PAD5700 week one MASTER OF PUBLIC ADMINISTRATION PROGRAM PAD 5700 -- Statistics for public management Fall 2013 Introduction and relative standing Statistic of the week ̅ The sample mean * Greetings, and welcome to PAD-5700 Statistics for public management. We will start this class with a bit of statistics, then follow this with course mechanics. Levin and Fox offer a useful definition of statistics: A set of techniques for the reduction of quantitative data (that is, a series of numbers) to a small number of more convenient and easily communicated descriptive terms. (p. 14) An introduction to the course Numbers are clean, crisp Table 1 and unambiguous, Size of government compared though they may clearly, Economic Size of Regulation Gov’t1 crisply and freedom government % GDP unambiguously G7+ represent a murky, US 7.93 7.13 7.78 16 sloppy and ambiguous Australia 7.83 6.80 7.91 17 reality; or may represent Canada 7.92 6.54 8.16 19 equally murky, sloppy France 7.20 5.43 6.45 23 and ambiguous research; Germany 7.47 5.64 6.34 18 may even on the odd Italy 6.75 5.71 5.77 21 occasion get distorted Japan 7.38 6.18 7.34 18 by dishonest Sweden 7.26 3.61 7.16 26 people! But descriptive UK 7.78 6.02 7.76 22 statistics can be very BRICs powerful ways of Brazil 6.18 6.39 5.00 20 making an argument. China 6.44 3.28 5.93 11 For instance, two big India 6.48 6.84 6.16 12 issues in today's Russia 6.57 7.27 5.69 18 political climate concerns out of control Laggards government in America. Pakistan 5.80 7.71 6.12 11 What do the numbers Nigeria 5.93 5.89 6.99 n/a show? Vietnam 6.15 6.27 6.34 6 Venezuela 4.35 5.09 4.91 14 Sources: The first three columns are from the Fraser Institute and Cato Institute’s Table 1 provides some 2010 Economic Freedom of the World Report. The data is on a 1-10 scale, with 10 data on this. This can equal to more economic freedom (i.e. less government ‘meddling’). The final also walk us through column is from the World Bank’s World Development Report 2011, pages 350-1. some of the basic Note: 1 -- Government final consumption, as % GDP. PAD5700 week one concepts that we will discuss in this course. Variables (see Berman & Wang, p. 21) – Economic freedom is more or less what we’re talking about: how ‘free’ is the US economy from this allegedly over-bearing ‘state’? Operationalization (Berman & Wang, pp. 48-52) – Having conceptualized the variable that we want to analyse, we now need to ‘operationalize’ this, or put it into operation mathematically. In plain English: we need to measure economic freedom. Two conservative thinktanks, the Cato and Fraser Institutes, have provided an ‘operationalization’ of economic freedom in their annual Economic Freedom of the World Report. The indicate how they ‘operationalize’ economic freedom in their Chapter One, and provide more extensive details in the Appendix. Descriptive statistics (Berman & Wang, pp. 103-4) – Having operationalized economic freedom, we can get some sense of how the US compares. Not that the Fraser/Cato economic freedom index measures economic freedom, so higher scores = more freedom, or less government meddling. Table 1 indicates that the US does quite well, indeed was the most ‘free’ economy of the countries listed. One can also go to the original report (linked in the sources) and go to page 7, which lists all countries. The US ranked 6th on this scale, with only Switzerland, Chile, New Zealand, Singapore and Hong Kong more ‘free’. As we will see below this brief introduction to the course, descriptive statistics especially include measures of central tendency, and measures of dispersion. In addition to describing datasets in terms of where they are centered, and how spread out they are; these measures (especially the standard deviation) also allows us to draw extremely powerful inferences. This is because the standard deviation also serves as a measure or relative standing. Inferential statistics (Berman & Wang, pp. 163-5) – We can also draw ‘inferences’ with data. As Berman & Wang put it: “[I]nferential statistics allow inferences to be made about characteristics of the population from which the data were drawn. A key application for these statistics is to address whether a relationship exists in the first place, and inferential statistics provide statistical evidence for answering this important question” (p. 163). Three especially powerful types of inferential methods that we’ll use will be hypothesis testing, correlation analysis (which Berman & Wand tend to treat as bivariate regression), and multi- variate regression analysis. Hypothesis testing. The date presented above are from 2008. Assume that we wanted to see if economic freedom has changed since ‘The Great Recession’. We can test this by comparing the mean economic freedom score in 2008, with the mean economic freedom score in 2012. Because I have a 2012 economic freedom score loaded onto this dataset for a competing index – The Index of Economic Freedom produced by the Heritage Foundation – I’ll use their figures. Heritage reports a 2008 score of 60.08 (they use a 100 point scale) and a 2012 score of 60.19: an increase. However the big question in hypothesis testing is, as Berman & Wang suggest above, whether a relationship exists between the passing of these four years, and economic freedom around the world. Or as I like to put it: how likely is it that the difference that we note could have come about as chance. An hypothesis test of Heritage’s 2008 and 2012 scores show a significant PAD5700 week one level of 0.684. In plain English, this tells us that even if there had been no change in the economic freedom score over these four years, 68.4% of the time pure chance would give you a difference as large as that we observe (between the 2008 score of 60.08, and the 2012 score of 60.19. Given that it is very likely this much change could have occurred randomly, we can not conclude that economic freedom has changed from 2008 to 2012, or to put it technically: the observed difference is not statistically significant. Correlation (Berman & Wang, from p. 239) – The implication of the concerns about out of control government in the US is that this hurts the country. So it is hypothesized that less economic freedom correlates with worse social and economic outcomes. If we were able to ‘operationalize’ social and economic outcomes, we could then look to see if these two are related in some way. Happily, such measures of socio-economic outcomes exist, an especially popular one is the Human Development Index, produced by the United Nations Development Program. For a description of the index, click here; for recent results, click here, page 16. Figure 2 is a ‘scatterplot (Berman & Wang, p. 240-1), which is a visual presentation of correlation results. Most folks can see that the trend is up and to the right: as economic freedom increases, so does human development. Correlation analysis can also be done quantitatively. SPSS for the same relationship presented in Figure 2, are presented in Table 3. The ‘N’ refers to the sample size: 139 countries Table 3 in the dataset used (my Correlation between economic freedom and human ‘Global Government’ development dataset, linked here), Human reported results for both of Economic development our variables. freedom (2008 - index, 2007 The Sig. (2 tailed) refers to the statistical - Cato) (HDR 2009) significance of this result. Economic freedom Pearson Correlation 1 .692** The likelihood that this (2008 -- Cato) Sig. (2-tailed) .000 result occurred randomly N 141 139 is close to zero (.000). ** Finally, the Pearson Human development Pearson Correlation .692 1 Correlation (Berman & index, 2007 Sig. (2-tailed) .000 Wang, pp. 245-6). It is a (HDR 2009) N 139 182 scale from -1 to 1. The positive number tells us **. Correlation is significant at the 0.01 level (2-tailed). the two variables are positively related. The number indicates the strength of that PAD5700 week one relationship. As a rule of thumb, a figure of 0-0.3 is considered a weak relationship; 0.3 to 0.6 a moderate relationship, and 0.6 to 1.0 a strong relationship. So that Pearson Correlation of 0.692 suggests that the there is a strong, positive relationship between economic freedom and human development. Multivariate regression analysis (Berman & Wang, from p. 252) – Here the idea is to look at relationships between a number of causes of outcomes (to grossly simplify here in the first hour of this course). We will use a simple model to illustrate. In the correlation analysis above, we looked at the effect of economic freedom on human development. Now we will look at the effect of economic freedom and effective public services on human development. For these multiple ‘independent’ variables, multivariate regression will look at the effect of economic freedom on human development, holding constant the quality of public services; then will look at the impact of public services on economic development, holding constant the degree of economic freedom. Results are presented in Table 4, below. Table 4 Regression of economic freedom and public services on human development Variable Coefficient Standardized T value Probability (standard error) coefficient Constant 0.346 5.86 0.000 Economic 0.018 0.089 1.71 0.090 Freedom (0.010) Public Services 0.063 0.842 16.21 0.000 (0.004) Adjusted r2 = 0.820 F(2, 135) = 313.4 p = .000 We’ll hold off on the details of interpreting multivariate regression for a couple of weeks but for now the key point is that the effect of economic freedom on human development drops dramatically once the quality of public services are held constant.