e.g. 90+) are less than 1.0, and weights for under-sampled elders (e.g. age 80-85) are greater than 1.0. The values of the weights vary (usually greater than 1.0 under age 88 and less than 1.0 above age 90), and it produces correct proportions of certain attributes within age groups by using the weights. However, SPSS (or other software) would not produce correct p-values for testing the statistical significance of the differences of the proportions among different age groups, since the sub-sample size of the age groups are altered after weighting the individual cases. Therefore, the weights need to be adjusted to make sure that the sub-sample size within each age group after weighting is exactly the same as the true sub-sample size. Denote Cj(s,r) as the adjusting factor for age group j (e.g. age group 90-95) with sex s and residence r; Tj(s,r) as the total number of interviewed persons of the age group j with sex s and residence r. The following equations must be fulfilled: Cj(s,r)*(xw(x,s,r) n(x,s,r) = Tj (s,r). Solving this equation, we obtain the adjusting factor, Cj (s,r) = Tj (s,r) / (x [w(x,s,r) n(x,s,r)]. (x here refers to the sum of the number of the persons over the age group (e.g. age group 90-95). The adjusted weights are: w(x,s,r) = w(x,s,r) * Cj (s,r). We should use the adjusted weights that produce both correct proportions, and correct sub-sample sizes and thus correct p-values for testing statistical significance of the differences of the proportions among various age groups. If one computes proportions of certain attributes of age groups with rural and urban combined, the adjusting factor is not rural-urban specific, but age group (j) and sex specific: Cj (s) = Tj (s) / (x (r [w(x,s,r) n(x,s,r)]. If one computes proportions of certain attributes of age groups with both rural and urban combined and sexes combined, the adjusting factor is neither rural-urban specific, nor sex-specific, but only age group (j) specific: Cj = Tj / (x (r (s [w(x,s,r) n(x,s,r)]. References Banister, J. 1990. Implications of aging of China's population. In: Zeng Yi, Zhang Chunyuan and Peng Songjian (eds.), Changing Family Structure and Population Aging in China: A Comparative Approach. Peking University Press, 1990. Beijing. And in: Dudley L. 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