Project for the Regional Advancement of Statistics in the Caribbean - PRASC

Transcription

1 Project for the Regional Advancement of Statistics in the Caribbean - PRASC

2 Descriptive Statistical Tools for Data Analysis Analysis Workshop - Module 2 2 March 21-24, 2016 Kingstown, Saint Vincent and the Grenadines

3 Descriptive statistics Descriptive statistics: tools for summarizing and describing data, whether for a sample or a population. Why do we use descriptive statistics? To understand the data To describe the data to our audience To illustrate and answer analytical questions Descriptive statistics are key in all analytical projects, even ones that involve complex statistical techniques 3

4 Objectives of this presentation Describe commonly used tools to help convey meaningful analytical messages with data Examples highlight how these tools are used to answer real-world analytical questions Demonstrate how descriptive statistics can be used in conjunction with charts and tables to communicate analytical messages effectively 4

5 Outline Part 1: Descriptive statistical tools Types of variables Measures used to describe a variable Measures of central tendency Frequency distribution Relative frequency and compositional analysis Changes over time Measures of dispersion Standardization techniques 5

6 Outline (cont d) Part 2: Presenting descriptive statistics efficiently Charts, tables and maps Part 3: Discussion and conclusion 6

7 Part 1: Descriptive statistical tools 7

8 Types of variables Variable: a characteristic that may assume more than one set of values to which a measure is assigned. Categorical (qualitative) variables: each response can be put into a specific, mutually exclusive and exhaustive category. Nominal variables: no natural ordering e.g., modes of transportation, sex, region of residence Ordinal variables can be ordered or ranked e.g., course evaluation ranking 8

9 Types of variables (cont d) Numeric (quantitative) variables: describes a numerically measured value Continuous variables can assume an infinite number of real values e.g., earnings, distance Discrete variables can only take a finite number of real values e.g., test scores Note: Measurement of a continuous variable is always a discrete approximation 9

10 Measures used to describe a variable Dispersion Central tendency Distribution Three characteristics of a variable: - Central tendency - Dispersion - Distribution 10

11 Measures of central tendency - Average Arithmetic Mean (average), for variable Y and sample size N Y 1 N Yi N i 1 Advantages: Intuitive Additive properties allow decomposition techniques to be applied useful for understanding the reason behind different means (of the same variable) across groups and/or over time: 11 If for every observation i Then Y X Z i i i Y X Z

12 Measures of central tendency - Average Disadvantages: Sensitive to outliers, or to very low or high values, especially in smaller samples May not accurately reflect the situation of most people in the sample e.g., income 12

13 Measures of central tendency - Average As a result of social and historical changes, the average household size in Canada has decreased from 6.2 in 1851 to 4.3 persons in 1941, to 2.5 persons in Conversely, the number of households has increased. Source:The shift to smaller households over the past century, Megatrends, 2016 Data sources: Statistics Canada, censuses of population, 1976 to 2011, catalogue no e and no

14 Measures of central tendency - Average Average monthly change in employment, by year, 1977 to 2013 thousands Source: Statistics Canada, Labour Force Survey (LFS). 14

15 Measures of central tendency: median and mode Median: the middle value of a set of ordered data No additive properties Not affected by extreme values Mode: most frequent value of a variable 15

16 Measures of central tendency: median Median age, by selected metropolitan area, Canada, 2014 CANADA Vancouver Edmonton Calgary Winnipeg Toronto Ottawa - Gatineau Montréal Québec Saguenay Halifax Age Source: Statistics Canada: Annual Estimates: Subprovincial Areas ( X) 16

17 Measures of central tendency: Which one to use? HOURLY WAGES N Mean Median Employed 16, Self-employed 2, Total 18, Density Density hourly_wage Kernel density estimate Normal density hourly_wage Kernel density estimate Normal density Source: Certification, Completion, and the Wages of Canadian Registered Apprentices, Analytical Studies Branch Research Paper Series (2012) Data source: Statistics Canada, National Apprenticeship Survey. 17 Employed Self-employed

18 Providing more than one measure This study looks at changes in income and wealth (total assets minus total debt) of Canadian families between 1999 to Family income (before tax) and net worth (wealth) by income quintile, 1999 and 2012 Average Median dollars (in thousands) Income Bottom quintile Second quintile Middle quintile Fourth quintile Top quintile Net worth Bottom quintile Second quintile Middle quintile Fourth quintile Top quintile Data source: Statistics Canada, Survey of Financial Security, 1999 and Source: Changes in wealth across the income distribution, 1999 to 2012, Insights on Canadian Society,

19 Frequency Distribution The distribution of a variable is the pattern of observed frequencies. Frequency distributions are portrayed as frequency tables or histograms. The frequency of a particular observation is the number of times the observation occurs in the data. Frequency distributions can be used for both categorical and numeric variables. Continuous variables are often summarized using class intervals. 19

20 Frequency distribution ratios and percentages Frequency distributions can show either the actual number of observations falling in each range or the percentage of observations (also called the relative frequency distribution). The relative frequency (ratio) of a particular observation or class interval is found by dividing the frequency (f) by the number of observations (n): that is, (f n). The percentage frequency is found by multiplying each relative frequency value by

21 Frequency distribution categorical variable and class intervals Aging needs topped the list of reasons for providing care to a family member or friend. Seniors represent the most common recipients of care. Reasons for Providing Care Age of Recipients of Care Aging Cancer Cardiovascular disease Percent of those receiving care Mental illness Alzheimer's disease or dementia 25 Neurological diseases Injury from an accident Arthritis Diabetes Back problems Developmental disability or disorder Respiratory problems Mobility or physical disability 5 Other health problem Percent 0 15 to to to to to to and older Sources: Spotlight on Canadians, X, no. 001, September 2013; X, no. 002, June Data source: General Social Survey,

22 Frequency distribution categorical variable Source: Guyana Population & Housing Census 2012, Preliminary Report Data Source: Guyana Bureau of Statistics, Census

23 Frequency distribution numerical variable Source: Statistics Canada: Annual Estimates: Subprovincial Areas ( X) 23

24 Frequency distribution class intervals 24

25 0 to 4 5 to 9 10 to to to to to to to to to to to to to to to to to to and over Frequency distribution numerical variable and class intervals 1,600,000 Estimates of population by age group, Women, Canada, ,400,000 1,200,000 1,000, , , , ,000 0 Age groups Data source: Statistics Canada. Table Estimates of population, Canada, annual Source: Female population Women in Canada: A Gender-based Statistical Report (2015) 25

26 Relative frequency Using Census of population data, this study examines changes in family circumstances and living arrangements of Canadians over 100 years. Growing participation of women in the labour force and in higher education plus legislative changes contributed to the increase in the number of divorces. Source: Living arrangements of children in Canada: A century of change in Canada, Insights on Canadian Society, (2014) Data sources: Statistics Canada, censuses of population, 1941 to The number of children living in lone-parent families increased. However, the proportion of lone-parent families headed by men declined between 1941 and 2011 (28% in 1941, 17% in 1991 and 20% in 2011)

27 Using ratios: earnings This study compares earnings of a cohort of immigrants to that of native-born workers over the 1991 to 2010 period. Average annual wages and salaries of immigrant and native-born workers, by sex and level of education, 1991 and 2010 All workers Men Women Immigrants Native-born Immigrants Native-born 2010 dollars (in thousands) Less-educated workers More-educated workers Recent immigrant-to-candian-born earnings ratio, by sex and education level, 1991 and 2010 Men with lesseducation Women with lesseducation Men with moreeducation Sex and education level Women with more-education Source: Twenty Years in the Careers of Immigrant and Native-born Workers, Economic Insights, 2013 Data sources: Statistics Canada, 1991 Census-Longitudinal Worker File 27

28 Compositional analysis This study looks at employment patterns of families with children (under 16) between 1976 and In 2014, 55% families were dual-earner families, up from 33% in Source: Employment patterns of families with children, Insights on Canadian Society, 2015 Data sources: Statistics Canada, Labour Force Survey, 1976 and

29 Compositional analysis In 2012, real estate assets represented 44% of the total assets of Canadian families. This result varies by income quintile. However: The charts do not take changes in debt into account. Comparisons over time: it is difficult to tell if differences are due to changes in asset composition or levels. 29 Source: Changes in wealth across the income distribution, 1999 to 2012, Insights on Canadian Society, 2015 Data sources: Statistics Canada, Survey of Financial Security, 1999 and 2012

30 Decomposing sources of growth Source: Recent changes in demographic trends in Canada, Insight on Canadian Society,

31 Tables with percentages: rows or columns? Table 2a: Distribution of Engineers (%) by Discipline and Origin Canadian Canadian Educated Foreign Educated Born Immigrant Immigrant All Biosystem Chemical Civil Computer Electric Environment Industrial Geo/mat/mining Mechanical Other Total # of observation 26,500 6,444 19,351 52,295 Source: Finnie, Laporte and Sweetman (2006) Percentage on columns Total column percentage is equal to 100. Of all the Canadian born engineers, 2% have biosystem as a discipline. 31

32 Tables with percentages: rows or columns? Table 2b: Composition of Engineers (%) by Discipline and Origin Canadian Canadian Educated Foreign Educated Born Immigrant Immigrant Total # of observations Biosystem Chemical ,542 Civil ,760 Computer ,739 Electric ,804 Environment ,434 Industrial ,647 Geo/mat/mining ,533 Mechanical ,076 Other ,858 All ,295 Source: Finnie, Laporte and Sweetman (2006) Percentage on rows Total row percentage is equal to 100. Of all the engineers with biosystem as a discipline, 58.4% were Canadian born. 32

33 Changes over time: percent change Percent change = [ (Value at end Value at start) / (Value at start) ] *100 Example (hypothetical): Below low-income cut-off: mean income rose from $1,000 to $1,500 (50% growth) Above low-income cut-off: mean income rose from $50,000 to $55,000 (10% growth) It is important to use judgment when comparing percentages across groups, as large (small) relative increases can reflect small (large) absolute changes. 33

34 Percent change vs percentage point change How do we describe changes in percentages? Percent change describes a relative change in a variable e.g., Average earnings rose by 10% between 2014 and Percent point change describes an absolute change in percentages. e.g., In 2014, the unemployment rate was 10%. In 2015, it was 15%. The unemployment rate rose five percentage points, or 50%, from 2014 to

35 Population growth rates (Population at end) (Population at start) Population growth rate = / population at start X 100 # of years in time span Region 8 (Potaro-Siparuni) experienced the highest annual population growth rate of any region (7%) between 1991 and In comparison, the growth rate of Region 4 (Demerara-Mahaica) was 0.4% over the same period. Source: Guyana Population & Housing Census 2012, Preliminary Report Data Source: Guyana Bureau of Statistics, Census

36 Population growth rates Growth rates are better interpreted in conjunction with absolute changes and total population data. Guyana Population Absolute Change Annual Growth rate Region 1 18,320 18,431 24,275 26, ,844 2, Region 2 42,321 43,455 49,253 46,810 1,134 5,798-2, Region 3 104,700 95, , ,416-8,723 7,084 4, Region 4 316, , , ,429-20,043 13,684 3, Region 5 54,583 51,651 52,428 49,723-2, , Region 6 152, , , ,431-10,177-18,801-14, Region 7 14,384 14,794 17,597 20, ,803 2, Region 8 4,482 5,616 10,095 10,190 1,134 4, Region 9 12,868 15,058 19,387 24,212 2,190 4,329 4, Region 10 38,554 39,559 41,112 39,452 1,005 1,553-1, Guyana 759, , , ,884-35,891 27,550-3, Coastal 709, , , ,261-39,736 10,095-13, Hinterland 50,054 53,899 71,354 81,623 3,845 17,455 10, Source: Guyana Population & Housing Census 2012, Preliminary Report Data Source: Guyana Bureau of Statistics, Census

37 Measures of dispersion Quantiles: Divisions of a frequency distribution into equal, ordered, subgroups. Most used: Quintiles and percentiles: Quintiles: The values that divide a frequency distribution into five equal parts. Q1, Q2 and Q3 and Q4. Percentiles: The values that divide a frequency distribution into 100 equal parts. Q1, Q2,., Q98, Q99. Source: The Cambridge Dictionnary of Statistics, Cambridge University Press,

38 Measures of dispersion: percentiles If you order the observations in your sample by the value of a variable of interest, e.g. income, from lowest to highest, then: The 20 th percentile is the income amount such that 20% of the sample has an income lower than that amount. Also called the first quintile. The 25 th percentile is also called the lower quartile (if dividing the sample into 4 groups of equal size). The 50 th percentile is also the 5 th decile or the median. Percentiles, or ratios of percentiles e.g., P90/P10, P75/P25, are also used to describe the distribution of a variable (as measures of income inequality). 38

39 Measures of dispersion: Quintiles Source: St-Vincent and the Grenadines Country Poverty Assessment 2007/2008 Data source: St-Vincent and the Grenadines, Survey of Living Conditions,

40 Measures of dispersion: Quintiles Source: St-Vincent and the Grenadines Country Poverty Assessment 2007/2008 Data source: St-Vincent and the Grenadines, Survey of Living Conditions,

41 Measures of dispersion: Quintiles Median earnings, in 2005 constant dollars, of full-time full-year earners1 by quintile, Canada, 1980 to 2005 Year Change Quintile to to constant dollars (in thousands) percentage Bottom 20% Middle 20% Top 20% Note: 1. Full-time full-year earners worked 49 to 52 weeks during the year preceding the census, mainly full time (i.e., 30 hours or more per week). Individuals with self-employment income are included. Those living in institutions are excluded. Sources: Statistics Canada, censuses of population, 1981, 1991, 2001 and Source: Statistics Canada, Earnings and Incomes of Canadians Over the Past Quarter Century, 2006 Census: Findings. 41

42 Standardization techniques Standardization techniques are useful to help understand the extent to which: a change in outcome between two periods is due to a change in the characteristics of the population a difference in outcome between two groups is due to a difference in characteristics Example: Observed decline in the labour force participation rate between 2007 and Could potentially signal a decline in labour force attachment 42

43 Standardization techniques Example (LFS) Population Population share Participation rate Population Population share Participation rate ('000s) (%) (%) ('000s) (%) (%) , , , , , , TOTAL , , Source: Statistics Canada. Labour Force Survey (LFS) 43

44 Standardization techniques Example (LFS) Participation rate: = (Population share 15-24, 2015 * Participation rate 15-24, 2015 ) + (Population share 25-54, 2015 * Participation rate 25-54, 2015 ) + (Population share 55+, 2015 * Participation rate 55+, 2015 ) Age-standardized participation rate: = (Population share 15-24, 2007 * Participation rate 15-24, 2015 ) + (Population share 25-54, 2007 * Participation rate 25-54, 2015 ) + (Population share 55+, 2007 * Participation rate 55+, 2015 ) 44

45 Standardization techniques Example (LFS) Population Population share Participation rate Participation rate Age standardized participation rate ('000s) (%) (%) (%) (%) , , , TOTAL , Source: Statistics Canada. Labour Force Survey (LFS) 45

46 Standardization techniques Example (LFS) Percent Actual versus age-standardized participation rates participation rate AS participation rate Notes: Age-standardized rates based on working-age population shares as of January

47 Standardization techniques Example (LFS) 64.5 Percent Actual versus age-standardized employment rates employment rate AS employment rate Notes: Age-standardized rates based on working-age population shares as of January

48 Part Two: Presenting descriptive statistics efficiently 48

49 Presenting results Tables more concise way to show multiple statistics per unit (e.g. per city, province) or to show statistics for several variables of interest at once (e.g. mean and median income, distribution of age, distribution of education, etc.) Charts more visually appealing than tables, easier to communicate key messages to a broad audience. Particularly useful for highlighting trends over time. Maps useful to highlight differences across geographic regions 49

50 Describing your data to the user Financial strategies Allocative Pooled Separate Variable Mean Percentage 50 Total [0.4] [0.5] [0.4] Gender Female [0.6] [0.7] [0.6] Male [0.6] [0.7] [0.6] Immigrant status Male Canadian born [0.5] [0.6] [0.5] Immigrant [1.0] [1.2] [0.9] Female Canadian born [0.4] [0.6] [0.5] Immigrant [1.0] [1.2] [0.9] Marital status Common law [1.1] [1.5] [1.6] Married [0.4] [0.5] [0.4] Duration of actual relation Less than 5 years [1.5] [2.0] [2.1] 5 to 9 years [1.4] [2.0] [2.0] 10 to 19 years [1.0] [1.3] [1.2] More than 20 years [0.5] [0.6] [0.5] Family type Couple without children [0.8] [1.0] [1.0] Couple with children [0.6] [0.7] [0.5] Intact [1.0] [1.1] [0.9] Other [2.6] [3.3] [3.3] Previously married No [0.5] [0.6] [0.5] Yes [0.8] [1.1] [1.0]

51 Chart or table? This table presents labour force participation rates by year, age group and gender for St. Kitts and Nevis. Source: Women and Men in CARICOM Member States, Labour Force Statistics, Volume I - Data series for 1980, 1990 and 2000 Round of Censuses, 2006 Data sources: St. Kitts and Nevis, Censuses 1981, 1991 and 2001 Note: 2001 refers to St.Kitts only 51

52 Chart or table? (cont d) Source: Women and Men in CARICOM Member States, Labour Force Statistics, Volume I - Data series for 1980, 1990 and 2000 Round of Censuses,

53 Using double-axis charts Participation rate and unemployment rate, population aged 15 to 24, 1976 to 2014 percent percent Participation rate (left scale) Unemployment rate (right scale) 0 Source: Statistics Canada, Labour Force Survey (CANSIM table ). 53

54 Using charts to show and explain aggregate trends The percentage of the population employed full time has increased slightly since 1976: 66% in 2014 compared to 62% in Source: Full-time Employment, 1976 to 2014 Data source: Statistics Canada, Labour Force Survey, 1976 to 2014 Differences between men and women: The proportion of men working full time fell by 10 percentage points, while the proportion of women working full time increased by 17 percentage points.

55 Using charts to show and explain aggregate trends Changes in the percentage of population employed full-time in their main job, by sex and age group, 1976 to 2014 percentage point Results differ substantially by sex and age group Men 17 to 24 Men 25 to 29 Men 30 to 54 Men 55 to 64 Women 17 to 24 Women 25 to 29 Women 30 to 54 Women 55 to to to 2014 Source: Full-time Employment, 1976 to 2014 Data source: Statistics Canada, Labour Force Survey, 1976 to

56 Using pie charts Percentage of inter-provincial workers moving to Alberta, Cohort of 2005 Never moved to Alberta 74% Moved to Alberta 26% One year 6% Two years 5% Three years 4% Four years 4% Five years 7% 56

57 Using maps 57

58 Highlighting pertinent information? Source: Lu, Schellenberg, Hou and Helliwell (2015) 58

59 Ten tips for effective charts 1. Convey an important message 2. Decide on a clear purpose 3. Draw attention to the message, not the source 4. Experiment with various options and chart styles 5. Use simple design for complex data 6. Make the data 'speak' 7. Adapt chart presentation to suit the target audience 8. Ensure that the visual perception process is easy and accurate 9. Avoid distortion and ambiguity 10. Optimize design and integrate style with text and tables 59

60 Part three: Discussion and conclusion 60

61 Descriptive statistics throughout the analytical process Know your data Define your sample of interest Describe your sample/population Motivate your analytical question Address your analytical question 61

62 Practical first steps Know the context and the subject-matter Make sure to read and understand survey documentation Check sample size to assess project feasibility Check coverage of survey questions If you are using derived variables, verify how they were constructed. If looking at multiple years of data, look for changes in survey designs, collection periods and definitions over time. 62

63 Practical first steps (cont d) Look for missing values Valid skips? Coding errors? Processing errors? Item nonresponse? Look for outliers and extreme values Depending on the analytical questions, you may want to drop or keep outliers or extreme values 63

64 Practical first steps (cont d) Summarize key variables in your project by presenting mean (and median) values and distribution where appropriate Ex.: Mean and median individual earnings, regional unemployment rate, sample distribution by education level and age groups, etc. Start with basic cross-tabulations to identify any potential warning signs Unemployment rate and earnings by region and education level 64

65 Causality vs. correlation Example: Individuals with higher education levels earn more than those with lower education levels (even after accounting for differences in many observable characteristics) Clearly earnings and education level are correlated. But does higher education cause higher earnings? In other words, if we picked a random person with a high school education and made them go to university, would their earnings increase once they graduated? 65

66 Causality vs. correlation If education does not cause higher earnings, then why are they correlated? What if it is innate ability that actually causes higher earnings? If more able people are more likely to choose higher education than the less able (selfselection), then education and earnings will be correlated even if education does not actually cause higher earnings Most datasets on individuals do not include a measure of ability (omitted variables bias). 66

67 Causality vs. correlation Understanding causal relationships and their magnitude important for many issues of interest to policymakers. Estimating causal relationships easiest with experimental data but experiments are rare and results may be difficult to generalize In the absence of an experiment, identifying causal relationships requires technically and theoretically sound research designs Estimating a model (e.g. using regression analysis) does not automatically identify a causal relationship between the variables of interest, even if it allows you to control for many differences between observations. 67

68 Using descriptive statistics Advantages Easy to calculate Easy to understand (usually) Used/useful throughout the research process Disadvantages Sometimes cumbersome to present Inefficient use of sample (sample size by cell too small) Interpreting results in absence of control variables can be difficult and potentially misleading Identifying causal relationships between variables next to impossible in practice (unless you have experimental data). Only correlative relationships can be identified. 68

69 Using descriptive statistics Understand how the tools that you re using work, their properties, and how these properties may affect your results Be creative: there are many ways to use descriptive statistics. Place your results in context (other literature, meaningful comparison group/benchmark) Avoid hasty conclusions, reading more into the results than your methodology allows (causality vs correlation) 69

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