<p> APPENDIX B</p><p>ESTIMATES OF SAMPLING ERRORS</p><p>The estimates from a sample survey are affected by two types of errors: non-sampling errors and sampling errors. Non-sampling errors are the results of mistakes made in implementing data collection and data processing, such as failure to locate and interview the correct household, misunderstanding of the questions on the part of either the interviewer or the respondent, and data entry errors. Although numerous efforts were made during the implementation of the [YYYY COUNTRY] Demographic and Health Survey [YYYY XDHS] to minimize this type of error, non-sampling errors are impossible to avoid and difficult to evaluate statistically.</p><p>Sampling errors, on the other hand, can be evaluated statistically. The sample of respondents selected in the [YYYY XDHS] is only one of many samples that could have been selected from the same population, using the same design and expected size. Each of these samples would yield results that differ somewhat from the results of the actual sample selected. Sampling errors are a measure of the variability between all possible samples. Although the degree of variability is not known exactly, it can be estimated from the survey results. </p><p>Sampling error is usually measured in terms of the standard error for a particular statistic (mean, percentage, etc.), which is the square root of the variance. The standard error can be used to calculate confidence intervals within which the true value for the population can reasonably be assumed to fall. For example, for any given statistic calculated from a sample survey, the value of that statistic will fall within a range of plus or minus two times the standard error of that statistic in 95 percent of all possible samples of identical size and design. </p><p>If the sample of respondents had been selected as a simple random sample, it would have been possible to use straightforward formulas for calculating sampling errors. However, the [YYYY XDHS] sample is the result of a multi-stage stratified design, and, consequently, it was necessary to use more complex formulae. Sampling errors are computed in either ISSA or SAS, using programs developed by ICF Macro. These programs use the Taylor linearization method of variance estimation for survey estimates that are means, proportions or ratios. The Jackknife repeated replication method is used for variance estimation of more complex statistics such as fertility and mortality rates.</p><p>The Taylor linearization method treats any percentage or average as a ratio estimate, r = y/x, where y represents the total sample value for variable y, and x represents the total number of cases in the group or subgroup under consideration. The variance of r is computed using the formula given below, with the standard error being the square root of the variance:</p><p>1 f H  m  mh z2  SE 2 (r)  var(r)  h  z2  h  2    hi  x h1 mh 1 i1 mh  in which</p><p> zhi  yhi  rxhi , and zh  yh  rxh where h represents the stratum which varies from 1 to H, th mh is the total number of clusters selected in the h stratum, th th yhi is the sum of the weighted values of variable y in the i cluster in the h stratum,</p><p>37 th th xhi is the sum of the weighted number of cases in the i cluster in the h stratum, and f is the overall sampling fraction, which is so small that it is ignored.</p><p>The Jackknife repeated replication method derives estimates of complex rates from each of several replications of the parent sample, and calculates standard errors for these estimates using simple formulae. Each replication considers all but one cluster in the calculation of the estimates. Pseudo- independent replications are thus created. In the [YYYY XDHS], there were [XXX] non-empty clusters. Hence, [XXX] replications were created. The variance of a rate r is calculated as follows:</p><p> k 2 1 2 SE (r)  var(r)   (ri  r) k(k  1) i1 in which</p><p> ri  kr  (k 1)r(i) where r is the estimate computed from the full sample of [XXX] clusters, th r(i) is the estimate computed from the reduced sample of [XXX] clusters (i cluster excluded), and k is the total number of clusters.</p><p>In addition to the standard error, the design effect (DEFT) for each estimate is also calculated The design effect is defined as the ratio between the standard error using the given sample design and the standard error that would result if a simple random sample had been used. A DEFT value of 1.0 indicates that the sample design is as efficient as a simple random sample, while a value greater than 1.0 indicates the increase in the sampling error due to the use of a more complex and less statistically efficient design. Relative standard errors and confidence limits for the estimates are also calculated.</p><p>Sampling errors for the [YYYY XDHS] are calculated for selected variables considered to be of primary interest. The results are presented in this appendix for the country as a whole, for urban and rural areas, and for [INSERT COUNTRY SPECIFIC INFORMATION ON REGIONS]. For each variable, the type of statistic (mean, proportion, or rate) and the base population are given in Table B.1. Tables B.2 through B.XX present the value of the statistic (R), its standard error (SE), the number of un-weighted (N) and weighted (WN) cases, the design effect (DEFT), the relative standard error (SE/R), and the 95 percent confidence limits (R±2SE), for each variable. The sampling errors for mortality rates are presented for the five year period preceding the survey for the whole country and for the ten year period preceding the survey by residence and region. The DEFT is considered undefined when the standard error considering a simple random sample is zero (when the estimate is close to 0 or 1). In the case of the total fertility rate, the number of un-weighted cases is not relevant, as there is no known un-weighted value for woman-years of exposure to childbearing.</p><p>The confidence interval (e.g., as calculated for children ever born to women age 40-49) can be interpreted as follows: the overall average from the national sample is [XXXX] and its standard error is [XXXX]. Therefore, to obtain the 95 percent confidence limits, one adds and subtracts twice the standard error to the sample estimate, i.e., [XXXX]±2×[XXXX]. There is a high probability (95 percent) that the true average number of children ever born to all women aged 40 to 49 is between [XXXX and XXXX].</p><p>For the total sample, the value of the DEFT, averaged over all variables, is [XXXX]. This means that, due to multi-stage clustering of the sample, the average standard error is increased by a factor of [XXXX] over that in an equivalent simple random sample.</p><p>38 FOR COUNTRY MANAGERS :</p><p>Table B.1 includes a list of the variables for which confidence intervals are shown. This list should be customized to the country. Additional variables of interest may be added and variables that are not relevant to the country should be deleted. In Table B.1, the primary school ages for the net attendance ratio need to be adapted to the country. In addition, indicators with very low percentages in the country (for example, less than around 5 percent) should be considered for deletion.</p><p>If the country measured the maternal mortality ratio (MMR), please remember to request the calculation of the confidence interval. This information must be included in the report and should be included in the text of the maternal mortality chapter itself rather than in Appendix B. The confidence interval for MMR is much wider than for other indicators reported in the survey, so it is important to present the confidence interval along side the estimate itself.</p><p>39 Table B.1 List of selected variables for sampling errors, [country, year]</p><p>–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Variable Estimate Base population –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– WOMEN –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Urban residence Proportion All women 15-49 Literacy Proportion All women 15-49 No education Proportion All women 15-49 Secondary education or higher Proportion All women 15-49 Net attendance ratio Ratio Household population [7-12] years Never married/in union Proportion All women 15-49 Currently married/in union Proportion All women 15-49 Married before age 20 Proportion All women 20-49 Had sexual intercourse before age 18 Proportion All women 20-49 Currently pregnant Proportion All women 15-49 Children ever born Mean All women 15-49 Children surviving Mean All women 15-49 Children ever born to women age 40-49 Mean All women 40-49 Know any contraceptive method Proportion Currently married women 15-49 Know a modern method Proportion Currently married women 15-49 Currently using any method Proportion Currently married women 15-49 Currently using a modern method Proportion Currently married women 15-49 Currently using a traditional method Proportion Currently married women 15-49 Currently using pill Proportion Currently married women 15-49 Currently using condoms Proportion Currently married women 15-49 Currently using injectables Proportion Currently married women 15-49 Currently using female sterilization Proportion Currently married women 15-49 Currently using withdrawal Proportion Currently married women 15-49 Currently using rhythm Proportion Currently married women 15-49 Used public sector source Proportion Current users of modern method Want no more children Proportion Currently married women 15-49 Want to delay next birth at least 2 years Proportion Currently married women 15-49 Ideal number of children Mean All women 15-49 Mothers protected against tetanus for last birth Proportion Women with a live birth in last five years Births with skilled attendant at delivery Proportion Births occurring 1-59 months before survey Had diarrhea in the past 2 weeks Proportion Children under 5 Treated with ORS Proportion Children under 5 with diarrhea in past 2 weeks Sought medical treatment Proportion Children under 5 with diarrhea in past 2 weeks Vaccination card seen Proportion Children 12-23 months Received BCG vaccination Proportion Children 12-23 months Received DPT vaccination (3 doses) Proportion Children 12-23 months Received polio vaccination (3 doses) Proportion Children 12-23 months Received measles vaccination Proportion Children 12-23 months Received all vaccinations Proportion Children 12-23 months Height-for-age (-2SD) Proportion Children under 5 who are measured Weight-for-height (-2SD) Proportion Children under 5 who are measured Weight-for-age (-2SD) Proportion Children under 5 who are measured Body Mass Index (BMI) <18.5 Proportion All women 15-49 who were measured Prevalence of anemia (children 6-59 months) Proportion All children 6-59 months who were tested Prevalence of anemia (women 15-49) Proportion All women 15-49 who were tested Had 2+ sexual partners in past 12 months Proportion All women 15-49 Condom use at last sex Proportion Women 15-49 with 2+ partners in past 12 months Abstinence among youth (never had sex) Proportion Never-married women 15-24 Sexually active in past 12 months among never-married youth Proportion Never-married women 15-24 Had an HIV test and received results in past 12 months Proportion All women 15-49 Accepting attitudes towards people with HIV Proportion All women who have heard of HIV/AIDS HIV prevalence among all women 15-49 Proportion All interviewed women with Dried Blood Sample (DBS) tested at the lab HIV prevalence among pregnant women 15-49 Proportion All interviewed pregnant women 15-49 with DBS tested at the lab HIV prevalence among young women 15-24 Proportion All interviewed women 15-24 with DBS tested at the lab HIV prevalence all respondents Proportion All interviewed women and men 15-49 with DBS tested at the lab Total fertility rate (3 years) Rate Women-years of exposure to childbearing Neonatal mortality rate¹ Rate Children exposed to the risk of mortality Post-neonatal mortality rate¹ Rate Children exposed to the risk of mortality Infant mortality rate¹ Rate Children exposed to the risk of mortality Child mortality rate¹ Rate Children exposed to the risk of mortality Under-five mortality rate¹ Rate Children exposed to the risk of mortality –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– MEN –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Urban residence Proportion All men 15-49 Literacy Proportion All men 15-49 No education Proportion All men 15-49 Secondary education or higher Proportion All men 15-49 Net attendance ratio Ratio Household population [7-12] years Never married/in union Proportion All men 15-49 Currently married/in union Proportion All men 15-49 Had sexual intercourse before age 18 Proportion All men 20-49 Know any contraceptive method Proportion Currently married men 15-49 Know a modern method Proportion Currently married men 15-49 Ever used any contraceptive method Proportion Currently married men 15-49 Want no more children Proportion Currently married men 15-49</p><p>40 Table B.2 Sampling errors for national sample, [country, year] ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Number of cases Stand- –––––––––––––––– Rela- ard Un- Weight- Design tive Confidence limits Value error weighted ed effect error –––––––––––––– Variable (R) (SE) (N) (WN) (DEFT) (SE/R) R-2SE R+2SE ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– WOMEN ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Urban residence Literacy No education Secondary education or higher Net attendance ratio Never married/in union Currently married/in union Married before age 20 Had sexual intercourse before age 18 Currently pregnant Children ever born Children surviving Children ever born to women age 40-49 Know any contraceptive method Know a modern method Ever used any contraceptive method Currently using any method Currently using a modern method Currently using a traditional method Currently using pill Currently using condoms Currently using injectables Currently using female sterilization Currently using withdrawal Currently using periodic abstinence Used public sector source Want no more children Want to delay nest birth at least 2 years Ideal number of children Mothers protected against tetanus for last birth Births with skilled attendant at delivery Had diarrhea in the past 2 weeks Treated with ORS Sought medical treatment Vaccination card seen Received BCG vaccination Received DPT vaccination (3 doses) Received polio vaccination (3 doses) Received measles vaccination Received all vaccinations Height-for-age (-2SD) Weight-for-height (-2SD) Weight-for-age (-2SD) Body Mass Index (BMI) <18.5 Prevalence of anemia (children 6-59 months) Prevalence of anemia (women 15-49) Had 2+ sexual partners in past 12 months Condom use at last sex Abstinence among youth (never had sex) Sexually active in past 12 months among never-married youth Had an HIV test and received results in past 12 months Accepting attitudes towards people with HIV HIV prevalence among all women 15-49 HIV prevalence among pregnant women 15-49 HIV prevalence among young women 15-24 HIV prevalence all respondents Total fertility rate (3 years) Neonatal mortality rate (0-4 years) Post-neonatal mortality rate (0-4 years) Infant mortality rate (0-4 years) Child mortality rate (0-4 years) Under-five mortality rate (0-4 years) ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– MEN ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Urban residence Literacy No education Secondary education or higher Never married/in union Currently married/in union Had sexual intercourse before age 18 Know any contraceptive method Know a modern method Ever used any contraceptive method</p><p>41 42</p>