# Inferential statistics pdf

This chapter discusses some of the basic concepts in inferential statistics. Inferential statistics is the mathematics and logic of how this generalization from. Inferential statistics are used to test hypotheses about the relationship between the independent and the dependent variables. ➢ Inferential statistics allow you to . They are best viewed with a pdf reader like Acrobat Reader (free download). • Make sure that “Single Inferential Statistics (testing hypotheses). Contents. Prev.

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Inferential statistics. We've seen how operational definition specifies the measurement operations that define a variable. Last week we considered how carrying. This book focuses on the meaning of statistical inference and estimation. Statistical inference is concerned with the problems of estimation of population parameters and testing hypotheses. The book will help readers to discover diverse perspectives of statistical theory followed. PDF | These lecture notes were written with the aim to provide an accessible though technically solid introduction to the logic of systematical analyses of.

Imagine there could be more worlds with more cases and the problem is fixed. Rather than being hidden behind a veil of statistics, the clear causal language demanded by descriptive statistics commits researchers more clearly to useful arguments; furthermore, in their clarity these can more easily be supported or refuted. The coefficient for the Ghent variable shows a substantial net difference between Ghent and non-Ghent systems of 27 percentage points. One also notices other relationships straight away, that, for example, only small countries with medium to strong left parties have the Ghent system. Why Exceptions?

As example, Goodchild considers this type of problem in the context of a study using data from U. But this strategy requires rejecting the vast majority of the available data, widening the confidence limits of conclusions, and possibly missing some important patterns and effects. The same problem applies to international and other similar datasets. The kinds of questions many social science researchers ask involve variation between cases each representing highly complex and unique spatial concatenations of political, economic, geographic, demographic, institutional, and cultural factors and the interdependencies between these.

The problem is not one of statistics that need to be fixed. Rather, it is a problem of the misapplication of inferential statistics to non-inferential situations. This is all summarized and shown clearly in Freedman , Western and Jackman and related statistical literature. We briefly hypothesize as to why a method that has been shown to be so substantially in error nonetheless continues to be used in the postscript.

Rather than reargue the case, it is more useful to 3 As with Czech history, so too the world: Economist Georgescu-Roegen makes a similar observation: Peirce that universes are not as common as peanuts. Because there is only one Western civilization, the question of whether its historical development merely follows a trajectory determined entirely by the initial condition or whether it represents a hysteretic process can be settled neither by an effective experiment nor by the analysis of observed data.

Likewise E. An immense amount of interesting data has been developed for comparative social studies for statistical analysis.

How can it be used? Shalev and shows that descriptive statistics can be used not only in place of the inferential statistical techniques commonly utilized, but that they are actually superior in expressing, supporting, rejecting, analyzing and forming new theoretical arguments.

Simple maps of data can do much that inferential statistics are imagined to do but more clearly. This is an increasingly common observation in recent years with an extensive literature so we do not discuss visual methods further.

One of their advantages over mapping and other complex visual methods is that descriptive statistics have 4 In the social science literature maps and other visual tools are seldom relied on to express or test theories Orford et. Indeed remarkably, even in geography the use of maps has become rare Martin Yet maps are able to convey a great deal of information with many of the benefits concerning descriptive statistics maintaining case identity, spatial juxtaposition in a manner that is fundamentally compatible with human cognitive skills.

A well known demonstration of the superiority of simple visualization of data versus statistical tables is provided in Tufte , concerning the space shuttle Challenger disaster. Data expressed with visual methods, ranging from tabular analysis to maps and other visualization methods allow researchers to effectively express subtle and complex meanings or gestalts Cleveland , with the same data that might otherwise be used in regressions and other statistical methods.

Indeed, one could argue that the form of presenting data in statistical arguments is highly maladapted for many of the purposes in the social sciences. This simplicity has the additional benefit that assumptions and manipulations are more transparent to end users than those used in frequentist and Bayesian statistics.

There are other significant advantages of descriptive statistics beyond simply being more accessible, however, as we hope to demonstrate.

## Difference Between Descriptive and Inferential Statistics (with Comparison Chart) - Key Differences

Shalev , argues, and we fully agree, that they are superior in many cases to other methods. Descriptive statistics — a natural solution to the superpopulation problem and many others It is interesting that when the problem of superpopulations is discussed, descriptive statistics are often cited as the natural or obvious solution. For example, Berk et.

Similarly Michael Goodchild, a leading expert in spatial statistics, more recently notes: This ideal situation occurs so rarely in geographic research that one wonders why the associated assumptions have persisted, and indeed dominated, for so long.

Why are we not content simply to describe specific parts of the heterogeneous world that we see around us [i. Simple methods of presenting the right data can not only replace inappropriately used inferential statistics.

They are superior to them for the types of questions asked in political economy and comparative development type studies. For example, as noted in footnote 2, Goodchild considers the problem in U. Goodchild says there are three options: This last option is the most problematic, because it flies in the face of the inferential tradition, despite the straightforward and compelling arguments that support it. They are slightly older, but they are used to illustrate, with as brief examples as possible, the ways in which descriptive statistics are useful.

This author has used similar approaches that provide more recent, extended examples in other development related fields Ballinger a, b, c, d, e. For what this author views as exemplary use of descriptive statistics see work by economic historian Paul Bairoch on complex relations and controversial theories concerning population, development, imperialism and related topics Bairoch and Bairoch Goertzel and Goertzel and Goertzel also present similar examples.

Rothstein uses multiple regression to attempt to discern which of these factors are important, and to what degree. Shalev slightly modifies6 and replicates the regressions, with the following result coefficients are standardized betas: The coefficient for the Ghent variable shows a substantial net difference between Ghent and non-Ghent systems of 27 percentage points.

This problem is compounded because, with only 17 cases, it would be impossible to add even a few other factors into the model, which limits further use of controls or modeling of interaction effects. Table 1 divides the group of countries into small and large, and then further subdivides these by the strength of Left parties and into Ghent and non-Ghent systems.

Beside each case is the percentage of union membership. If one looks at the Ghent cases, it is clear that they have a significantly higher percentage of union membership. One also notices other relationships straight away, that, for example, only small countries with medium to strong left parties have the Ghent system. It makes clear precisely the things he wants to demonstrate: In particular, it must be questioned whether the Ghent system alone can explain the very large differences in density between the members of two otherwise well-matched pairs of countries: Other factors seem likely to explain these particular cases, such as the fact that Belgian unions are present in the workplace, whereas in the Netherlands they are not.

The difference between Norway and Sweden may be attributable to differences in sectors in the countries, such as differences in gender in the workplace, private sector trade and services, and percentage of white collar workers. Two other anomalies the chart suggests deserve further research are the wide gap between the United States and Canada, and the unexpectedly high union membership in Ireland.

Descriptive statistics make conceptual errors more obvious and analysis more clear — e. This makes it difficult to see important aspects of the information, such as when cases or variables should be included that are not, the existence of spatial autocorrelation in data, and anomalies that might fruitfully lead to more refined or new theories. The inclusion of these would completely eliminate the statistical basis of their argument, adding sixteen cases, all strongly counter to their hypothesis, to an original dataset of 41 cases.

It is based on a study of the common idea in political economy that independent central banks have a strong favorable effect on economic performance.

Hall and Franzese argue that while it is true that independent central banks are anti-inflationary, they can have negative effects on unemployment; specifically, in economies with uncoordinated wage bargaining, central banks might fail to respond to employment signals, resulting in higher unemployment. Using data for 18 OECD countries over the period , they support their argument first in a simple tabular format without case identity , and then with the application of multiple regression with controls for economic, political and institutional variables.

This method is not useful for the long-term questions of recent development studies where it is precisely the influence on cross- sectional variation from longitudinal variation that is of interest. Even in short-term studies Shalev and others argue that pooling as a method of increasing sample size has serious problems, especially the assumption that cross-sectional and longitudinal variation are comparable.

The upper table uses numerical data expressing unemployment percentages. The lower table shows the corresponding real cases. Coordination of Wage Bargaining Central Bank 0 0. However, this might be explained by the controls Hall and Franzese use in their regression although again, the meaningfulness of these are questionable in such a small sample size.

The hypothesis that in countries with strongly independent central banks coordinated wage bargaining reduces unemployment is supported by the unemployment difference between Austria, Germany and Switzerland versus uncoordinated North American countries. The important point, however, is the ease with which spatial autocorrelation is noticed and how descriptive statistics with case identity maintained allows for data gathered for multiple regression analysis to be analyzed in a way that is sensitive to this problem, as well as to the problems of a small number of cases and the interaction of factors.

For example, why is Japan clustered with Scandinavian countries, or the antipodean countries with France and Italy?

These types of anomalies may reveal interesting hitherto unsuspected relations between factors. Ross and Homer was one exception; Bollen et. But with real-world data, what is the point of losing the real cases, with the rich bundle of real-world context and information each conveys, for a single numerical measure such as provided by statistical tests of autocorrelation?

As Ballinger a shows, even with larger datasets, in development type studies autocorrelation is easy to see, and can be examined in more nuanced and useful ways than numerical measures.

They actually work better than inferential statistics, more clearly expressing and testing the types of causal relations made in comparative political economic and development research. However, descriptive statistics can be utilized in far more sophisticated ways than is generally realized. Combining the methods such as those Shalev demonstrates for reanalyzing the arguments by Rothstein and by Hall and Franzese with other forms of visualization of data footnote 4 is most appropriate for the study of uneven development.

There is no correction for what is at bottom not a shortcoming of statistical methods but a misapplication of them. Simply pointing it out and moving on are not an option, it can only be either a ignored completely or b visual and descriptive statistics turned to. There is no point in paraphrasing what has already been said clearly: Human geography provides an example. This is unfortunate, as Graeber notes concerning anthropology , Methods that are entrenched in graduate programs at leading universities and published in prestigious journals tend to be perpetuated.

In , David Freedman, a distinguished sociologist at the University of California at Berkeley and the author of textbooks on quantitative research methods, shook the foundations of regression modeling when he frankly stated "I do not think that regression can carry much of the burden in a causal argument.

Nor do regression equations, by themselves, give much help in controlling for confounding variables" Freedman, Freedman's article provoked a number of strong reactions. Richard Berk It goes to the heart of their empirical enterprise and in so doing, puts entire professional careers in jeopardy.

This applies equally or more so to the improper use of inferential statistics in development studies and related fields that use similar data.

To us this is a very good thing to commit researchers to doing. Rather than being hidden behind a veil of statistics, the clear causal language demanded by descriptive statistics commits researchers more clearly to useful arguments; furthermore, in their clarity these can more easily be supported or refuted.

This is due to fundamental differences between correlational versus causal assumptions, two of which are: Causal assumptions, as we have seen before, are deprived of that honor, and thus become immediately suspect of informal, anecdotal or metaphysical thinking.

Assumptions about abstract properties of density functions or about conditional independencies among variables are, cognitively speaking, rather opaque, hence they tend to be forgiven, rather than debated.

## Difference Between Descriptive and Inferential Statistics

Indeed, since the bulk of scientific knowledge is organized in causal schema, scientists are incredibly creative in constructing competing alternatives to any causal hypothesis, however plausible. Statistical hypotheses in contrast, having been several levels removed from our store of knowledge, are relatively protected from such challenges, and offer therefore a safer ride toward the conclusion.

Economist Bryan Caplan lists ten of the most influential ideas of mainstream academic economics since Human capital theory 2. Rational expectations macroeconomics 3. The random walk view of financial markets 4. Signaling models 5. Public choice theory 6. Natural rate models of unemployment 7.

Time consistency 8. The Ricardian equivalence argument for debt-neutrality Even there, intuition, not math, probably played the leading role. Truly, this is a case of looking for car keys underneath the streetlight because it is brighter there.

Cities and Economic Development. Translated by Christopher Braider. University of Chicago Press. Bairoch, Paul. Economics and World History: Myths and Paradoxes. Harvester Wheatsheaf. Ballinger, Clint. Dissertation, Department of Geography, University of Cambridge. Available online at: Comparative Economics in a World Divided: Spatial Autocorrelation and World Regions.

Acemoglu, Johnson, and Robinson: Natural Experiments or Geographic Theories of Development? Mercantilism and Uneven Development. Statistical Inference for Apparent Populations.

Sociological Methodology Berk, Richard A. Reply to Bollen, Firebaugh, and Rubin. Bertin, J. Semiology of Graphics. University of Wisconsin Press. Macrocomparative research methods. So, there is a big difference between descriptive and inferential statistics, i. Basis for Comparison Descriptive Statistics Inferential Statistics Meaning Descriptive Statistics is that branch of statistics which is concerned with describing the population under study.

Inferential Statistics is a type of statistics, that focuses on drawing conclusions about the population, on the basis of sample analysis and observation. What it does? Organize, analyze and present data in a meaningful way. Compares, test and predicts data. To explain the chances of occurrence of an event.

Function It explains the data, which is already known, to summarize sample. It attempts to reach the conclusion to learn about the population, that extends beyond the data available.

Descriptive Statistics refers to a discipline that quantitatively describes the important characteristics of the dataset. For the purpose of describing properties, it uses measures of central tendency, i. The data is summarised by the researcher, in a useful way, with the help of numerical and graphical tools such as charts, tables, and graphs, to represent data in an accurate way. Moreover, the text is presented in support of the diagrams, to explain what they represent.

Inferential Statistics is all about generalising from the sample to the population, i. It is a convenient way to draw conclusions about the population when it is not possible to query each and every member of the universe.

The sample chosen is a representative of the entire population; therefore, it should contain important features of the population. Inferential Statistics is used to determine the probability of properties of the population on the basis of the properties of the sample, by employing probability theory.

Methods of inferential statistics:. The difference between descriptive and inferential statistics can be drawn clearly on the following grounds:. So, we have enough discussion on the two subjects, all you need to know is that descriptive statistics is all about illustrating your current dataset whereas inferential statistics focuses on making assumptions on the additional population, that is beyond the dataset under study.

While descriptive statistics provide the summation of the data the researcher has actually studied whereas inferential statistics, makes the generalisation, which means the data provided to you is not actually studied. Bundle of thanks , Its a really helpful for me to understand basic concept of descriptive and inferential statistical analysis with comparison.

Thanks…it helps a lot..