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126-426: Although questionnaires are often designed for statistical analysis of the responses, this is not always the case. Questionnaires have advantages over some other types of survey tools in that they are cheap, do not require as much effort from the questioner as verbal or telephone surveys, and often have standardized answers that make it simple to compile data. However, such standardized answers may frustrate users as

252-469: A population , for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics . Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population. Consider independent identically distributed (IID) random variables with

378-432: A state , a country" ) is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data . In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing

504-532: A clear preference. Point scores on each of the dichotomies can vary considerably from person to person, even among those with the same type. However, Isabel Myers considered the direction of the preference (for example, E vs. I) to be more important than the degree of the preference (for example, very clear vs. slight). The expression of a person's psychological type is more than the sum of the four individual preferences. The preferences interact through type dynamics and type development . Myers–Briggs literature uses

630-411: 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

756-418: A decade earlier in 1795. The modern field of statistics emerged in the late 19th and early 20th century in three stages. The first wave, at the turn of the century, was led by the work of Francis Galton and Karl Pearson , who transformed statistics into a rigorous mathematical discipline used for analysis, not just in science, but in industry and politics as well. Galton's contributions included introducing

882-458: A given probability distribution : standard statistical inference and estimation theory defines a random sample as the random vector given by the column vector of these IID variables. The population being examined is described by a probability distribution that may have unknown parameters. A statistic is a random variable that is a function of the random sample, but not a function of unknown parameters . The probability distribution of

1008-484: A given probability of containing the true value is to use a credible interval from Bayesian statistics : this approach depends on a different way of interpreting what is meant by "probability" , that is as a Bayesian probability . In principle confidence intervals can be symmetrical or asymmetrical. An interval can be asymmetrical because it works as lower or upper bound for a parameter (left-sided interval or right sided interval), but it can also be asymmetrical because

1134-454: A given set of rules. Those who prefer feeling tend to come to decisions by associating or empathizing with the situation, looking at it 'from the inside' and weighing the situation to achieve, on balance, the greatest harmony, consensus and fit, considering the needs of the people involved. Thinkers usually have trouble interacting with people who are inconsistent or illogical, and tend to give very direct feedback to others. They are concerned with

1260-471: A given situation and carry the computation, several methods have been proposed: the method of moments , the maximum likelihood method, the least squares method and the more recent method of estimating equations . Interpretation of statistical information can often involve the development of a null hypothesis which is usually (but not necessarily) that no relationship exists among variables or that no change occurred over time. The best illustration for

1386-548: A mathematical discipline only took shape at the very end of the 17th century, particularly in Jacob Bernoulli 's posthumous work Ars Conjectandi . This was the first book where the realm of games of chance and the realm of the probable (which concerned opinion, evidence, and argument) were combined and submitted to mathematical analysis. The method of least squares was first described by Adrien-Marie Legendre in 1805, though Carl Friedrich Gauss presumably made use of it

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1512-1028: 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

1638-499: A novice is the predicament encountered by a criminal trial. The null hypothesis, H 0 , asserts that the defendant is innocent, whereas the alternative hypothesis, H 1 , asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H 0 (status quo) stands in opposition to H 1 and is maintained unless H 1 is supported by evidence "beyond a reasonable doubt". However, "failure to reject H 0 " in this case does not imply innocence, but merely that

1764-404: A population, so results do not fully represent the whole population. Any estimates obtained from the sample only approximate the population value. Confidence intervals allow statisticians to express how closely the sample estimate matches the true value in the whole population. Often they are expressed as 95% confidence intervals. Formally, a 95% confidence interval for a value is a range where, if

1890-412: 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 a census ). This may be organized by governmental statistical institutes. Descriptive statistics can be used to summarize

2016-542: A project of reading biographies and subsequently developed a typology wherein she proposed four temperaments: meditative (or thoughtful), spontaneous , executive , and social . After the publication in 1923 of an English translation of Carl Jung's book Psychological Types (first published in German as Psychologische Typen in 1921), Briggs recognized that Jung's theory resembled, but went far beyond, her own. Briggs's four types were later identified as corresponding to

2142-550: A questionnaire in regards to the order that the questions are asked. The order is as follows: Screens are used as a screening method to find out early whether or not someone should complete the questionnaire. Warm-ups are simple to answer, help capture interest in the survey, and may not even pertain to research objectives. Transition questions are used to make different areas flow well together. Skips include questions similar to "If yes, then answer question 3. If no, then continue to question 5." Difficult questions are towards

2268-497: 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.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location ) seeks to characterize the distribution's central or typical value, while dispersion (or variability ) characterizes

2394-473: A scale or index. Questionnaires with questions that measure separate variables, could, for instance, include questions on: Questionnaires with questions that are aggregated into either a scale or index include for instance questions that measure: Usually, a questionnaire consists of a number of questions ( test items ) that the respondent has to answer in a set format. A distinction is made between open-ended and closed-ended questions. An open-ended question asks

2520-457: A sequence of four cognitive functions (thinking, feeling, sensation, and intuition), each having one of two polar tendencies (extraversion or introversion), giving a total of eight dominant functions. The MBTI is based on these eight hypothetical functions, although with some differences in expression from Jung's model. While the Jungian model proposes the first three dichotomies, Myers and Briggs added

2646-624: A series of category mistakes; it provides, at best, a limited and incomplete account of type related phenomena"; and "type dynamics relies on anecdotal evidence, fails most efficacy tests, and does not fit the empirical facts". His studies gave the clear result that the descriptions and workings of type dynamics do not fit the real behavior of people. He suggests getting completely rid of type dynamics, because it does not help, but hinders understanding of personality. The presumed order of functions 1 to 4 did only occur in one out of 540 test results. The four pairs of preferences or "dichotomies" are shown in

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2772-460: A statistician would use a modified, more structured estimation method (e.g., difference in differences estimation and instrumental variables , among many others) that produce consistent estimators . The basic steps of a statistical experiment are: Experiments on human behavior have special concerns. The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of

2898-637: A test and confidence intervals . Jerzy Neyman in 1934 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

3024-662: A third and a half of the published material on the MBTI has been produced for the special conferences of the Center for the Application of Psychological Type (which provide the training in the MBTI, and are funded by sales of the MBTI) or as papers in the Journal of Psychological Type (which is edited and supported by Myers–Briggs advocates and by sales of the indicator). It has been argued that this reflects

3150-399: A transformation is sensible to contemplate depends on the question one is trying to answer." A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features of a collection of information , while descriptive statistics in the mass noun sense is the process of using and analyzing those statistics. Descriptive statistics

3276-419: A value accurately rejecting the null hypothesis (sometimes referred to as the p-value ). The standard approach is to test a null hypothesis against an alternative hypothesis. A critical region is the set of values of the estimator that leads to refuting the null hypothesis. The probability of type I error is therefore the probability that the estimator belongs to the critical region given that null hypothesis

3402-450: 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

3528-432: Is a question where the testee has to complete a sentence (sentence completion item). In general, questions should flow logically from one to the next. To achieve the best response rates , questions should flow from the least sensitive to the most sensitive, from the factual and behavioural to the attitudinal, and from the more general to the more specific. There typically is a flow that should be followed when constructing

3654-555: Is a self-report questionnaire that makes pseudoscientific claims to categorize individuals into 16 distinct " psychological types " or "personality types". The MBTI was constructed during World War II by Americans Katharine Cook Briggs and her daughter Isabel Briggs Myers , inspired by Swiss psychiatrist Carl Jung 's 1921 book Psychological Types . The test assigns a binary value to each of four categories: introversion or extraversion, sensing or intuition, thinking or feeling, and judging or perceiving. One letter from each category

3780-774: Is a systematic reaction of the respondents to the scale used to formulate the survey question. Thus, the exact formulation of a survey question and its scale is crucial, since they affect the level of measurement error. Further, if the questionnaires are not collected using sound sampling techniques, often the results can be non-representative of the population—as such a good sample is critical to getting representative results based on questionnaires. Questionnaire are of different types as per Paul: 1)Structured Questionnaire. 2)Unstructured Questionnaire. 3)Open ended Questionnaire. 4)Close ended Questionnaire. 5)Mixed Questionnaire. 6)Pictorial Questionnaire. Statistics Statistics (from German : Statistik , orig. "description of

3906-575: Is another type of observational study in which people with and without the outcome of interest (e.g. lung cancer) are invited to participate and their exposure histories are collected. 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

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4032-465: Is appropriate to apply different kinds of statistical methods to data obtained from different kinds of measurement procedures is complicated by issues concerning the transformation of variables and the precise interpretation of research questions. "The relationship between the data and what they describe merely reflects the fact that certain kinds of statistical statements may have truth values which are not invariant under some transformations. Whether or not

4158-834: Is called error term, disturbance or more simply noise. Both linear regression and non-linear regression are addressed in polynomial least squares , which also describes the variance in a prediction of the dependent variable (y axis) as a function of the independent variable (x axis) and the deviations (errors, noise, disturbances) from the estimated (fitted) curve. 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.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems. Most studies only sample part of

4284-459: Is directed outward toward people and objects, whereas the introvert's is directed inward toward concepts and ideas. Contrasting characteristics between extraverted and introverted people include: Jung identified two pairs of psychological functions: According to Jung's typology model, each person uses one of these four functions more dominantly and proficiently than the other three; however, all four functions are used at different times depending on

4410-428: Is distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aims to summarize a sample , rather than use the data to learn about the population that the sample of data is thought to represent. Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution . Inferential statistical analysis infers properties of

4536-403: Is dominant in an individual, a majority of the time. In MBTI theory, the four categories are introversion/extraversion , sensing/intuition, thinking/feeling, and judging/perceiving. According to the MBTI, each person is said to have one preferred quality from each category, producing 16 unique types. The MBTI emphasizes the value of naturally occurring differences. "The underlying assumption of

4662-449: Is especially vocal against MBTI. He called it "the fad that won't die" in a Psychology Today article. Psychometric specialist Robert Hogan wrote: "Most personality psychologists regard the MBTI as little more than an elaborate Chinese fortune cookie ". Nicholas Campion comments that this is "a fascinating example of 'disguised astrology', masquerading as science in order to claim respectability." It has been estimated that between

4788-427: Is generally used in a more conscious and confident way. This dominant function is supported by the secondary (auxiliary) function, and to a lesser degree the tertiary function. The fourth and least conscious function is always the opposite of the dominant function. Myers called this inferior function the "shadow." The four functions operate in conjunction with the attitudes (extraversion and introversion). Each function

4914-486: Is introverted, then the other functions are extraverted and vice versa. The MBTI Manual summarizes Jung's work of balance in psychological type as follows: "There are several references in Jung's writing to the three remaining functions having an opposite attitudinal character. For example, in writing about introverts with thinking dominant ... Jung commented that the counterbalancing functions have an extraverted character." Using

5040-413: Is often considered to be more associated with the unconscious, being most evident in situations such as high stress (sometimes referred to as being "in the grip" of the inferior function). However, the use of type dynamics is disputed: in the conclusion of various studies on the subject of type dynamics, James H. Reynierse writes, "Type dynamics has persistent logical problems and is fundamentally based on

5166-418: 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. A case-control study

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5292-451: Is proposed for the statistical relationship between the two data sets, 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

5418-444: Is recommended in the questionnaire translation process to include subject-matter experts and persons helpful to the process. For example, even when project managers and researchers do not speak the language of the translation, they know the study objectives well and the intent behind the questions, and therefore have a key role in improving questionnaire translation. While questionnaires are inexpensive, quick, and easy to analyze, often

5544-408: Is rejected when it is in fact true, giving a "false positive") and Type II errors (null hypothesis fails to be rejected when it is in fact false, giving a "false negative"). Multiple problems have come to be associated with this framework, ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis. Statistical measurement processes are also prone to error in regards to

5670-630: Is taken to produce a four-letter test result representing one of 16 possible types, such as "INFP" or "ESTJ". The perceived accuracy of test results relies on the Barnum effect , flattery , and confirmation bias , leading participants to personally identify with descriptions that are somewhat desirable, vague, and widely applicable. As a psychometric indicator, the test exhibits significant deficiencies, including poor validity , poor reliability , measuring supposedly dichotomous categories that are not independent , and not being comprehensive. Most of

5796-528: Is that often the people who do return the questionnaire are those who have a very positive or a very negative viewpoint and want their opinion heard. The people who are most likely unbiased either way typically do not respond because it is not worth their time. One key concern with questionnaires is that they may contain quite large measurement errors. These errors can be random or systematic. Random errors are caused by unintended mistakes by respondents, interviewers, and/or coders. Systematic error can occur if there

5922-402: Is true ( statistical significance ) and the probability of type II error is the probability that the estimator does not belong to the critical region given that the alternative hypothesis is true. The statistical power of a test is the probability that it correctly rejects the null hypothesis when the null hypothesis is false. Referring to statistical significance does not necessarily mean that

6048-474: Is used in either an extraverted or introverted way. A person whose dominant function is extraverted intuition, for example, uses intuition very differently from someone whose dominant function is introverted intuition. Myers and Briggs added another dimension to Jung's typological model by identifying that people also have a preference for using either the judging function (thinking or feeling) or their perceiving function (sensing or intuition) when relating to

6174-449: Is widely employed in government, business, and natural and social sciences. The mathematical foundations of statistics developed from discussions concerning games of chance among mathematicians such as Gerolamo Cardano , Blaise Pascal , Pierre de Fermat , and Christiaan Huygens . Although the idea of probability was already examined in ancient and medieval law and philosophy (such as the work of Juan Caramuel ), probability theory as

6300-760: 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 arithmetic . 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. For example, Mosteller and Tukey (1977) distinguished grades, ranks, counted fractions, counts, amounts, and balances. Nelder (1990) described continuous counts, continuous ratios, count ratios, and categorical modes of data. (See also: Chrisman (1998), van den Berg (1991). ) The issue of whether or not it

6426-586: The Educational Testing Service , a private assessment-organization. Under these auspices, the first MBTI "manual" was published, in 1962. The MBTI received further support from Donald W. MacKinnon , head of the Institute of Personality and Social Research at the University of California, Berkeley ; W. Harold Grant, a professor at Michigan State University and Auburn University ; and Mary H. McCaulley of

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6552-590: The IXXXs (Introverts: "meditative"), EXXPs (Extraverts & Prospectors: "spontaneous"), EXTJs (Extraverts, Thinkers & Judgers: "executive") and EXFJs (Extraverts, Feelers & Judgers: "social"). Her first publications were two articles describing Jung's theory, in The New Republic , "Meet Yourself Using the Personality Paint Box" (1926) and "Up From Barbarism" (1928). After extensively studying

6678-474: The NEO-PI factor of neuroticism ). This factor's scales indicate a sense of overall comfort and confidence versus discomfort and anxiety. They also load onto one of the four type-dimensions: Also included is a composite of these called "strain". There are also scales for type-scale consistency and comfort-scale consistency. Reliability of 23 of the 27 TDI subscales is greater than 0.50, "an acceptable result given

6804-449: The University of Florida . The publication of the MBTI was transferred to Consulting Psychologists Press in 1975, and the Center for Applications of Psychological Type was founded as a research laboratory. After Myers' death in May 1980, Mary McCaulley updated the MBTI manual, and the second edition was published in 1985. The third edition appeared in 1998. In 1987, an advanced scoring-system

6930-477: 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

7056-546: The 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 , as well as 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 . Formal discussions on inference date back to

7182-432: The limit to the true value of such parameter. Other desirable properties for estimators include: UMVUE estimators that have the lowest variance for all possible values of the parameter to be estimated (this is usually an easier property to verify than efficiency) and consistent estimators which converges in probability to the true value of such parameter. This still leaves the question of how to obtain estimators in

7308-707: The mathematicians and cryptographers of the Islamic Golden Age between the 8th and 13th centuries. Al-Khalil (717–786) wrote the Book of Cryptographic Messages , which contains one of the first uses of permutations and combinations , to list all possible Arabic words with and without vowels. Al-Kindi 's Manuscript on Deciphering Cryptographic Messages gave a detailed description of how to use frequency analysis to decipher encrypted messages, providing an early example of statistical inference for decoding . Ibn Adlan (1187–1268) later made an important contribution on

7434-464: The 16 four-preference types, one function is the most dominant and is likely to be evident earliest in life. A secondary or auxiliary function typically becomes more evident (differentiated) during teenage years and provides balance to the dominant. In normal development, individuals tend to become more fluent with a third, tertiary function during mid-life, while the fourth, inferior function remains least consciously developed. The inferior function

7560-644: The Educational Testing Service in 1962. It is estimated that 50 million people have taken the Myers-Briggs Type Indicator and that 10,000 businesses, 2,500 colleges and universities, and 200 government agencies in the United States use the MBTI. Briggs began her research into personality in 1917. Upon meeting her future son-in-law, she observed marked differences between his personality and that of other family members. Briggs embarked on

7686-640: The INTP type as an example, the orientation according to Jung would be as follows: Jung's typological model regards psychological type as similar to left or right handedness : people are either born with, or develop, certain preferred ways of perceiving and deciding. The MBTI sorts some of these psychological differences into four opposite pairs, or " dichotomies ", with a resulting 16 possible psychological types. None of these are considered to be "better" or "worse"; however, Briggs and Myers theorized that people innately "prefer" one overall combination of type differences. In

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7812-503: The J indicates that the dominant function is the preferred judging function (extraverted thinking). The ENTJ type introverts the auxiliary perceiving function (introverted intuition). Their tertiary function is sensing and their inferior function is introverted feeling. Conversely, because the INTJ type is introverted, the J instead indicates that the auxiliary function is the preferred judging function (extraverted thinking). The INTJ type introverts

7938-428: The MBTI and Verifying Type Despite its popularity, the MBTI has been widely regarded as pseudoscience by the scientific community. The validity ( statistical validity and test validity ) of the MBTI as a psychometric instrument has been the subject of much criticism. Media reports have called the test "pretty much meaningless", and "one of the worst personality tests in existence". The psychologist Adam Grant

8064-441: The MBTI is that we all have specific preferences in the way we construe our experiences, and these preferences underpin our interests, needs, values , and motivation ." The MBTI Manual states that the indicator "is designed to implement a theory; therefore, the theory must be understood to understand the MBTI". Fundamental to the MBTI is the hypothesis of psychological types as originally developed by Carl Jung. Jung proposed

8190-503: The adjacent table. The terms used for each dichotomy have specific technical meanings relating to the MBTI, which differ from their everyday usage. For example, people who prefer judgment over perception are not necessarily more "judgmental" or less "perceptive", nor does the MBTI instrument measure aptitude ; it simply indicates for one preference over another. Someone reporting a high score for extraversion over introversion cannot be correctly described as more extraverted: they simply have

8316-415: The belief that a knowledge of personality preferences would help women entering the industrial workforce for the first time to identify the sorts of war-time jobs that would be the "most comfortable and effective" for them. The Briggs Myers Type Indicator Handbook , published in 1944, was re-published as "Myers–Briggs Type Indicator" in 1956. Myers' work attracted the attention of Henry Chauncey , head of

8442-598: The brevity of the subscales". In 1989, a scoring system was developed for only the 20 subscales for the original four dichotomies. This was initially known as "Form K" or "the Expanded Analysis Report". This tool is now called the MBTI Step II. Form J or the TDI included the items (derived from Myers' and McCaulley's earlier work) necessary to score what became known as Step III. (The 1998 MBTI Manual reported that

8568-407: The case of intuition, which uses the abbreviation "N" to distinguish it from introversion). For instance: These abbreviations are applied to all 16 types. The interaction of two, three, or four preferences is known as "type dynamics". Although type dynamics has received little or no empirical support to substantiate its viability as a scientific theory , Myers and Briggs asserted that for each of

8694-455: The circumstances. Because each function can manifest in either an extraverted or an introverted attitude, Jung's model includes eight combinations of functions and attitudes, four of which are largely conscious and four unconscious. John Beebe created a model that combines ideas of archetypes and the dialogical self with functions, each function viewed as performing the role of an archetype within an internal dialog. Sensing and intuition are

8820-742: The cognitive functions can operate in the external world of behavior, action, people, and things ("extraverted attitude") or the internal world of ideas and reflection ("introverted attitude"). The MBTI assessment sorts for an overall preference for one or the other. People who prefer extraversion draw energy from action: they tend to act, then reflect, then act further. If they are inactive, their motivation tends to decline. To rebuild their energy, extraverts need breaks from time spent in reflection. Conversely, those who prefer introversion "expend" energy through action: they prefer to reflect, then act, then reflect again. To rebuild their energy, introverts need quiet time alone, away from activity. An extravert's flow

8946-439: The collection, analysis, interpretation or explanation, and presentation of data , or as a branch of mathematics . Some consider statistics to be a distinct mathematical science rather than a branch of mathematics. While many scientific investigations make use of data, statistics is generally concerned with the use of data in the context of uncertainty and decision-making in the face of uncertainty. In applying statistics to

9072-535: 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 and eyelash length among others. Pearson developed the Pearson product-moment correlation coefficient , defined as a product-moment, the method of moments for the fitting of distributions to samples and the Pearson distribution , among many other things. Galton and Pearson founded Biometrika as

9198-538: The concepts of sufficiency , ancillary statistics , Fisher's linear discriminator and Fisher information . He also 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". In his 1930 book The Genetical Theory of Natural Selection , he applied statistics to various biological concepts such as Fisher's principle (which A. W. F. Edwards called "probably

9324-425: The data that they generate. Many of these errors are classified as random (noise) or systematic ( bias ), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems. Statistics is a mathematical body of science that pertains to

9450-423: The data. Thinking and feeling are the decision-making (judging) functions. The thinking and feeling functions are both used to make rational decisions, based on the data received from their information-gathering functions (sensing or intuition). Those who prefer thinking tend to decide things from a more detached standpoint, measuring the decision by what seems reasonable, logical, causal, consistent, and matching

9576-427: The discipline of psychology , and both were self-taught in the field of psychometric testing . Myers therefore apprenticed herself to Edward N. Hay (1891–1958), the head personnel officer for a large Philadelphia bank . From Hay, Myers learned rudimentary test construction , scoring , validation , and statistical methods. Briggs and Myers began creating their indicator during World War II (1939–1945) in

9702-503: The dominant perceiving function (introverted intuition). Their tertiary function is feeling and their inferior function is extraverted sensing. ... a major task in interpretation is to help respondents with less clear reported preferences arrive at a comfortable and accurate assessment of their type. This is accomplished in an interpretation session mainly through an exploration of how type preferences appear in client behaviors. The MBTI Manual, Chapter 6: Interpreting Results of

9828-406: 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. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements with different levels using

9954-576: The end because the respondent is in "response mode." Also, when completing an online questionnaire, the progress bars lets the respondent know that they are almost done so they are more willing to answer more difficult questions. Classification , or demographic question should be at the end because typically they can feel like personal questions which will make respondents uncomfortable and not willing to finish survey. Within social science research and practice, questionnaires are most frequently used to collect quantitative data using multi-item scales with

10080-495: The evidence was insufficient to convict. So the jury does not necessarily accept H 0 but fails to reject H 0 . While one can not "prove" a null hypothesis, one can test how close it is to being true with a power test , which tests for type II errors . What statisticians call an alternative hypothesis is simply a hypothesis that contradicts the null hypothesis. Working from a null hypothesis , two broad categories of error are recognized: Standard deviation refers to

10206-551: The existence of two dichotomous pairs of cognitive functions: Jung believed that for every person, each of the functions is expressed primarily in either an introverted or extraverted form. Based on Jung's original concepts, Briggs and Myers developed their own theory of psychological type, described below, on which the MBTI is based. According to psychologist Hans Eysenck writing in 1995 the 16 personality types used in MBTI are incomplete, as Jung's theory used 32 types, 16 of which could not be measured by questionnaire. Per Eysenck, it

10332-478: The expected value assumes on a given sample (also called prediction). Mean squared error is used for obtaining efficient estimators , a widely used class of estimators. Root mean square error is simply the square root of mean squared error. Many statistical methods seek to minimize the residual sum of squares , and these are called " methods of least squares " in contrast to Least absolute deviations . The latter gives equal weight to small and big errors, while

10458-474: 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

10584-402: The extent to which individual observations in a sample differ from a central value, such as the sample or population mean, while Standard error refers to an estimate of difference between sample mean and population mean. A statistical error is the amount by which an observation differs from its expected value . A residual is the amount an observation differs from the value the estimator of

10710-450: The extent to which members of the distribution depart from its center and each other. Inferences made using mathematical statistics employ the framework of probability theory , which deals with the analysis of random phenomena. A standard statistical procedure involves the collection of data leading to a test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis

10836-432: The first journal of mathematical statistics and biostatistics (then called biometry ), and the latter founded the world's first university statistics department at University College London . The second wave of the 1910s 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

10962-412: The following characteristics: Main modes of questionnaire administration include: Questionnaires are translated from a source language into one or more target languages, such as translating from English into Spanish and German. The process is not a mechanical word placement process. Best practice includes parallel translation, team discussions, and pretesting with real-life people, and is integrated in

11088-402: The former gives more weight to large errors. Residual sum of squares is also differentiable , which provides a handy property for doing regression . Least squares applied to linear regression is called ordinary least squares method and least squares applied to nonlinear regression is called non-linear least squares . Also in a linear regression model the non deterministic part of the model

11214-605: 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,

11340-411: The information-gathering (perceiving) functions. They describe how new information is understood and interpreted. People who prefer sensing are more likely to trust information that is in the present, tangible, and concrete: that is, information that can be understood by the five senses. They tend to distrust hunches, which seem to come "out of nowhere". They prefer to look for details and facts. For them,

11466-532: The judgment-perception preference. The most notable addition of Myers' and Briggs' ideas to Jung's original thought is their concept that a given type's fourth letter (J or P) indicates a person's most preferred extraverted function, which is the dominant function for extraverted types and the auxiliary function for introverted types. Jung hypothesized that the dominant function acts alone in its preferred world: exterior for extraverts and interior for introverts. The remaining three functions, he suggested, operate in

11592-400: The meaning is in the data. On the other hand, those who prefer intuition tend to trust information that is less dependent upon the senses, that can be associated with other information (either remembered or discovered by seeking a wider context or pattern). They may be more interested in future possibilities. For them, the meaning is in the underlying theory and principles which are manifested in

11718-407: The model TRAPD (Translation, Review, Adjudication, Pretest, and Documentation). A theoretical framework is also provided by sociolinguistics , which states that to achieve the equivalent communicative effect as the source language, the translation must be linguistically appropriate while incorporating the social practices and cultural norms of the target language. Besides translators, a team approach

11844-424: The most celebrated argument in evolutionary biology ") and Fisherian runaway , a concept in sexual selection about a positive feedback runaway effect 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 1930s. They introduced the concepts of " Type II " error, power of

11970-417: The opposite orientation. Some MBTI practitioners, however, place doubt on this concept as being a category error with next to no empirical evidence backing it relative to other findings with correlation evidence, yet as a theory it still remains part of Myers' and Briggs' extrapolation of their original theory despite being discounted. Jung's hypothesis can be summarized as: if the dominant cognitive function

12096-420: The outside world (extraversion). They held that types with a preference for judging show the world their preferred judging function (thinking or feeling). Those types who prefer perception show the world their preferred perceiving function (sensing or intuition). According to Myers, judging types like to "have matters settled", while perceptive types prefer to "keep decisions open". So, TJ types tend to appear to

12222-412: The overall result is significant in real world terms. For example, in a large study of a drug it may be shown that the drug has a statistically significant but very small beneficial effect, such that the drug is unlikely to help the patient noticeably. Although in principle the acceptable level of statistical significance may be subject to debate, the significance level is the largest p-value that allows

12348-415: 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

12474-544: 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

12600-548: The possible answers may not accurately represent their desired responses. Questionnaires are also sharply limited by the fact that respondents must be able to read the questions and respond to them. Thus, for some demographic groups conducting a survey by questionnaire may not be concretely feasible. One of the earliest questionnaires was Dean Milles' Questionnaire of 1753. A distinction can be made between questionnaires with questions that measure separate variables, and questionnaires with questions that are aggregated into either

12726-494: 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

12852-466: The publication of Natural and Political Observations upon the Bills of Mortality by John Graunt . Early applications of statistical thinking revolved around the needs of states to base policy on demographic and economic data, hence its stat- etymology . 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

12978-704: The questionnaire can have more problems than benefits. For example, unlike interviews, the people conducting the research may never know if the respondent understood the question that was being asked. Also, because the questions are so specific to what the researchers are asking, the information gained can be minimal. Often, questionnaires such as the Myers-Briggs Type Indicator , give too few options to answer; respondents can answer either option but must choose only one response. Questionnaires also produce very low return rates, whether they are mail or online questionnaires. The other problem associated with return rates

13104-503: The research supporting the MBTI's validity has been produced by the Center for Applications of Psychological Type, an organization run by the Myers–Briggs Foundation, and published in the center's own journal, the Journal of Psychological Type (JPT) , raising questions of independence, bias and conflict of interest . Despite controversies over validity, the instrument has demonstrated widespread influence since its adoption by

13230-444: The respondent to formulate his own answer, whereas a closed-ended question asks the respondent to pick an answer from a given number of options. The response options for a closed-ended question should be exhaustive and mutually exclusive. Four types of response scales for closed-ended questions are distinguished: A respondent's answer to an open-ended question is coded into a response scale afterward. An example of an open-ended question

13356-461: 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 . 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 —for which

13482-434: The same way that writing with the left hand is difficult for a right-hander, so people tend to find using their opposite psychological preferences more difficult, though they can become more proficient (and therefore behaviorally flexible) with practice and development. The 16 types are typically referred to by an abbreviation of four letters – the initial letters of each of their four type preferences (except in

13608-439: The sample data to draw inferences about the population represented while accounting for randomness. These inferences may take the form of answering yes/no questions about the data ( hypothesis testing ), estimating numerical characteristics of the data ( estimation ), describing associations within the data ( correlation ), and modeling relationships within the data (for example, using regression analysis ). Inference can extend to

13734-399: 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 are needed. It uses patterns in

13860-405: 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 that can lessen these issues at the outset of a study, strengthening its capability to discern truths about

13986-412: The sampling and analysis were repeated under the same conditions (yielding a different dataset), the interval would include the true (population) value in 95% of all possible cases. This does not imply that the probability that the true value is in the confidence interval is 95%. From the frequentist perspective, such a claim does not even make sense, as the true value is not a random variable . Either

14112-408: The statistic, though, may have unknown parameters. Consider now a function of the unknown parameter: an estimator is a statistic used to estimate such function. Commonly used estimators include sample mean , unbiased sample variance and sample covariance . A random variable that is a function of the random sample and of the unknown parameter, but whose probability distribution does not depend on

14238-405: The terms extraversion and introversion as Jung first used them. Extraversion means literally outward-turning and introversion, inward-turning. These specific definitions differ somewhat from the popular usage of the words. Extraversion is the spelling used in MBTI publications. The preferences for extraversion and introversion are often called " attitudes ". Briggs and Myers recognized that each of

14364-408: The test to reject the null hypothesis. This test is logically equivalent to saying that the p-value is the probability, assuming the null hypothesis is true, of observing a result at least as extreme as the test statistic . Therefore, the smaller the significance level, the lower the probability of committing type I error. Myers-Briggs Type Indicator The Myers–Briggs Type Indicator ( MBTI )

14490-420: The true value is or is not within the given interval. However, it is true that, before any data are sampled and given a plan for how to construct the confidence interval, the probability is 95% that the yet-to-be-calculated interval will cover the true value: at this point, the limits of the interval are yet-to-be-observed random variables . One approach that does yield an interval that can be interpreted as having

14616-574: The truth and view it as more important. As noted already, people who prefer thinking do not necessarily, in the everyday sense, "think better" than their feeling counterparts, in the common sense; the opposite preference is considered an equally rational way of coming to decisions (and, in any case, the MBTI assessment is a measure of preference, not ability). Similarly, those who prefer feeling do not necessarily have "better" emotional reactions than their thinking counterparts. According to Jung, people use all four cognitive functions. However, one function

14742-534: The two instruments were one and the same ) Step III was developed in a joint project involving the following organizations: the Myers–Briggs Company, the publisher of all the MBTI works; the Center for Applications of Psychological Type (CAPT), which holds all of Myers' and McCaulley's original work; and the MBTI Trust headed by Katharine and Peter Myers. CAPT advertised Step III as addressing type development and

14868-416: The two sided interval is built violating symmetry around the estimate. Sometimes the bounds for a confidence interval are reached asymptotically and these are used to approximate the true bounds. Statistics rarely give a simple Yes/No type answer to the question under analysis. Interpretation often comes down to the level of statistical significance applied to the numbers and often refers to the probability of

14994-485: The unknown parameter is called a pivotal quantity or pivot. Widely used pivots include the z-score , the chi square statistic and Student's t-value . Between two estimators of a given parameter, the one with lower mean squared error is said to be more efficient . Furthermore, an estimator is said to be unbiased if its expected value is equal to the true value of the unknown parameter being estimated, and asymptotically unbiased if its expected value converges at

15120-620: The use of sample size in frequency analysis. Although the term statistic was introduced by the Italian scholar Girolamo Ghilini in 1589 with reference to a collection of facts and information about a state, it was the German Gottfried Achenwall in 1749 who started using the term as a collection of quantitative information, in the modern use for this science. The earliest writing containing statistics in Europe dates back to 1663, with

15246-434: The use of "perception and judgment" by respondents. The MBTI is based on the influential theory of psychological types proposed by Swiss psychiatrist Carl Jung in 1921, which was partially based on the four elements of classical cosmology. Jung speculated that people experience the world using four principal psychological functions— sensation , intuition , feeling , and thinking —and that one of these four functions

15372-619: The work of Jung, Briggs and her daughter extended their interest in human behavior into efforts to turn the theory of psychological types to practical use. Isabel Myers was particularly fascinated by the concept of introversion and she typed herself as an "INFP". However, she felt the book was too complex for the general public, and therefore she tried to organize the Jungian cognitive functions to make it more accessible. Although Myers graduated from Swarthmore College in political science in 1919, neither Myers nor Briggs were formally educated in

15498-454: The world as logical and FJ types as empathetic . SP types tend to appear as concrete and NP types as abstract. The J or P indicates the dominant function for extraverts, whereas for introverts, the J or P indicates their auxiliary function. Introverts tend to show their dominant function outwardly only in matters "important to their inner worlds". For example, because the ENTJ type is extraverted,

15624-462: The world. Fisher's most important publications were his 1918 seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance (which was the first to use the statistical term, variance ), his classic 1925 work Statistical Methods for Research Workers and his 1935 The Design of Experiments , where he developed rigorous design of experiments models. He originated

15750-520: Was developed for the MBTI. From this was developed the Type Differentiation Indicator (TDI), which is a scoring system for the longer MBTI, Form J, which includes the 290 items written by Myers that had survived her previous item analyses. It yields 20 subscales (five under each of the four dichotomous preference scales), plus seven additional subscales for a new "comfort-discomfort" factor (which parallels, though not perfectly measuring,

15876-416: Was unfair to Jung to claim the scale accurately measured Jungian concepts. Both Jung's original model and the simplified MBTI remain hypothetical, with no controlled scientific studies supporting either. Jung did not see the type preferences (such as introversion and extraversion) as dualistic, but rather as tendencies: both are innate and have the potential to balance. Jung's typology theories postulated

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