Bookmark Us!

## Tuesday, 29 November 2011

### Hypothesis Testing

Null Hypothesis ( H0 )
Statement of zero or no change. If the original claim includes equality (<=, =, or >=), it is the null hypothesis. If the original claim does not include equality (<, not equal, >) then the null hypothesis is the complement of the original claim. The null hypothesis always includes the equal sign. The decision is based on the null hypothesis.
Alternative Hypothesis ( H1 or Ha )
Statement which is true if the null hypothesis is false. The type of test (left, right, or two-tail) is based on the alternative hypothesis.
Type I error
Rejecting the null hypothesis when it is true (saying false when true). Usually the more serious error.
Type II error
Failing to reject the null hypothesis when it is false (saying true when false).
alpha
Probability of committing a Type I error.
beta
Probability of committing a Type II error.
Level of Significance (Significance Level)
The probability of committing a type I error, also known as alpha. This is how unusual something must be before we call it too rare to have happened just by chance. The area in the critical region.
Probability Value (P-value)
The probability of getting the results obtained if the null hypothesis is true. If this probability is too small (smaller than the level of significance), then we reject the null hypothesis. If the level of significance is the area beyond the critical values, then the probability value is the area beyond the test statistic.
Test statistic
Sample statistic used to decide whether to reject or fail to reject the null hypothesis.
Critical region
Set of all values which would cause us to reject H0
Critical value(s)
The value(s) which separate the critical region from the non-critical region. The critical values are determined independently of the sample statistics.
Significance level ( alpha )
The probability of rejecting the null hypothesis when it is true. alpha = 0.05 and alpha = 0.01 are common. If no level of significance is given, use alpha = 0.05. The level of significance is the complement of the level of confidence in estimation.
Decision
A statement based upon the null hypothesis. It is either "reject the null hypothesis" or "fail to reject the null hypothesis". We will never accept the null hypothesis.
Conclusion
A statement which indicates the level of evidence (sufficient or insufficient), at what level of significance, and whether the original claim is rejected (null) or supported (alternative).

### ANOVA

F-distribution
The ratio of two independent chi-square variables divided by their respective degrees of freedom. If the population variances are equal, this simplifies to be the ratio of the sample variances.
Analysis of Variance (ANOVA)
A technique used to test a hypothesis concerning the means of three or mor populations.
One-Way Analysis of Variance
Analysis of Variance when there is only one independent variable. The null hypothesis will be that all population means are equal, the alternative hypothesis is that at least one mean is different.
Between Group Variation
The variation due to the interaction between the samples, denoted SS(B) for Sum of Squares Between groups. If the sample means are close to each other (and therefore the Grand Mean) this will be small. There are k samples involved with one data value for each sample (the sample mean), so there are k-1 degrees of freedom.
Between Group Variance
The variance due to the interaction between the samples, denoted MS(B) for Mean Square Between groups. This is the between group variation divided by its degrees of freedom.
Within Group Variation
The variation due to differences within individual samples, denoted SS(W) for Sum of Squares Within groups. Each sample is considered independently, no interaction between samples is involved. The degrees of freedom is equal to the sum of the individual degrees of freedom for each sample. Since each sample has degrees of freedom equal to one less than their sample sizes, and there are k samples, the total degrees of freedom is k less than the total sample size: df = N - k.
Within Group Variance
The variance due to the differences within individual samples, denoted MS(W) for Mean Square Within groups. This is the within group variation divided by its degrees of freedom.
Scheffe' Test
A test used to find where the differences between means lie when the Analysis of Variance indicates the means are not all equal. The Scheffe' test is generally used when the sample sizes are different.
Tukey Test
A test used to find where the differences between the means lie when the Analysis of Variance indicates the means are not all equal. The Tukey test is generally used when the sample sizes are all the same.
Two-Way Analysis of Variance
An extension to the one-way analysis of variance. There are two independent variables. There are three sets of hypothesis with the two-way ANOVA. The first null hypothesis is that there is no interaction between the two factors. The second null hypothesis is that the population means of the first factor are equal. The third null hypothesis is that the population means of the second factor are equal.
Factors
The two independent variables in a two-way ANOVA.
Treatment Groups
Groups formed by making all possible combinations of the two factors. For example, if the first factor has 3 levels and the second factor has 2 levels, then there will be 3x2=6 different treatment groups.
Interaction Effect
The effect one factor has on the other factor
Main Effect
The effects of the independent variables.

### Correlation & Regression

Coefficient of Determination
The percent of the variation that can be explained by the regression equation
Correlation
A method used to determine if a relationship between variables exists
Correlation Coefficient
A statistic or parameter which measures the strength and direction of a relationship between two variables
Dependent Variable
A variable in correlation or regression that can not be controlled, that is, it depends on the independent variable.
Independent Variable
A variable in correlation or regression which can be controlled, that is, it is independent of the other variable.
Pearson Product Moment Correlation Coefficient
A measure of the strength and direction of the linear relationship between two variables
Regression
A method used to describe the relationship between two variables.
Regression Line
The best fit line.
Scatter Plot
An plot of the data values on a coordinate system. The independent variable is graphed along the x-axis and the dependent variable along the y-axis
Standard Error of the Estimate
The standard deviation of the observed values about the predicted values

### Journal List

The following is a nearly comprehensive list of journals which publish articles in statistics, based on the Current Index to Statistics list of core journals. Note that journal home pages maintained by publishing houses change frequently. If the journal link given here is no longer active, try the NYU Stern journal page.

### Random Variables

When the numerical value of a variable is determined by a chance event, that variable is called a random variable.

## Discrete and Continuous Random Variables

Random variables can be discrete or continuous.
• Discrete. Discrete random variables take on integer values, usually the result of counting. Suppose, for example, that we flip a coin and count the number of heads. The number of heads results from a random process - flipping a coin. And the number of heads is represented by an integer value - a number between 0 and plus infinity. Therefore, the number of heads is a discrete random variable.
• Continuous. Continuous random variables, in contrast, can take on any value within a range of values. For example, suppose we flip a coin many times and compute the average number of heads per flip. The average number of heads per flip results from a random process - flipping a coin. And the average number of heads per flip can take on any value between 0 and 1, even a non-integer value. Therefore, the average number of heads per flip is a continuous random variable.

## Monday, 28 November 2011

### Operations research

Operations research (also referred to as decision science, or management science) is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations. In contrast, many other science & engineering disciplines focus on technology giving secondary considerations to its use.
Employing techniques from other mathematical sciences – such as mathematical modeling, statistical analysis, and mathematical optimization – operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Because of its emphasis on human-technology interaction and because of its focus on practical applications, operations research has overlap with other disciplines, notably industrial engineering and operations management, and draws on psychology and organization science. Operations Research is often concerned with determining the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost) of some real-world objective. Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries.

## Problems of operational research

• critical path analysis or project planning: identifying those processes in a complex project which affect the overall duration of the project
• floorplanning: designing the layout of equipment in a factory or components on a computer chip to reduce manufacturing time (therefore reducing cost)
• network optimization: for instance, setup of telecommunications networks to maintain quality of service during outages
• Allocation problems
• Facility location
• Assignment Problems:
• Assignment problem
• Generalized assignment problem
• Quadratic assignment problem
• Weapon target assignment problem
• Bayesian search theory : looking for a target
• optimal search
• routing, such as determining the routes of buses so that as few buses are needed as possible
• supply chain management: managing the flow of raw materials and products based on uncertain demand for the finished products
• efficient messaging and customer response tactics
• automation: automating or integrating robotic systems in human-driven operations processes
• globalization: globalizing operations processes in order to take advantage of cheaper materials, labor, land or other productivity inputs
• transportation: managing freight transportation and delivery systems (Examples: LTL Shipping, intermodal freight transport)
• scheduling:
• personnel staffing
• manufacturing steps
• network data traffic: these are known as queueing models or queueing systems.
• sports events and their television coverage
• blending of raw materials in oil refineries
• determining optimal prices, in many retail and B2B settings, within the disciplines of pricing science
Operational research is also used extensively in government where evidence-based policy is used.

### Techniques

• Data mining
• Decision analysis
• Engineering
• Forecasting
• Game theory
• Industrial engineering
• Logistics
• Mathematical modeling
• Mathematical optimization
• Probability and statistics
• Project management
• Simulation
• Social network/Transportation forecasting models
• Supply chain management
• Financial engineering

### Applications of management science

Applications of management science are abundant in industry as airlines, manufacturing companies, service organizations, military branches, and in government. The range of problems and issues to which management science has contributed insights and solutions is vast. It includes:
• scheduling airlines, including both planes and crew,
• deciding the appropriate place to site new facilities such as a warehouse, factory or fire station,
• managing the flow of water from reservoirs,
• identifying possible future development paths for parts of the telecommunications industry,
• establishing the information needs and appropriate systems to supply them within the health service, and
• identifying and understanding the strategies adopted by companies for their information systems
Management science is also concerned with so-called ”soft-operational analysis”, which concerns methods for strategic planning, strategic decision support, and Problem Structuring Methods (PSM). In dealing with these sorts of challenges mathematical modeling and simulation are not appropriate or will not suffice. Therefore, during the past 30 years, a number of non-quantified modeling methods have been developed. These include:
• stakeholder based approaches including metagame analysis and drama theory
• morphological analysis and various forms of influence diagrams.
• approaches using cognitive mapping
• the Strategic Choice Approach
• robustness analysis
Journals
INFORMS publishes twelve scholarly journals about operations research, including the top two journals in their class, according to 2005 Journal Citation Reports. They are:

### Biostatistics

Biostatistics (a contraction of biology and statistics; sometimes referred to as biometry or biometrics) is the application of statistics to a wide range of topics in biology. The science of biostatistics encompasses the design of biological experiments, especially in medicine and agriculture; the collection, summarization, and analysis of data from those experiments; and the interpretation of, and inference from, the results.

## Bio-statistics and the history of biological thought

Biostatistical reasoning and modeling were of critical importance to the foundation theories of modern biology. In the early 1900s, after the rediscovery of Mendel's work, the gaps in understanding between genetics and evolutionary Darwinism led to vigorous debate among biometricians, such as Walter Weldon and Karl Pearson, and Mendelians, such as Charles Davenport, William Bateson and Wilhelm Johannsen. By the 1930s, statisticians and models built on statistical reasoning had helped to resolve these differences and to produce the neo-Darwinian modern evolutionary synthesis.
The leading figures in the establishment of this synthesis all relied on statistics and developed its use in biology.
• Sir Ronald A. Fisher developed several basic statistical methods in support of his work The Genetical Theory of Natural Selection
• Sewall G. Wright used statistics in the development of modern population genetics
• J. B. S Haldane's book, The Causes of Evolution, reestablished natural selection as the premier mechanism of evolution by explaining it in terms of the mathematical consequences of Mendelian genetics.
These individuals and the work of other bio-statisticians, mathematical biologists, and statistically-inclined geneticists helped bring together evolutionary biology and genetics into a consistent, coherent whole that could begin to be quantitatively modeled.
In parallel to this overall development, the pioneering work of D'Arcy Thompson in On Growth and Form also helped to add quantitative discipline to biological study.
Despite the fundamental importance and frequent necessity of statistical reasoning, there may nonetheless have been a tendency among biologists to distrust or deprecate results which are not qualitatively apparent. One anecdote describes Thomas Hunt Morgan banning the Friden calculator from his department at Caltech, saying "Well, I am like a guy who is prospecting for gold along the banks of the Sacramento River in 1849. With a little intelligence, I can reach down and pick up big nuggets of gold. And as long as I can do that, I'm not going to let any people in my department waste scarce resources in placer mining." Educators are now adjusting their curricula to focus on more quantitative concepts and tools.

## Applications of bio-statistics

• Public health, including epidemiology, health services research, nutrition, and environmental health
• Design and analysis of clinical trials in medicine
• Population genetics, and statistical genetics in order to link variation in genotype with a variation in phenotype. This has been used in agriculture to improve crops and farm animals (animal breeding). In biomedical research, this work can assist in finding candidates for gene alleles that can cause or influence predisposition to disease in human genetics
• Analysis of genomics data, for example from microarray or proteomics experiments. Often concerning diseases or disease stages.
• Ecology, ecological forecasting
• Biological sequence analysis
• Systems biology for gene network inference or pathways analysis.
Statistical methods are beginning to be integrated into medical informatics, public health informatics, bioinformatics and computational biology.

## Bio-statistics journals

### Actuarial science

Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in the insurance and finance industries. Actuaries are professionals who are qualified in this field through education and experience. In many countries, actuaries must demonstrate their competence by passing a series of rigorous professional examinations.
Actuarial science includes a number of interrelating subjects, including probability, mathematics, statistics, finance, economics, financial economics, and computer programming. Historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through revolutionary changes during the last 30 years due to the proliferation of high speed computers and the union of stochastic actuarial models with modern financial theory (Frees 1990).
Many universities have undergraduate and graduate degree programs in actuarial science. In 2010, a study published by job search website CareerCast ranked actuary as the #1 job in the United States (Needleman 2010). The study used five key criteria to rank jobs: environment, income, employment outlook, physical demands, and stress. A similar study by U.S. News & World Report in 2006 included actuaries among the 25 Best Professions that it expects will be in great demand in the future (Nemko 2006).

## Life insurance, pensions and healthcare

Actuarial science became a formal mathematical discipline in the late 17th century with the increased demand for long-term insurance coverages such as Burial, Life insurance, and Annuities. These long term coverages required that money be set aside to pay future benefits, such as annuity and death benefits many years into the future. This requires estimating future contingent events, such as the rates of mortality by age, as well as the development of mathematical techniques for discounting the value of funds set aside and invested. This led to the development of an important actuarial concept, referred to as the Present value of a future sum. Pensions and healthcare emerged in the early 20th century as a result of collective bargaining. Certain aspects of the actuarial methods for discounting pension funds have come under criticism from modern financial economics.
• In traditional life insurance, actuarial science focuses on the analysis of mortality, the production of life tables, and the application of compound interest to produce life insurance, annuities and endowment policies. Contemporary life insurance programs have been extended to include credit and mortgage insurance, key man insurance for small businesses, long term care insurance and health savings accounts (Hsiao 2001).
• In health insurance, including insurance provided directly by employers, and social insurance, actuarial science focuses on the analysis of rates of disability, morbidity, mortality, fertility and other contingencies. The effects of consumer choice and the geographical distribution of the utilization of medical services and procedures, and the utilization of drugs and therapies, is also of great importance. These factors underlay the development of the Resource-Base Relative Value Scale (RBRVS) at Harvard in a multi-disciplined study. (Hsiao 2004) Actuarial science also aids in the design of benefit structures, reimbursement standards, and the effects of proposed government standards on the cost of healthcare (CHBRP 2004).
• In the pension industry, actuarial methods are used to measure the costs of alternative strategies with regard to the design, maintenance or redesign of pension plans. The strategies are greatly influenced by collective bargaining; the employer's old, new and foreign competitors; the changing demographics of the workforce; changes in the internal revenue code; changes in the attitude of the internal revenue service regarding the calculation of surpluses; and equally importantly, both the short and long term financial and economic trends. It is common with mergers and acquisitions that several pension plans have to be combined or at least administered on an equitable basis. When benefit changes occur, old and new benefit plans have to be blended, satisfying new social demands and various government discrimination test calculations, and providing employees and retirees with understandable choices and transition paths. Benefit plans liabilities have to be properly valued, reflecting both earned benefits for past service, and the benefits for future service. Finally, funding schemes have to be developed that are manageable and satisfy the Financial Accounting Standards Board (FASB).
• In social welfare programs, the Office of the Chief Actuary (OCACT), Social Security Administration plans and directs a program of actuarial estimates and analyses relating to SSA-administered retirement, survivors and disability insurance programs and to proposed changes in those programs. It evaluates operations of the Federal Old-Age and Survivors Insurance Trust Fund and the Federal Disability Insurance Trust Fund, conducts studies of program financing, performs actuarial and demographic research on social insurance and related program issues involving mortality, morbidity, utilization, retirement, disability, survivorship, marriage, unemployment, poverty, old age, families with children, etc., and projects future workloads. In addition, the Office is charged with conducting cost analyses relating to the Supplemental Security Income (SSI) program, a general-revenue financed, means-tested program for low-income aged, blind and disabled people. The Office provides technical and consultative services to the Commissioner, to the Board of Trustees of the Social Security Trust Funds, and its staff appears before Congressional Committees to provide expert testimony on the actuarial aspects of Social Security issues.

## Actuarial science applied to other forms of insurance

Actuarial science is also applied to Property, Casualty, Liability insurance, and General insurance. In these forms of insurance, coverage is generally provided on a renewable period, (such as a yearly). Coverage can be cancelled at the end of the period by either party.
Property and casualty insurance companies tend to specialize because of the complexity and diversity of risks. One division is to organize around personal and commercial lines of insurance. Personal lines of insurance are for individuals and include fire, auto, homeowners, theft and umbrella coverages. Commercial lines address the insurance needs of businesses and include property, business continuation, product liability, fleet/commercial vehicle, workers compensation, fidelity & surety, and D&O insurance. The insurance industry also provides coverage for exposures such as catastrophe, weather-related risks, earthquakes, patent infringement and other forms of corporate espionage, terrorism, and "one-of-a-kind" (e..g, satellite launch). Actuarial science provides data collection, measurement, estimating, forecasting, and valuation tools to provide financial and underwriting data for management to assess marketing opportunities and the nature of the risks. Actuarial science often helps to assess the overall risk from catastrophic events in relation to its underwriting capacity or surplus.
In the reinsurance fields, actuarial science can be used to design and price reinsurance and retro-reinsurance schemes, and to establish reserve funds for known claims and future claims and catastrophes.
Related Articles:(PDF)

### ESBStats - Statistical Analysis Software 2.0.0

ESBStats - Statistical Analysis Software 2.0.0 is a shareware application tool which can help you in all your statistical calculations and analysis. This Windows based application allows you to perform various statistical functions like calculating mean, mode, median, variance etc, solving Time Series, Linear Regression and much more. This application also provides you with features like Online Help, Tutorials, Graphs, Summaries, Import/Export, Customizable Interface, Calculator, Live Spell Check etc. Other important features of this application are as follows - it allows you to perform Single, Dual and Multiple Data Analysis. You can work on various types of data like Sample or Population type Raw Data, Grouped Data or Summary Data with this application. You can also covert raw data to grouped data. You can perform Time Series Analysis. You can also store data in the data lists in the workbook. It allows you to create reports based on your analysis. This one is a great analysis tool for the statistically inclined. Try it

## Publisher's description:

Statistical Analysis and Inference Software for Windows covering everything from Average, Mode and Variance through to Hypothesis Analysis, Time Series and Linear Regression. Includes Online Help, Tutorials, Graphs, Summaries, Import/Export, Customisable Interface, Calculator, Live Spell Check, Install/Uninstall and much more.

- Single, Dual (paired and unpaired) and Multiple Data Analysis (Multivariate analysis not in Lite Version).
- Data can be either for Sample or Population.
- Data can be Time Based for Time Series Analysis.
- Data can be entered as Raw Data, Grouped Data, or as Summary Data.
- Raw Data can be converted into Grouped Data.
- Raw Data can have in-built Transformations applied to them.
- Raw Data can have Random values meeting user defined criteria.
- Data can be fully documented and stored in DataLists.
- Standardisation of Data around given mean/standard deviation.
- DataLists are grouped together in Workbooks - one Workbook is opened at a time and can contain many DataLists.
- Sample Size calculations.
- Random Value Lists for Sampling.
- Statistical Summary including: mean, median, mode, variance, standard deviation, kurtosis, skew, etc.
- Comparison of Statistics for Raw and Grouped of the same Data.
- Graphs and Charts including: Histograms, Line Graphs, Pie Graphs, Ogives, Scatter Diagrams, Rootograms, Bar Charts and more.
- Inference and Hypothesis Analysis of a Single Population - including the Mean, the Variance and Proportions.
- Inference and Hypothesis Analysis of Two Populations - including Difference of the Mean, Ratio of the Variance, Difference of Proportions.
- Analysis of Variance (ANOVA) (not in Lite Version).
- Linear Regression with Transformations of the dependent variable.
- Multiple Regression with Transformations of the dependent variables (not in Lite Version).
- Moving Averages.
- Trend Analysis of Time Series Data.
PLUS MORE.

### AM statistical software

AM is still in Beta release, and the new Beta Version 0.06.00 adds substantial capability. Some of the enhancements include:
• Graphics. For the first time, AM offers statistical graphics. Right now, it produces bar charts, line charts, and the new Sectioned Density Plot. The sectioned density plot is designed to compare distributions—we think of it as the next generation of the box-and-whisker plot. Look to future releases for expanded graphic capability.
• New import/export facilities that enable you to easily import/export data to/from nearly 150 different data file formats, as well as over ODBC. See File | Import | General Import and File | Export | General Export on AM's main menu.
• Sample-design consistent Wald tests of model fit for all regression models, including the point-and-click ability to test the significance of subsets of regressors.
• A new Mantel-Haenszel stratified chi-square test of the type typically used to evaluate differential item function on tests. As with all AM procedures, this one provides significance tests that are appropriate for complex sample designs.
• An expanded set of models when the preferred variance estimation method is one of the replication methods.
AM is still in Beta release, though we have put it through substantial testing. Please let us know about any problems as soon as you find them. As always, AM will remain free in future releases.

### Free Statistical Softwares

General Purpose Packages

BioEstat (5.0)

Screen Shot
Descriptive and Multivariate Analysis (Be careful: software has only a portuguese version) Freeware
Dataplot (01-2009)

Screen Shot
Software for Scientific Visualization, Statistical Analysis, and Non-Linear Modeling....   full review Freeware
Instat + (3.36)

Screen Shot
General Statistical Package particurarly aimed at Analysis of Climatic Data....   full review Free for personal use

44.6 MB
MacAnova (5.05)

Screen Shot
An Interactive Program for Statistical Analysis and Matrix Algebra....   full review Open Source
MicrOsiris (11.0)

Screen Shot
Statistical and Data Management Package Freeware

6.2 MB
R (2.13)

Screen Shot
A Programming Environment for Data Analysis and Graphics....   full review Open Source
Tanagra (1.4.36)

Screen Shot
Data Mining Software for Research and Education....   full review Open Source

2.7 MB
ViSta (7.9)

Screen Shot
Statistical Visualizations highly Dynamic and very Interactive....   full review Open Source
WinIDAMS (1.3)

Screen Shot
Software Package for the Validation, Manipulation and Statistical Analysis of Data....   full review Freeware

## Friday, 25 November 2011

General statistical computing package

## What is Instat?

Instat is a general statistical package. It is simple enough to be useful in teaching statistical ideas, yet has the power to assist research in any discipline that requires the analysis of data.
Instat began life on a BBC microcomputer. It was first used on a training course on 'statistics in agriculture' held in Sri Lanka during 1983. The BBC micro version was marketed commercially from mid-1985, with the DOS version for PCs becoming available in 1987. From 1994 Instat was free-of-charge. Updated DOS versions were released in 1996 and 1997.
Instat has been used widely in the UK and elsewhere by a range of companies, research institutes, schools, colleges, universities and private individuals. At Reading it has been used extensively on training courses run by the SSC. It has also been used in many countries on statistics courses and on courses related to health, agriculture and climatology.
'Instat+' (i.e. the Windows version of Instat) has been developed mainly because of its continued use for the analysis of climatic data. Funding from the UK Met Office for a new climatic version, supplemented by support from the SSC and the efforts of other friendly collaborators, led to the Windows version, which was first used on training courses in 1999.
The full version of Instat may be downloaded and used for non-commercial purposes by any individual free of charge. There is no copy-protection, time limit or data size restriction, other than Instat's inherent size limitations.
Instat can be supplied on a CD, for which there is a minimum charge of £40. When the software is supplied on CD, a printed copy of the tutorial (pdf, 679KB) is also provided.

Get Instat now.

## SSC-Stat(Excel Add on packs)

The full version of SSC-Stat may be downloaded and used for non-commercial purposes by any individual free of charge. There is no copy-protection, time limit or special data size restriction.
SSC-Stat can be supplied on a CD, for which there is a minimum charge of £40. When the software is supplied on CD, a printed copy of the SSC-Stat Tutorial (pdf, 290KB) is also provided.

Get SSC-Stat now.

Diversity index Calculator(Add-in for MS-EXCEL)

Diversity indices are used in the analysis of multi-species ecological data. Several indices have been proposed, each with its own strengths. There are two aspects to diversity: species richness and evenness. Indices are available that measure these two components separately.
A good introductory reference is the book Ecological Diversity and its Measurement (1988) by Anne Magurran. A revised and updated version, entitled Measuring Biological Diversity, was recently published by Blackwell Science.
The SSC's Diversity Add-In for Microsoft® Excel™ contains functions for the most widely-used indices. Once the add-in is loaded, its functions are used in much the same way as Excel's built in-functions.

Get the Diversity Add-In now (zip file, 36KB)

The zip file contains the add-in itself (Diversity.xla), some notes on installing and using it, and an Excel workbook with some examples﻿.

## Thursday, 24 November 2011

### Introduction to Bayesian inference

Bayesian inference is one of two dominant approaches to statistical inference. The word "Bayesian" refers to the influence of Reverend Thomas Bayes, who introduced what is now known as Bayes' theorem. Bayesian inference was developed prior to what is incorrectly called classical statistics, which is more appropriately referred to as frequentest inference. Bayesian inference is a modern revival of the classical definition of probability, associated with Pierre-Simon Laplace, in contrast to the frequentest definition of probability, most often associated with R. A. Fisher.
Bayesian analysis
A decision-making analysis that '…permits the calculation of the probability that one treatment is superior based on the observed data and prior beliefs…subjectivity of beliefs is not a liability, but rather explicitly allows different opinions to be formally expressed and evaluated.' See Algorithm, Critical pathway, Decision analysis.
In statistics, Bayesian inference is a method of statistical inference in which evidence is used to update the uncertainties of competing probability models. Bayesian inference is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection.
In the Bayesian interpretation of probability, probability measures confidence that something is true, and may be termed uncertainty, confidence or belief. Suppose there is a process generating events with unknown probabilities. The state of belief concerning this process is the set of possible probability models and corresponding uncertainties. The uncertainties are subjective, but always sum to 1. When events are freshly observed, these may be compared to those predicted by each model and the uncertainties updated. A Bayesian inference step uses Bayes' theorem to calculate the updated uncertainties. For each uncertainty, the initial value is called the prior, while the updated value is called the posterior. Typically, as steps occur, the uncertainty of one model tends to 1 while that of the rest tend to 0.
To determine the parameter of a model $M(\theta \in \Theta)$, the state of belief may be defined over the set of models $\{M(\theta) : \theta \in \Theta \}$. After performing Bayesian inference, a point estimate of θ may be made - typically as the most likely value of θ, or the expectation of θ.
In Bayesian model selection, the uncertainty of different models is compared as inference steps occur. For further details of the use of Bayesian inference in model selection, see Bayesian model selection.
Some Bayesian inference PDF:

### Introduction to Statistical inference

Statistical inference is the act of using observed data to infer unknown properties and characteristics of the probability distribution from which the observed data have been generated. The set of data that is used to make inferences is called sample.
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation. More substantially, the terms statistical inference, statistical induction and inferential statistics are used to describe systems of procedures that can be used to draw conclusions from data sets arising from systems affected by random variation. Initial requirements of such a system of procedures for inference and induction are that the system should produce reasonable answers when applied to well-defined situations and that it should be general enough to be applied across a range of situations.
Scope
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:
• a statistical model of the random process that is supposed to generate the data, and
• a particular realization of the random process; i.e., a set of data.
The conclusion of a statistical inference is a statistical proposition. Some common forms of statistical proposition are:
• an estimate; i.e., a particular value that best approximates some parameter of interest,
• a confidence interval (or set estimate); i.e., an interval constructed from the data in such a way that, under repeated sampling of datasets, such intervals would contain the true parameter value with the probability at the stated confidence level,
• a credible interval; i.e., a set of values containing, for example, 95% of posterior belief,
• rejection of a hypothesis
• clustering or classification of data points into groups
PDF Files(Statistical inference)
Introduction of Statistical inference(PDF)
An Introduction to Statistical. Inference and Its Applications