Module 7: Construction of Indicators

1. Tools for Civil Society to Understand and Use Development Data: Improving MDG Policymaking and Monitoring Module 7: Construction of Indicators

2. What you will be able to do by the end of this module: Understand the major types of quantitative indicators, and how they are formulated Understand the role that a measure of variation plays in using and interpreting indicators

3. Quantitative Indicators: Formulation Means Ratios Proportions Percentages Rates Quantiles Gini coefficient

4. Means ‘Average’ of two or more values: Simple: Sum of values/number of values Weighted: Multiply values by some weighting factor before summing, then divide by the sum of weights

5. Price increase

6. Price increase (2)

7. Price increase (3)

8. Ratios A ratio is the division of two numbers which are both measured in the same units - Compares like quantities - Result has no units Example: - MDG I9: Ratio of girls to boys in primary, secondary and tertiary education

9. Ratios (2) Source: World Development Indicators, World Bank, 2008

10. Proportions When the ratio takes the form of a part divided by the whole, it is called a proportion Proportions therefore have no units

11. Proportions (2) Example. Rural population as a proportion of total population, 2006 Source: World Development Indicators, World Bank, 2008

12. Percentages To express a proportion as a percentage, multiply it by 100% So, in 2006 in rural areas lived 0.273 ∙ 100%=27.3% and 0.530 ∙ 100%=53.0% of the total population in Belarus and Moldova correspondingly

13. Rates When the numerator and denominator of a quotient do not have the same units, but are related in some other way, the result is a rate We usually use the word ‘per’ in the description of a rate

14. Rates (2) Example. Infant mortality rate (IMR), 2004 Source: Health for All Database, WHO Regional Office for Europe, 2006

15. Standardized Rates Example. Crude (unweighted) and standardized (weighted) death rates in urban and rural areas of Romania Source: Mark Woodward, 2005, “Epidemiology: Study Design and Data Analysis, 2nd ed.”, Chapman & Hall/CRC, Boca Raton

16. Standardized Rates (2) Crude death rate, per 1,000 population (CDR) = =1000 ∙ total deaths / total population Urban CDR = 1000 ∙ (3526+1010 + …+ 25909)/ 12406204 = 8.66 Rural CDR = 1000 ∙ (4997+1049 + … +49561)/ 10349056 = 15.06 Seems to be a large difference between urban and rural CDRs, which could depend, however, on age structure of the population

17. Standardized Rates (3) Standardized death rate, per 1,000 population (SDR) = = The weights used to calculate the SDR for both urban and rural areas must be the same and must be equal to the shares of each age group’s population in total population

18. Standardized Rates (4) Age 0-9 - Urban CDR = 1000 ∙ 3526 / 1800680 = 1.96 - Rural CDR = 1000 ∙ 4997 / 1359501 = 3.68 - Weight = (1800680 + 1359501) / 22755260 = 0.139 Age 10-19 - Urban CDR = 1000 ∙ 1010 / 2128150 = 0.47 - Rural CDR = 1000 ∙ 1049 / 1642941 = 0.64 - Weight = (2128150 + 1642941) / 22755260 = 0.166 Etc.

19. Standardized Rates (5) Urban SDR = 1000 ∙ (1.96∙ 0.139 + 0.47∙ 0.166 + + … + 147.85∙ 0.020) / 1* = 11.24 Rural SDR = 1000 ∙ (3.68 ∙ 0.139 + 0.64 ∙ 0.166 + + … + 170.28∙ 0.020) / 1* = 11.99 Unlike crude death rates, there is only minor difference in standardized death rates between urban and rural areas * 1 = Sum of weights

20. Q1 Q2 Q3 Quantiles Quantiles are a set of points that, according to their values, divide a set of ordered values into a defined number of groups each containing the same number of values E.g., three quantiles divide a set of numbers into four groups The following quantiles are used often: median (two groups), tertiles (three groups), quartiles (four groups), quintiles (five groups), deciles (ten groups), percentiles (one hundred groups)

21. Quantiles (2) Example: Find the tertiles of the numbers 9,6,2,14,8,15,7,3,14,11,12,5,10,1,17,12,13,8 Note: two values are needed to divide this set of values into three groups First, put the 18 values in order from smallest to largest, and then divide them into groups of size 6. 1,2,3,5,6,7,8,8,9,10,11,12,12,13,14,14,15,17 t1 t2 Here, t1 = 7.5 and t2 = 12

22. Quantiles (3) Example. Indicator for MDG1: Share of the poorest quintile in national consumption Estimate household consumption (from household survey data) Adjust consumption for household size (to get per capita consumption); to determine per capita consumption, divide household consumption by the (equivalent) number of people in the household

23. Quantiles (4) Rank people by per capita consumption (smallest to largest) Find the first quintile (Q1) Aggregate all consumption less than Q1, and aggregate all consumption Divide the sum of all consumption below Q1 by the sum of all consumption This ratio multiplied by 100% is the value of MDG indicator

24. Gini Coefficient This is a special indicator used to measure inequality 1 → complete inequality, 0 → complete equality Gini coefficient = Area A/(Area A + Area B) A B

25. Gini Coefficient (2) Sources: Social Environment and Living Standards in the Republic of Belarus. Statistical Book, 2005, Minsk Statistical Yearbook of the Republic of Moldova, 2005, Chisinau

26. Indicators and Variability An indicator such as a percentage or a quintile gives a ‘snapshot’ picture of some particular aspect of the process it represents Example. Per capita income in Kyrgyzstan by settlement type, thousand Kyrgyz soms Source: ADB Study on Remittances and Poverty in Central Asia and Caucasus, 2007

27. Indicators and Variability (2) Looks like income per capita is higher in capital city than in two other types of settlements, and in other towns it is higher than in rural areas Need to be able to prove this, by using information about the standard error of the variable as evidence

28. Indicators and Variability (3) The estimated standard error is a measure of sampling error; usually the larger sample size the smaller this error In fact, we usually prefer to convert this into a range of values within which we expect to find the estimate We describe the likelihood of the range containing the estimate with a percentage – usually 95%

29. Indicators and Variability (4) With probability 95% it is possible to claim that per capita income in the capital city is higher than in other settlements But, with 5% error probability it is impossible to claim that there is a difference in per capita income between other urban and rural areas

30. Indicators and Variability (5) Maternal mortality estimates, with confidence intervals Source: UNICEF

31. Summary We have looked at the major types of quantitative indicators in terms of - Formulation - Characteristics - Uses - Interpretation We have discussed the role that variability and measures of it can play in enhancing the interpretation and use of indicators

32. Practical 7 Why are quantiles useful as indicators of national and sub-national development? Why use rates as indicators rather than actual numbers? Why is standardization useful for comparing the situation between sub-populations?

33. Practical 7 (2) Look at the following examples, and say whether a real difference exists: Ratio of girls to boys in secondary school: 1995: 0.94 95% confidence interval (0.93, 0.95) 2000: 0.95 95% confidence interval (0.88, 1.02) Population below the food poverty line: 1991/92: 21.6% 95% confidence interval (20.5, 22.7) 2000/01: 18.7% 95% confidence interval (17.7, 19.7) The following sequence of infant mortality rates: Year Infant Mortality Rate 1990 30 1994 28 1997 22 2000 21 2003 18