statistics and data analysis pdf

Statistics And Data Analysis Pdf

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Introduction to Statistics and Data Analysis

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples.

Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.

In contrast, an observational study does not involve experimental manipulation. Two main statistical methods are used in data analysis : descriptive statistics , which summarize data from a sample using indexes such as the mean or standard deviation , and inferential statistics , which draw conclusions from data that are subject to random variation e. Inferences on mathematical statistics are made under the framework of probability theory , which deals with the analysis of random phenomena.

A standard statistical procedure involves the collection of data leading to test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test.

Working from a null hypothesis, two basic forms of error are recognized: Type I errors null hypothesis is falsely rejected giving a "false positive" and Type II errors null hypothesis fails to be rejected and an actual relationship between populations is missed giving a "false negative".

Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random noise or systematic bias , but other types of errors e. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.

The earliest writings on probability and statistics, statistical methods drawing from probability theory , date back to Arab mathematicians and cryptographers , notably Al-Khalil — [7] and Al-Kindi — In more recent years statistics has relied more on statistical software. Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data , [11] or as a branch of mathematics.

While many scientific investigations make use of data, statistics is concerned with the use of data in the context of uncertainty and decision making in the face of uncertainty.

In applying statistics to a problem, it is common practice to start with a population or process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Ideally, statisticians compile data about the entire population an operation called census.

This may be organized by governmental statistical institutes. Descriptive statistics can be used to summarize the population data.

Numerical descriptors include mean and standard deviation for continuous data like income , while frequency and percentage are more useful in terms of describing categorical data like education. When a census is not feasible, a chosen subset of the population called a sample is studied. Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or experimental setting. Again, descriptive statistics can be used to summarize the sample data.

However, drawing the sample contains an element of randomness; hence, the numerical descriptors from the sample are also prone to uncertainty.

To draw meaningful conclusions about the entire population, inferential statistics is needed. It uses patterns in the sample data to draw inferences about the population represented while accounting for randomness.

Inference can extend to forecasting , prediction , and estimation of unobserved values either in or associated with the population being studied. It can include extrapolation and interpolation of time series or spatial data , and data mining. Mathematical statistics is the application of mathematics to statistics. Mathematical techniques used for this include mathematical analysis , linear algebra , stochastic analysis , differential equations , and measure-theoretic probability theory.

The earliest writings on probability and statistics date back to Arab mathematicians and cryptographers , during the Islamic Golden Age between the 8th and 13th centuries. Al-Khalil — wrote the Book of Cryptographic Messages , which contains the first use of permutations and combinations , to list all possible Arabic words with and without vowels.

In his book, Al-Kindi gave a detailed description of how to use statistics and frequency analysis to decipher encrypted messages. This text laid the foundations for statistics and cryptanalysis. Ibn Adlan — later made an important contribution, on the use of sample size in frequency analysis. The earliest European writing on statistics dates back to , with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt.

The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in government, business, and natural and social sciences. The mathematical foundations of modern statistics were laid in the 17th century with the development of the probability theory by Gerolamo Cardano , Blaise Pascal and Pierre de Fermat.

Mathematical probability theory arose from the study of games of chance , although the concept of probability was already examined in medieval law and by philosophers such as Juan Caramuel. The modern field of statistics emerged in the late 19th and early 20th century in three stages. Galton's contributions included introducing the concepts of standard deviation , correlation , regression analysis and the application of these methods to the study of the variety of human characteristics—height, weight, eyelash length among others.

Ronald Fisher coined the term null hypothesis during the Lady tasting tea experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation".

The second wave of the s and 20s was initiated by William Sealy Gosset , and reached its culmination in the insights of Ronald Fisher , who wrote the textbooks that were to define the academic discipline in universities around the world.

Fisher's most important publications were his seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance which was the first to use the statistical term, variance , his classic work Statistical Methods for Research Workers and his The Design of Experiments , [26] [27] [28] where he developed rigorous design of experiments models.

He originated the concepts of sufficiency , ancillary statistics , Fisher's linear discriminator and Fisher information. Edwards called "probably the most celebrated argument in evolutionary biology " and Fisherian runaway , [31] [32] [33] [34] [35] [36] a concept in sexual selection about a positive feedback runaway affect found in evolution. The final wave, which mainly saw the refinement and expansion of earlier developments, emerged from the collaborative work between Egon Pearson and Jerzy Neyman in the s.

They introduced the concepts of " Type II " error, power of a test and confidence intervals. Jerzy Neyman in showed that stratified random sampling was in general a better method of estimation than purposive quota sampling. Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a collated body of data and for making decisions in the face of uncertainty based on statistical methodology. The use of modern computers has expedited large-scale statistical computations and has also made possible new methods that are impractical to perform manually.

Statistics continues to be an area of active research for example on the problem of how to analyze big data. When full census data cannot be collected, statisticians collect sample data by developing specific experiment designs and survey samples.

Statistics itself also provides tools for prediction and forecasting through statistical models. To use a sample as a guide to an entire population, it is important that it truly represents the overall population.

Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. A major problem lies in determining the extent that the sample chosen is actually representative. Statistics offers methods to estimate and correct for any bias within the sample and data collection procedures.

There are also methods of experimental design for experiments that can lessen these issues at the outset of a study, strengthening its capability to discern truths about the population. Sampling theory is part of the mathematical discipline of probability theory.

Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures.

The use of any statistical method is valid when the system or population under consideration satisfies the assumptions of the method. The difference in point of view between classic probability theory and sampling theory is, roughly, that probability theory starts from the given parameters of a total population to deduce probabilities that pertain to samples.

Statistical inference, however, moves in the opposite direction— inductively inferring from samples to the parameters of a larger or total population. A common goal for a statistical research project is to investigate causality , and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables.

There are two major types of causal statistical studies: experimental studies and observational studies. In both types of studies, the effect of differences of an independent variable or variables on the behavior of the dependent variable are observed.

The difference between the two types lies in how the study is actually conducted. Each can be very effective. Instead, data are gathered and correlations between predictors and response are investigated.

While the tools of data analysis work best on data from randomized studies , they are also applied to other kinds of data—like natural experiments and observational studies [39] —for which a statistician would use a modified, more structured estimation method e. Experiments on human behavior have special concerns. The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of the Western Electric Company.

The researchers were interested in determining whether increased illumination would increase the productivity of the assembly line workers. The researchers first measured the productivity in the plant, then modified the illumination in an area of the plant and checked if the changes in illumination affected productivity.

It turned out that productivity indeed improved under the experimental conditions. However, the study is heavily criticized today for errors in experimental procedures, specifically for the lack of a control group and blindness. The Hawthorne effect refers to finding that an outcome in this case, worker productivity changed due to observation itself.

Those in the Hawthorne study became more productive not because the lighting was changed but because they were being observed. An example of an observational study is one that explores the association between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis.

In this case, the researchers would collect observations of both smokers and non-smokers, perhaps through a cohort study , and then look for the number of cases of lung cancer in each group. Various attempts have been made to produce a taxonomy of levels of measurement. The psychophysicist Stanley Smith Stevens defined nominal, ordinal, interval, and ratio scales.

Nominal measurements do not have meaningful rank order among values, and permit any one-to-one injective transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and permit any order-preserving transformation. Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary as in the case with longitude and temperature measurements in Celsius or Fahrenheit , and permit any linear transformation.

Ratio measurements have both a meaningful zero value and the distances between different measurements defined, and permit any rescaling transformation. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables , whereas ratio and interval measurements are grouped together as quantitative variables , which can be either discrete or continuous , due to their numerical nature.

Such distinctions can often be loosely correlated with data type in computer science, in that dichotomous categorical variables may be represented with the Boolean data type , polytomous categorical variables with arbitrarily assigned integers in the integral data type , and continuous variables with the real data type involving floating point computation.

But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented. Other categorizations have been proposed.

Data Collection And Analysis Pdf

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Introduction to Statistics and Data Analysis With Exercises, Solutions and Applications in R

Help Advanced Search. We gratefully acknowledge support from the Simons Foundation and member institutions. Data Analysis, Statistics and Probability Authors and titles for physics.

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This introductory statistics textbook conveys the essential concepts and tools needed to develop and nurture statistical thinking. It presents descriptive, inductive and explorative statistical methods and guides the reader through the process of quantitative data analysis. In the experimental sciences and interdisciplinary research, data analysis has become an integral part of any scientific study. Issues such as judging the credibility of data, analyzing the data, evaluating the reliability of the obtained results and finally drawing the correct and appropriate conclusions from the results are vital.

Police managers recognize that competent analysts provide important information to decision makers.

With Exercises, Solutions and Applications in R

The journal consists of four refereed sections which are divided into the following subject areas:. I Computational Statistics - Manuscripts dealing with: 1 the explicit impact of computers on statistical methodology e. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. Your Paper Your Way We now differentiate between the requirements for new and revised submissions. You may choose to submit your manuscript as a single Word or PDF file to be used in the refereeing process.

A newer version is available on his channel — Learning to program with Python 3. The course is the online equivalent of Statistics 2, a week introductory course taken in Berkeley by about 1, students each year. Logistic regression is a type of generalized linear model GLM for response variables where regular multiple regression does not work very well. Taking all three courses would be too in depth for the purpose of this guides. To summarize, visualize or analyze these Numbers, we need to do some math and here comes the use of Statistics. It's divided into 2 parts: Basics and Projects and Projects part has got 3 projects - a game, a data visualization project and a web application with an introduction to Django. Initial Setup.

Mathematical Statistics and Data Analysis

1 comments

Elsira C.

Use of the characteristic function to find the p.d.f. of an estimator are two main interpretations of probability commonly used in data analysis. The most.

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