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Je recommande cette application.Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.

Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole.

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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 test of the relationship between two statistical data sets, or a data set and synthetic data drawn from 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 difference between populations is missed giving a "false negative").

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. Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. 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.

Mathematical techniques used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory. Populations can be diverse topics such as "all persons 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 types (like income), while frequency and percentage are more useful in terms of describing categorical data (like race). 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, the drawing of the sample has been subject to an element of randomness, hence the established numerical descriptors from the sample are also due to uncertainty.

To still 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, accounting for randomness.

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.

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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.The data from a randomized study can be analyzed to consider secondary hypotheses or to suggest new ideas. A secondary analysis of the data from a planned study uses tools from data analysis.

While the tools of data analysis work best on data from randomized studies, they are also applied to other kinds of data --- for example, from natural experiments and observational studies, in which case the inference is dependent on the model chosen by the statistician, and so subjective.

More complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures. A probability distribution can either be univariate or multivariate. Important and commonly encountered univariate probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. The multivariate normal distribution is a commonly encountered multivariate distribution.

Statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation. Inferential statistics are used to test hypotheses and make estimations using sample data.

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Whereas descriptive statistics describe a sample, inferential statistics infer predictions about a larger population that the sample represents. The outcome of statistical inference may be an answer to the question "what should be done next. For the most part, statistical inference makes propositions about populations, using data drawn from the population of interest via some form of random sampling.

More generally, data about a random process is obtained from its observed behavior during a finite period of time. Given a parameter or hypothesis about which one wishes to make inference, statistical inference most often uses:In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables.

More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables.

Many techniques for carrying out regression analysis have been developed. Nonparametric statistics are statistics not based on parameterized families of probability distributions. They include both descriptive and inferential statistics. The typical parameters are the mean, variance, etc. Unlike parametric statistics, nonparametric statistics make no assumptions about the probability distributions of the variables being assessed.

Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences.

In terms of levels of measurement, non-parametric methods result in "ordinal" data. As non-parametric methods make fewer assumptions, their applicability is much wider than the corresponding parametric methods. In particular, they may be applied in situations where less is known about the application in question. Also, due to the reliance on fewer assumptions, non-parametric methods are more robust. Another justification for the use of non-parametric methods is simplicity.

In certain cases, even when the use of parametric methods is justified, non-parametric methods may be easier to use. Due both to this simplicity and to their greater robustness, non-parametric methods are seen by some statisticians as leaving less room for improper use and misunderstanding. Mathematical statistics has substantial overlap with the discipline of statistics.

Statistical theorists study and improve statistical procedures with mathematics, and statistical research often raises mathematical questions. Statistical theory relies on probability and decision theory. Mathematicians and statisticians like Gauss, Laplace, and C. New York: John Wiley and Sons. John Wiley and Sons, New York. Testing Statistical Hypotheses (2nd ed. Theory of Point Estimation (2nd ed. Mathematical Statistics: Basic and Selected Topics.The software is very easy to use, and I appreciate the continual improvement that seems to be made.

You and your colleagues have done something incredible here. It will help me gain confidence with conducting data analysis using R. I have tried a few R MOOCs in the past which helped me start out using R but I had not found a comprehensive intro to R that I could use more broadly - this course really succeeds with accomplishing that.

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This course has given me a much better understanding of biostatistics and will allow me to gain more from my campus based studies. This course supplied a solid foundation for identifying statistical outliers in demand patterns for business planning purposes. I much enjoyed your text mining course last year and plan to take the deep learning one - thanks for creating itThis course fundamentally deepened my understanding of statistics and studies.

I will certainly apply the knowledge gained as often as possible. Absolutely vital course for understanding basic epidemiology, studies and statistics. I would recommend that everyone get a copy of the textbook before class though. It complements the ActivEpi CD extremely well. This course will greatly contribute to my work as an environmental data scientist and division director. This course was a great introduction of how to use R to fit the models and how to interpret the R output.

Great explanations provided by the course instructor in the videos and on the discussion board. The Assistant Teacher was very diligent and professional in reaching out to me and giving me every opportunity to be successful in this course.

Definitely a wonderful experience!!. Using information gleaned from the course concerning a not-well-known distance measure (Gower dissimilarity) useful for cluster models that combine data from mixed variables, including nominal, ordinal, and numeric variables, I was able to refine a model I was working on for an academic conference paper.

More broadly, the subject of identifying anomalies is a central task of academic historians, and this course allowed me the welcome luxury to reflect on their nature and methods of discovery. I am now confident that I can use R and continue learning on my own. The course also helped me to explore other resources within the R community online. I'm looking forward to using R in data analysis for my masters thesis and beyond.

The two instructors are to be congratulated in putting together a jewel of a short course, one of my very favorite among the many I have taken at Statistics. The discussion with such experts was particularly valuable and greatly enhanced the value of the course.

If there were an extension to this course, I would gladly take it. I felt this class did a good job of reinforcing concepts and their application, and not getting caught up in the algorithms.

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The TA feedback was invaluable to me. There are many things I like about your educational product. You include variety, such as the videos, the homework, the quizzes, the textbook, and the discussion board. You have well-thought out curriculum that shows a respect for good pedagogy. Your instructors are amazing. They are brilliant, and they respond very quickly. You apply real-world needs to the material being taught instead of having students memorize formulas or be confined within an academic-only practice of modeling.

I realized that I deal with statistics every day. We covered issues that pertain to real life and I now feel I have knowledge about important issues I was previously unaware about.This variable might contain information about the state in which the study was conducted (either Nebraska or New York).

GENDER SODA STATE case 1 case 2 case 3 case 4 case 5. NEBRASKA NEW YORK NEBRASKA NEBRASKA NEW YORK. The crosstabulation of these variables would result in a 3-way table: STATE: NEW YORK STATE: NEBRASKA SODA: A SODA: B SODA: A SODA: B G:MALE 20 30 50 5 45 50 G:FEMALE 30 20 50 45 5 50 50 50 100 50 50 100 Theoretically, an unlimited number of variables can be crosstabulated in a single multi-way table. However, research practice shows that it is usually difficult to examine and "understand" tables that involve more than 4 variables.

It is recommended to analyze relationships between the factors in such tables using modeling techniques such as Log-Linear Analysis or Correspondence Analysis. Graphical Representations of Multi-way Tables. You can produce "double categorized" histograms, 3D histograms,Batches (cascades) of graphs can be used to summarize higher-way tables (as shown in the graph below).

Crosstabulations generally allow us to identify relationships between the crosstabulated variables. The following table illustrates an example of a very strong relationship between two variables: variable Age (Adult vs. Child) and variable Cookie preference (A vs. COOKIE: A COOKIE: B AGE: ADULT 50 0 50 AGE: CHILD 0 50 50 50 50 100 All adults chose cookie A, while all children chose cookie B. However, in real-life, relations between variables are typically much weaker, and thus the question arises as to how to measure those relationships, and how to evaluate their reliability (statistical significance).

The techniques used to analyze simultaneous relations between more than two variables in higher order crosstabulations are discussed in the context of the Log-Linear Analysis module and the Correspondence Analysis. The Pearson Chi-square is the most common test for significance of the relationship between categorical variables.

This measure is based on the fact that we can compute the expected frequencies in a two-way table (i. For example, suppose we ask 20 males and 20 females to choose between two brands of soda pop (brands A and B). If there is no relationship between preference and gender, then we would expect about an equal number of choices of brand A and brand B for each sex.

The value of the Chi-square and its significance level depends on the overall number of observations and the number of cells in the table. Consistent with the principles discussed in Elementary Concepts, relatively small deviations of the relative frequencies across cells from the expected pattern will prove significant if the number of observations is large.

The only assumption underlying the use of the Chi-square (other than random selection of the sample) is that the expected frequencies are not very small.

For further discussion of this issue refer to Everitt (1977), Hays (1988), or Kendall and Stuart (1979). In practice, the M-L Chi-square is usually very close in magnitude to the Pearson Chi- square statistic.

For more details about this statistic refer to Bishop, Fienberg, and Holland (1975), or Fienberg, S. The approximation of the Chi-square statistic in small 2 x 2 tables can be improved by reducing the absolute value of differences between expected and observed frequencies by 0.

For small n, this probability can be computed exactly by counting all possible tables that can be constructed based on the marginal frequencies. Thus, the Fisher exact test computes the exact probability under the null hypothesis of obtaining the current distribution of frequencies across cells, or one that is more uneven. This test is applicable in situations where the frequencies in the 2 x 2 table represent dependent samples.

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For example, in a before-after design study, we may count the number of students who fail a test of minimal math skills at the beginning of the semester and at the end of the semester. The Phi-square is a measure of correlation between two categorical variables in a 2 x 2 table. For more details concerning this statistic see Castellan and Siegel (1988, p. This statistic is also only computed for (applicable to) 2 x 2 tables. If the 2 x 2 table can be thought of as the result of two continuous variables that were (artificially) forced into two categories each, then the tetrachoric correlation coefficient will estimate the correlation between the two.

The coefficient of contingency is a Chi-square based measure of the relation between two categorical variables (proposed by Pearson, the originator of the Chi-square test). Its advantage over the ordinary Chi-square is that it is more easily interpreted, since its range is always limited to 0 through 1 (where 0 means complete independence). Interpretation of Contingency Measures.

An important disadvantage of measures of contingency (reviewed above) is that they do not lend themselves to clear interpretations in terms of probability or "proportion of variance," as is the case, for example, of the Pearson r (see Correlations). There is no commonly accepted measure of relation between categories that has such a clear interpretation. Statistics Based on Ranks.What software to buy. Are camera-binoculars a necessity or novelty.

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