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'''Statistics''' can be described as "the practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample."<ref>Soanes, C. and Stevenson, A. (eds.) (2005) 'Oxford Dictionary of English (2nd edition revised)' Oxford University Press, Oxford, U.K.</ref> It involves all stages of data collection and processing from the initial collection, to the analysis and ultimately to the conclusions and interpretations of the data. It is used in all research oriented disciplines from physics, chemistry and biology to economics, anthropology and psychology as well as many thousands of other fields. It is also used in businesses and governments.   

'''Statistics''' can be described as "the practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample."<ref>Soanes, C. and Stevenson, A. (eds.) (2005) 'Oxford Dictionary of English (2nd edition revised)' Oxford University Press, Oxford, U.K.</ref> It involves all stages of data collection and processing from the initial collection, to the analysis and ultimately to the conclusions and interpretations of the data. It is used in all research oriented disciplines from physics, chemistry and biology to economics, anthropology and psychology as well as many thousands of other fields. It is also used in businesses and governments.   

Statistics analyzes data in two primary ways, the first is called [[descriptive statistics]] which describes and summarizes the data. Often this will include things like: [[mean|the mean]], [[standard error]], or [[standard deviation]] each of these is an example of a [[statistic]]. Also statistics can attempt to infer relationships between the data collected and various hypothesis or populations, this is called [[inferential statistics]]. Both descriptive and inferential statistics comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.

Statistics analyzes data in two primary ways, the first is called descriptive statistics which describes and summarizes the data. Often this will include things like: [[mean|the mean]], [[standard error]], or [[standard deviation]] each of these is an example of a [[statistic]]. Also statistics can attempt to infer relationships between the data collected and various hypothesis or populations, this is called inferential statistics. Both descriptive and inferential statistics comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.

Statistics takes its name from the fact that it was traditionally taught to monarchs to enable them to manage affairs of state.<ref>http://www.etymonline.com/index.php?term=statistics</ref>

Statistics takes its name from the fact that it was traditionally taught to monarchs to enable them to manage affairs of state.<ref>http://www.etymonline.com/index.php?term=statistics</ref>

===Descriptive statistics===

===Descriptive statistics===

Frequentist approaches to descriptive statistics mostly involve averaging. For example, the mean of a sample is calculated as the total value of all observations divided by total number of trials, and the standard error is calculated by taking the total error size for all samples and dividing by total number of trials.

Frequentist approaches to descriptive statistics mostly involve averaging. For example, the mean of a sample is calculated as the total value of all observations divided by total number of observations, the standard deviation as <math> \sqrt (1/N)</math> times the square root of the mean², and the standard error as the T* or Z* of the statistic times μ divided by the square root of N.

These methods stem from the view of data as ratios probabilities.

These methods stem from the view of data as ratios and probabilities.

===Inferential statistics===

===Inferential statistics===

[[Analysis of variance]]

[[Analysis of variance]]

[[Chi-Square test]] (either of independence/association, homogeneity, or goodness-of-fit)

[[Chi-Square test]] (the test could be of independence/association, homogeneity, or goodness-of-fit, depending on the circumstance)

[[Students t-test]]

[[Students t-test]]

[[Z test|Z-test]]

[[Z test|Z-test]]

[[Linear regression]]

[[Linear regression]]

[[Bayesian inference|Bayesian statistics]] is a method of applying [[Bayes theorem]] to data analysis. One of the biggest difference between Bayesian approaches and frequentist approaches is that Bayesians attempt to determine the probability that a given hypothesis is true given the data, while frequentist attempt to define the probability of getting the data given that a particular hypothesis is true.  

[[Bayesian inference|Bayesian statistics]] is a method of applying [[Bayes theorem]] to data analysis. One of the biggest difference between Bayesian approaches and frequentist approaches is that Bayesians attempt to determine the probability that a given hypothesis is true given the data, while frequentist attempt to define the probability of getting the data given that a particular hypothesis is true.  

Bayesian approaches are becoming more and more popular in science because what most people are interested in is the probability of the proposed hypothesis, not the probability of the data. It also does not need to make prior assumptions about the data such as [[Normal distribution|normality]] and [[homogeneity of variance]]. However, Bayesian methods have come under fire from many frequentist proponents. This has led to very heated debate in statistical circles, though this has largely died now, about the respective validity of both methods. The primary complaint leveled at Bayesian statistics is that it must use a [[prior probability]] of a hypothesis in its analysis. This prior is intended to build contextual information into the analysis, but it may be seen by its critics as subjective or arbitrary.  Commonly used prior distributions include the [[uniform distribution]] and [[beta distribution]].   

Bayesian approaches are becoming more and more popular in science because what most people are interested in is the probability of the proposed hypothesis, not the probability of the data. It also does not need to make prior assumptions about the data such as [[Normal distribution|normality]] and [[homogeneity of variance]]. However, Bayesian methods have come under fire from many frequentist proponents. This has led to very heated debate in statistical circles, though this has largely died now, about the respective validity of both methods. The primary complaint leveled at Bayesian statistics is that it must use a [[prior probability]] of a hypothesis in its analysis. This prior is intended to build contextual information into the analysis, but it may be seen by its critics as [[Subjectivism|subjective]] or arbitrary.  Commonly used prior distributions include the [[uniform distribution]] and [[beta distribution]].   

===Descriptive statistics===

===Descriptive statistics===