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In Chapter 5, we discussed the Pearson product-moment correlation coefficient used to assess the degree of linear relationship between two variables. Recall that in that chapter we assessed the degree of linear relationship between fat grams and calories by type of McDonald’s hamburger as one example. In Chapter 6, we discussed how this linear relationship could be used to develop a linear prediction system (a linear regression equation) to predict the value of one variable when the value of the other variable is known.
Now that you have become familiar with an array of statistical methods for analyzing your data, it is time to learn how to use Stata to produce professionally styled tables to include in your reports or papers for publication, and, more generally, to make your results easily accessed by those who do not have Stata, but who do have Excel. We will use the ice cream sales data set (Ice Cream.dta) to illustrate how to reproduce a table of univariate summary statistics, a correlation matrix, a table of regression output, and a graph in Excel.
Up to this point, we have been examining data univariately; that is, one variable at a time. We have examined the location, spread, and shape of several variables in the NELS data set, such as socioeconomic status, mathematics achievement, expected income at age 30, and self-concept. Interesting questions often arise, however, that involve the relationship between two variables. For example, using the NELS data set we may be interested in knowing if self-concept relates to socioeconomic status; if gender relates to science achievement in twelfth grade; if sex relates to nursery school attendance; or if math achievement in twelfth grade relates to geographical region of residence.
When we ask whether one variable relates to another, we are really asking about the shape, direction, and strength of the relationship between the two variables.
One population parameter that is of particular interest to the behavioral scientist is the mean µ of a population. In this chapter, we will discuss two approaches to statistical inference involving the mean of a population: interval estimation and hypothesis testing. Although these approaches are both carried out using samples and they give essentially equivalent results, there is a basic difference between them and it is important to know what this difference is.
In the previous chapter we presented statistical models for answering questions about population means when the design involves either one or two groups and when the population standard deviation is not known. In the case of two groups, we distinguished between paired and independent group designs and presented statistical models tailored to each.
By this time, you, no doubt, have begun to appreciate the important role analytic methods play in the research process by their ability to enable us to uncover the story contained in our data. The overall research process, however, begins not with the analysis of data, but rather with the posing of questions that interest us. It is the questions we ask that motivate us to conduct research, and it is the nature of these questions, from most simple to most challenging, that gives rise to how we design a research study, how we define and measure relevant variables, and how we collect and analyze our data to answer these questions.
In our examination of univariate distributions in Chapter 2, three summarizing characteristics of a distribution were discussed. First, its shape (as denoted by its skewness or its symmetry, by how many peaks and/or outliers it has, and so on). Second, its location (as denoted by its middle score, Q). Third, its spread (as denoted by both the range of values and the interquartile range, which is the range of values within which its middle 50 percent falls). In this chapter, we will expand upon that discussion by introducing other summary statistics for characterizing the location, spread, and shape of a distribution.
Accountability, or the way people explain and justify specific social situations, ‘is part of the general fabric of human interchange’ (Strathern 2000a: 4). It is a concept of central importance to the understanding of social action (Garfinkel 1967: 1). Futhermore, public accountability is evidently required for good governance, redistributive justice and fair resource allocation as it can minimise unpredictability and arbitrariness and can control discretion (Dowdle 2006; Mashaw 2006). How quantitative forms of accountability shape the way people work and experience their accountability in different organisational fields is therefore an important social question worthy of (more) sustained investigation. This is especially the case when one considers that the pressure for quantitative evaluation and demands for quantitative accountability have been on the rise over the past two decades.
Prosecutors are powerful actors in the South African criminal justice system as in many other jurisdictions worldwide (UN 1990; Schönteich 2001; 2002; Jehle, Wade and Elsner 2008; Luna and Wade 2012; Tonry 2012a, 2012b). In South Africa the National Prosecuting Authority Act 32 of 1998 and Section 179 of the Constitution of the Republic of South Africa 1996 equip them with extensive powers of discretion to initiate or discontinue criminal proceedings on behalf of the state, backed by the power of the state.
They decide who to charge with a criminal offence, what charges to file and when to dismiss or withdraw a case.