⊿ Point. {R} Glossary. ◥ University. {q} PhD. {t} Themes. {t} Maths-Stats. ⚫ UK. ↂ EndNote. ⬛ RSS. ✊ Harvey (2009) ◇ NASH, John. ◇ NEUMANN, John von. Foundations of mathematics. Foundations of mathematics is the study of the basic mathematical concepts (number, geometrical figure, set, function...) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their models giving a meaning to formulas, definitions, proofs, algorithms...) also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a central question of the philosophy of mathematics; the abstract nature of mathematical objects presents special philosophical challenges.
The foundations of mathematics as a whole does not aim to contain the foundations of every mathematical topic. Historical context[edit] See also: History of logic and History of mathematics. Ancient Greek mathematics[edit] Platonism as a traditional philosophy of mathematics[edit] Middle Ages and Renaissance[edit] Cipher. Codes generally substitute different length strings of characters in the output, whilst ciphers generally substitute the same number of characters as are input. There are exceptions and some cipher systems may use slightly more, or fewer, characters when output versus the number that were input. Codes operated by substituting according to a large codebook which linked a random string of characters or numbers to a word or phrase. For example, "UQJHSE" could be the code for "Proceed to the following coordinates". When using a cipher the original information is known as plaintext, and the encrypted form as ciphertext.
The ciphertext message contains all the information of the plaintext message, but is not in a format readable by a human or computer without the proper mechanism to decrypt it. Most modern ciphers can be categorized in several ways Etymology[edit] "Cipher" is alternatively spelled "cypher"; similarly "ciphertext" and "cyphertext", and so forth. Versus codes[edit] Types[edit] Cipher code. Code (cryptography) Terms like code and cipher are often used to refer to any form of encryption. However, there is an important distinction between codes and ciphers in technical work; it is, essentially, the scope of the transformation involved. Codes operate at the level of meaning; that is, words or phrases are converted into something else.
Ciphers work at the level of individual letters, or small groups of letters, or even, in modern ciphers, with individual bits. While a code might transform "change" into "CVGDK" or "cocktail lounge", a cipher transforms elements below the semantic level, i.e., below the level of meaning. The "a" in "attack" might be converted to "Q", the first "t" to "f", the second "t" to "3", and so on. Ciphers are more convenient than codes in some situations, there being no need for a codebook, with its inherently limited number of valid messages, and the possibility of fast automatic operation on computers.
"Operated on this morning. Forest plot. For private plots producing forest products, see Woodlot. An example forest plot of five odds ratios (squares, proportional to weights used in meta-analysis), with the summary measure (centre line of diamond) and associated confidence intervals (lateral tips of diamond), and solid vertical line of no effect. Names of (fictional) studies are shown on the left, odds ratios and confidence intervals on the right. A forest plot, also known as a blobbogram, is a graphical display of estimated results from a number of scientific studies addressing the same question, along with the overall results.[1] It was developed for use in medical research as a means of graphically representing a meta-analysis of the results of randomized controlled trials.
In the last twenty years, similar meta-analytical techniques have been applied in observational studies (e.g. environmental epidemiology) and forest plots are often used in presenting the results of such studies also. See also[edit] Sources[edit] 1370.0 - Measures of Australia's Progress, 2010. Psychologist. A psychologist evaluates, diagnoses, treats, and studies behavior and mental processes.[1] Some psychologists, such as clinical and counseling psychologists, provide mental health care, and some psychologists, such as social or organizational psychologists conduct research and provide consultation services.. Clinical, counseling, and school psychologists who work with patients in a variety of therapeutic contexts (contrast with psychiatrists, who are physician specialists).Industrial/organizational and community psychologists who apply psychological research, theories and techniques to "real-world" problems, questions and issues in business, industry, social benefit organizations, and government.[2][3][4]Academics conducting psychological research or teaching psychology in a college or university; Most typically, people encounter psychologists and think of the discipline as involving the work of clinical psychologists or counseling psychologists.
Licensing and regulation[edit] Lies, damned lies, and statistics. "Lies, damned lies, and statistics" is a phrase describing the persuasive power of numbers, particularly the use of statistics to bolster weak arguments. It is also sometimes colloquially used to doubt statistics used to prove an opponent's point. The term was popularised in the United States by Mark Twain (among others), who attributed it to the 19th-century British Prime Minister Benjamin Disraeli (1804–1881): "There are three kinds of lies: lies, damned lies, and statistics. " However, the phrase is not found in any of Disraeli's works and the earliest known appearances were years after his death. Other coiners have therefore been proposed, and the phrase is often attributed to Twain himself.
History[edit] Mark Twain popularized the saying in "Chapters from My Autobiography", published in the North American Review in 1906. The American Dialect Society list archives includes numerous posts by Stephen Goranson that cite research into uses soon after the above. . Uses[edit] References[edit] Statistical hypothesis testing. A statistical hypothesis test is a method of statistical inference using data from a scientific study. In statistics, a result is called statistically significant if it has been predicted as unlikely to have occurred by chance alone, according to a pre-determined threshold probability, the significance level. The phrase "test of significance" was coined by statistician Ronald Fisher.[1] These tests are used in determining what outcomes of a study would lead to a rejection of the null hypothesis for a pre-specified level of significance; this can help to decide whether results contain enough information to cast doubt on conventional wisdom, given that conventional wisdom has been used to establish the null hypothesis.
The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis. Variations and sub-classes[edit] The testing process[edit] An alternative process is commonly used: Interpretation[edit] Statistical significance. Statistical significance is the probability that an effect is not due to just chance alone.[1][2] It is an integral part of statistical hypothesis testing where it is used as an important value judgment. In statistics, a result is considered significant not because it is important or meaningful, but because it has been predicted as unlikely to have occurred by chance alone.[3] The present-day concept of statistical significance originated from Ronald Fisher when he developed statistical hypothesis testing in the early 20th century.[4][5][6] These tests are used to determine whether the outcome of a study would lead to a rejection of the null hypothesis based on a pre-specified low probability threshold called p-values, which can help an investigator to decide if a result contains sufficient information to cast doubt on the null hypothesis.[7] History[edit] Role in statistical hypothesis testing[edit] Defining significance in terms of sigma (σ)[edit] Effect size[edit] See also[edit]
Effect size. In statistics, an effect size is a measure of the strength of a phenomenon[1] (for example, the change in an outcome after experimental intervention). An effect size calculated from data is a descriptive statistic that conveys the estimated magnitude of a relationship without making any statement about whether the apparent relationship in the data reflects a true relationship in the population. In that way, effect sizes complement inferential statistics such as p-values. Among other uses, effect size measures play an important role in meta-analysis studies that summarize findings from a specific area of research, and in statistical power analyses. The concept of effect size already appears in everyday language. Overview[edit] Population and sample effect sizes[edit] The term effect size can refer to a statistic calculated from a sample of data, or to a parameter of a hypothetical statistical population.
Being the estimate of the parameter Relationship to test statistics[edit] Types[edit] or. Cohen's d. Cohen's d is an effect size used to indicate the standardised difference between two means. It can be used, for example, to accompany reporting of t-test and ANOVA results. It is also widely used in meta-analysis. Cohen's d is an appropriate effect size for the comparison between two means.
APA style strongly recommends use of ESs. Partial eta-squared covers how much variance in a DV is explained by an IV, but that IV possibly has multiple levels and hence partial eta-squared doesn't explain the size of difference between each of the pairwise mean differences. Cohen's d can be calculated as the difference between the means divided by the pooled SD:: or Cohen's d, etc. is not available in PASW, hence use a calculator such as those listed in external links.
In an ANOVA, you need to be clear about which two means you are interested in knowing about the size of difference between. See also[edit] Cohen's d (Wikipedia) External links[edit] Sample size determination. Sample sizes may be chosen in several different ways: expedience - For example, include those items readily available or convenient to collect. A choice of small sample sizes, though sometimes necessary, can result in wide confidence intervals or risks of errors in statistical hypothesis testing.using a target variance for an estimate to be derived from the sample eventually obtainedusing a target for the power of a statistical test to be applied once the sample is collected.
Introduction[edit] Larger sample sizes generally lead to increased precision when estimating unknown parameters. For example, if we wish to know the proportion of a certain species of fish that is infected with a pathogen, we would generally have a more accurate estimate of this proportion if we sampled and examined 200 rather than 100 fish. In some situations, the increase in accuracy for larger sample sizes is minimal, or even non-existent.
Sample sizes are judged based on the quality of the resulting estimates. . Power analysis. A diagram of differential power analysis. In cryptography, power analysis is a form of side channel attack in which the attacker studies the power consumption of a cryptographic hardware device (such as a smart card, tamper-resistant "black box", or integrated circuit). The attack can non-invasively extract cryptographic keys and other secret information from the device. Simple power analysis (SPA) involves visually interpreting power traces, or graphs of electrical activity over time. Differential power analysis (DPA) is a more advanced form of power analysis which can allow an attacker to compute the intermediate values within cryptographic computations by statistically analyzing data collected from multiple cryptographic operations.
SPA and DPA were introduced in the open cryptologic community in 1998 by Cryptography Research's Paul Kocher, Joshua Jaffe and Benjamin Jun.[1] Simple power analysis[edit] Differential power analysis[edit] High-order differential power analysis[edit] Statistics, Probability, and Survey Sampling. Data. The word data is the traditional plural form of the now-archaic datum, neuter past participle of the Latin dare, "to give", hence "something given".
In discussions of problems in geometry, mathematics, engineering, and so on, the terms givens and data are used interchangeably. This usage is the origin of data as a concept in computer science or data processing: data are accepted numbers, words, images, etc. Data is also increasingly used in humanities (particularly in the growing digital humanities) the highly interpretive nature whereof might oppose the ethos of data as "given". Usage in English[edit] Datum means "an item given". In cartography, geography, nuclear magnetic resonance and technical drawing it often refers to a reference datum wherefrom distances to all other data are measured. Data is most often used as a singular mass noun in educated everyday usage.[11][12] Some major newspapers such as The New York Times use it either in the singular or plural.
See also[edit] Microsoft Excel. Caret. The caret and circumflex are not to be confused with other chevron-shaped characters, such as U+028C ʌ latin letter turned v or U+2227 ∧ logical and, which may occasionally be called carets too.[5][6] Origins[edit] Proofreading mark[edit] The caret was originally used, and continues to be, in handwritten form as a proofreading mark to indicate where a punctuation mark, word, or phrase should be inserted in a document.[7] The term comes from the Latin caret, "it lacks", from carēre, "to lack; to be separated from; to be free from".[8] The caret symbol is written below the line of text for a line-level punctuation mark such as a comma, or above the line as an inverted caret (cf.
U+02C7 ˇ caron) for a higher character such as an apostrophe;[9] the material to be inserted may be placed inside the caret, in the margin, or above the line. Circumflex accent[edit] As regards computer systems, the original 1963 version of the ASCII standard reserved the code point 5Ehex for an up-arrow (↑). Statistician. A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects. Nature of the work[edit] According to the United States Bureau of Labor Statistics, as of 2010, 25,100 jobs were classified as statistician in the United States.[1] Of these people, approximately 30 percent worked for governments (federal, state, or local). Most employment as a statistician requires a minimum of a masters degree in statistics or a related field.
See also[edit] List of statisticians References[edit] External links[edit] Bayesian Statistcs. Bayesian Statistics. Statistics. Data, statistics and graphics. Pearson product-moment correlation coefficient. Data Analysis - Quantitative Analysis - Pearson's Correlation Coefficient, r. Sample, Spaces, Events, Probability. Simple linear regression. Linear regression. Correlation. Pearson product-moment correlation coefficient. Significance Tests for Correlation and Regression. Significance of a Correlation Coefficient. Correlation and dependence. Negative relationship. Intro to Linear Regression. Statistical Tables Calculator. Normal distribution. Standard deviation. Variance. Statistical power. DSS Research: Statistical Power Calculator. Probability. Probability. Student's t-test. Student's t-test. T-Test. Triangle. Index of /Courses. Confidence Intervals. Nearest Neighbourhood. Nearest Neighbour Rule. Darren Barton. Clustering of News Sources. Alexander Gray.
The FASTlab. Spring 08 Course: Computational Data Analysis: Foundations of Machine Learning and Data Mining. Random Experiments, Sample Space and Events. Foundations of Machine Learning. Vector Classification. Bayesian Statistics. INF2B.