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

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

Quantitative Indicators: Formulation MeansMeans RatiosRatios ProportionsProportions PercentagesPercentages RatesRates QuantilesQuantiles Gini coefficientGini coefficient

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

Price increase % of price increase Income spent % of income spent Meat Bread Fruit Food average ???

Price increase (2) % of price increase Income spent % of income spent Meat Bread Fruit Food average ( )/3 =

Price increase (3) % of price increase Income spent % of income spent Meat Bread Fruit Food average 12∙50/100+20∙ 40/ ∙10/ 100=

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

Ratios (2) Country, year IndicatorGirlsBoysRatio Belarus, 2006 Net enrollment in general secondary education Moldova, 2006 Gross enrollment in general secondary education Source: World Development Indicators, World Bank, 2008

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

Proportions (2) Example. Rural population as a proportion of total population, 2006 Country Rural population, thousand people Total population, thousand people Proportion Belarus Moldova Source: World Development Indicators, World Bank, 2008

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

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

Rates (2) Example. Infant mortality rate (IMR), 2004 Country Infant deaths Number of live births IMR, per 1,000 live births Belarus61488, ∙614/ 88,943=6.9 Moldova46438, ∙464/ 38,272=12.1 Source: Health for All Database, WHO Regional Office for Europe, 2006

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 PopulationDeaths Age group UrbanRuralTotalUrbanRural Total

Standardized Rates (2) Crude death rate, per 1,000 population (CDR) = =1000 ∙ total deaths / total population Urban CDR = 1000 ∙ ( … )/ = 8.66 Rural CDR = 1000 ∙ ( … )/ = Rural CDR = 1000 ∙ ( … )/ = Seems to be a large difference between urban and rural CDRs, which could depend, however, on age structure of the population

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

Standardized Rates (4) Age Urban CDR = 1000 ∙ 3526 / = Rural CDR = 1000 ∙ 4997 / = Weight = ( ) / = Age 10-19Age Urban CDR = 1000 ∙ 1010 / = Rural CDR = 1000 ∙ 1049 / = Weight = ( ) / = Etc.Etc.

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

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 valuesQuantiles 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 groupsE.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)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) Q1Q1Q1Q1 Q2Q2Q2Q2 Q3Q3Q3Q3

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 t 1 t 2 t 1 t 2 Here, t 1 = 7.5 and t 2 = 12

Quantiles (3) Example. Indicator for MDG1: Share of the poorest quintile in national consumption Estimate household consumption (from household survey data)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 householdAdjust 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

Quantiles (4) Rank people by per capita consumption (smallest to largest)Rank people by per capita consumption (smallest to largest) Find the first quintile (Q 1 )Find the first quintile (Q 1 ) Aggregate all consumption less than Q 1, and aggregate all consumptionAggregate all consumption less than Q 1, and aggregate all consumption Divide the sum of all consumption below Q 1 by the sum of all consumptionDivide the sum of all consumption below Q 1 by the sum of all consumption This ratio multiplied by 100% is the value of MDG indicatorThis ratio multiplied by 100% is the value of MDG indicator

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

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

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 Remittances and Poverty in Central Asia and in Central Asia and Caucasus, 2007 Caucasus, 2007

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 areasLooks 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 evidenceNeed to be able to prove this, by using information about the standard error of the variable as evidence

Indicators and Variability (3) The estimated standard error is a measure of sampling error; usually the larger sample size the smaller this errorThe 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 estimateIn 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%We describe the likelihood of the range containing the estimate with a percentage – usually 95%

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 settlementsWith 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 areasBut, with 5% error probability it is impossible to claim that there is a difference in per capita income between other urban and rural areas

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

Summary We have looked at the major types of quantitative indicators in terms ofWe 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 indicatorsWe have discussed the role that variability and measures of it can play in enhancing the interpretation and use of indicators

Practical 7 1.Why are quantiles useful as indicators of national and sub-national development? 2.Why use rates as indicators rather than actual numbers? 3.Why is standardization useful for comparing the situation between sub-populations?

Practical 7 (2) 4.Look at the following examples, and say whether a real difference exists: Ratio of girls to boys in secondary school:Ratio of girls to boys in secondary school: 1995: % confidence interval (0.93, 0.95) 1995: % confidence interval (0.93, 0.95) 2000: % confidence interval (0.88, 1.02) 2000: % confidence interval (0.88, 1.02) Population below the food poverty line:Population below the food poverty line: 1991/92: 21.6% 95% confidence interval (20.5, 22.7) 1991/92: 21.6% 95% confidence interval (20.5, 22.7) 2000/01: 18.7% 95% confidence interval (17.7, 19.7) 2000/01: 18.7% 95% confidence interval (17.7, 19.7) The following sequence of infant mortality rates:The following sequence of infant mortality rates: Year Infant Mortality Rate