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We will apply the basic concepts and methods of statistics you ve already learned in the previous statistics course to the real world problems. The course is tailored to meet your needs in the statistical business-data analysis using widely available commercial statistical computer packages such as SAS and SPSS. These tools allow you to construct numerical examples to understand the concepts, and to find their significance for yourself.
By doing this, you will inevitably find yourself asking questions about the data and the method proposed, and you will have the means at your disposal to settle these questions to your own satisfaction. Accordingly, all the applications problems are borrowed from business and economics. By the end of this course you ll be able to think statistically while performing any data analysis. There are two general views of teaching learning statistics Greater and Lesser Statistics.
Greater statistics is everything related to learning from data, from the first planning or collection, to the last presentation or report. Lesser statistics is the body of statistical methodology. This is a Greater Statistics course. There are basically two kinds of statistics courses. The real kind shows you how to make sense out of data. These courses would include all the recent developments and all share a deep respect for data and truth. The imitation kind involves plugging numbers into statistics formulas.
The emphasis is on doing the arithmetic correctly. These courses generally have no interest in data or truth, and the problems are generally arithmetic exercises. If a certain assumption is needed to justify a procedure, they will simply tell you to assume the. are normally distributed -- no matter how unlikely that might be.
It seems like you all are suffering from an overdose of the latter. This course will bring out the joy of statistics in you. Statistics is a science assisting you to make decisions under uncertainties based on some numerical and measurable scales. Decision making process must be based on data neither on personal opinion nor on belief. It is already an accepted fact that Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.
So, let us be ahead of our time. Popular Distributions and Their Typical Applications. Example What is the probability of 7 or more heads in 10 tosses of a fair coin. Comments Can sometimes be approximated by normal or by Poisson distribution. Example Four companies are bidding for each of three contracts, with specified success probabilities. What is the probability that a single company will receive all the orders. Comments Generalization of binomial distribution for ore than 2 outcomes.
What is the probability that a sample of five will yield not more than one defective. Comments May be approximated by binomial distribution when n is small related to N. Example Determination of probability of requiring exactly five tests firings before first success is achieved. Example What is the probability that the third success takes place on the 10th trial.
Negative Binomial. Application Gives probability similar to Poisson distribution when events do not occur at a constant rate and occurrence rate is a random variable that follows a gamma distribution. Example Given a lot with 21 good units and four defective. Example Distribution of number of cavities for a group of dental patients. Comments Generalization of Pascal distribution when s is not an integer.
Many authors do not distinguish between Pascal and negative binomial distributions. Example Used to represent distribution of number of defects in a piece of material, customer arrivals, insurance claims, iq option iniciante telephone calls, alpha particles emitted, and so on. Comments Frequently used as approximation to binomial distribution.
Example Distribution of physical measurements on living organisms, intelligence test scores, product dimensions, average temperatures, and so on. A so-called Generalized Gaussian distribution has the following pdf. exp -B x nwhere A, B, n are constants. Comments Many methods of statistical analysis presume normal distribution. For n 1 and 2 it is Laplacian and Gaussian distribution respectively. This distribution approximates reasonably good data in some image coding application.Continuous Bivariate DistributionsRumsby Sci.
Publications, 1990. Example Distribution of time between re calibrations of instrument that needs re calibration after k uses; time between inventory restocking, time to failure for a system with standby components. Comments Erlangian, exponential, and chi- square distributions are special cases. The Dirichlet is a multidimensional extension of the Beta distribution. Distribution of a product of iid uniform 0, 1 random. Like many problems with products, this becomes a familiar problem when turned into a problem about sums.
If X is uniform for simplicity of notation make it U 0,1Y -log X is exponentially distributed, so the log of the product of X1, X2. Xn is the sum of Y1, Y2. Yn which has a gamma scaled chi-square distribution. Thus, it is a gamma density with shape parameter n and scale 1. Example Distribution of time between arrival of particles at a counter. Also life distribution of complex nonredundant systems, and usage life of some components - in particular, when these are exposed to initial burn-in, and preventive maintenance eliminates parts before wear-out.
Comments Special case of both Weibull and gamma distributions. Application A basic distribution of statistics for variables bounded at both sides - for example x between o and 1. Useful for both theoretical and applied problems in many areas. This site offers information on statistical data analysis. Example Distribution of proportion of population located between lowest and highest value in sample; distribution of daily per cent yield in a manufacturing process; description of elapsed times to task completion PERT.
To generate beta, generate two random values from a gamma, g 1g 2. Comments Uniform, right triangular, and parabolic distributions are special cases. The ratio g 1 g 1 g 2 is distributed like a beta distribution. The beta distribution can also be thought of as the distribution of X1 given X1 X2when X1 and X2 are independent gamma random variables. There is also a relationship between the Beta and Normal distributions. Slash distribution is the distribution of the ratio of a normal random variable to an independent uniform random variable, see Hutchinson T.
The conventional calculation is that given a PERT Beta with highest value as b lowest as a and most likely as m, the equivalent normal distribution has a mean and mode of a 4M b 6 and a standard deviation of b - a 6. 2 of, Introduction to Probability by J. Laurie Snell New York, Random House, 1987 for a link between beta and F distributions with the advantage that tables are easy to find.
Example Used to generate random valued. Comments Special case of beta distribution. The density of geometric mean of n independent uniforms 0,1 is. P X x n x n-1 Log 1 x n n-1 n-1. z L U L - 1-U L L is said to have Tukey s symmetrical l -distribution. In the case where the data are lognormally distributed, the geometric mean acts as a better data descriptor than the mean. The more closely the data follow a lognormal distribution, the closer the geometric mean is to the median, since the log re-expression produces a symmetrical distribution.
Example Distribution of sizes from a breakage process; distribution of income size, inheritances and bank deposits; distribution of various biological phenomena; life distribution of some transistor types. The ratio of two log-normally distributed variables is log-normal. Example Bomb-sighting problems; amplitude of noise envelope when a linear detector is used. Comments Special case of Weibull distribution. Example Distribution of ratio of standardized noise readings; distribution of tan x when x is uniformly distributed.
Applications The most widely applications of Chi-square distribution are Chi-square Test for Association is a non-parametric, therefore can be used for nominal data test of statistical significance widely used bivariate tabular association analysis. Typically, the hypothesis is whether or not two different populations are different enough in some characteristic or aspect of their behavior based on two random samples.
This test procedure is also known as the Pearson chi-square test. Chi-square Goodness-of-fit Test is used to test if an observed distribution conforms to any particular distribution. Calculation of this goodness of fit test is by comparison of observed data with data expected based on the particular distribution. The Weibull distribution is often used to model time until failure.
In this manner, it is applied in actuarial science and in engineering work. It is also an appropriate distribution for describing data corresponding to resonance behavior, such as the variation with energy of the cross section of a nuclear reaction or the variation with velocity of the absorption of radiation in the Mossbauer effect. Iq option iniciante Rayleigh and exponential distribution are special cases. Example Life distribution for some capacitors, ball bearings, relays, and so on.
Extreme value. t distributions. Example Distribution of breaking strength of some materials, capacitor breakdown voltage, gust velocities encountered by airplanes, bacteria extinction times. Note that there are different t distributions, it is a class of distributions. When we speak of a specific t distribution, we have to specify the degrees of freedom. The t density curves are symmetric and bell-shaped like the normal distribution and have their peak at 0.
However, the spread is more than that of the standard normal distribution. The larger the degrees of freedom, the closer the t-density is to the normal density. Why Is Every Thing Priced One Penny Off the Dollar. Yet another motivation Psychologically 9. 99 might look better than 10. 00, but there is a more basic reason too. The assistant has to give you change from your ten dollars, and has to ring the sale up through his her cash register to get at the one cent.
This forces the transaction to go through the books, you get a receipt, and the assistant can t just pocket the 10 him herself. There s sales tax for that. Mind you, there s nothing to stop a particularly untrustworthy employee going into work with a pocketful of cents. For either price at least in the USyou ll have to pay sales tax too. So that solves the problem of opening the cash register.
That, plus the security cameras. There has been some research in marketing theory on the consumer s behavior at particular price points. Essentially, these are tied up with buyer expectations based on prior experience. A critical case study in UK on price pointing of pantyhose tights shown that there were distinct demand peaks at buyer anticipated price points of 59p, 79p, 99p, Ј1. In the UK, for example, prices of wine are usually set at key price points.
Demand at intermediate price points was dramatically below these anticipated points for similar quality goods. The wine retailers also confirm that sales at different prices even a penny or so different does result in dramatically different sales volumes. Other studies showed the opposite where reduced price showed reduced sales volumes, consumers ascribing quality in line with price. Other similar research turns on the behavior of consumers to variations in price. The key issue here is that there is a Just Noticeable Difference JND below which consumers will not act on a price increase.
However, it is not fully tested to determine if sales volume continued to increase with price. This has practical application when increasing charge rates and the like. As an empirical experiment, try overcharging clients by 1, 2. The JND is typically 5 and this provides the opportunity for consultants etc to increase prices above prior rates by less than the JND without customer complaint. 5, 6 and watch the reaction.
Conversely, there is no point in offering a fee reduction of less than 5 as clients will not recognize the concession you have made. Up to 5 there appears to be no negative impact. A Short History of Probability and Statistics. Equally, in periods of price inflation, price rises should be staged so that the individual price rise is kept under 5perhaps by raising prices by 4 twice per year rather than a one off 8 rise.
The birth of statistics occurred in mid-17 th century. A commoner, named John Graunt, who was a native of London, begin reviewing a weekly church publication issued by the local parish clerk that listed the number of births, christenings, and deaths in each parish. These so called Bills of Mortality also listed the causes of death. Graunt who was a shopkeeper organized this data in the forms we call descriptive statistics, which was published as Natural and Political Observation Made upon the Bills of Mortality.
Thus, statistics has to borrow some concepts from sociology, such as the concept of Population. Shortly thereafter, he was elected as a member of Royal Society. It has been argued that since statistics usually involves the study of human behavior, it cannot claim the precision of the physical sciences. Probability has much longer history.
Probability is derived from the verb to probe meaning to find out what is not too easily accessible or understandable. The word proof has the same origin that provides necessary details to understand what is claimed to be true. Probability originated from the study of games of chance and gambling during the sixteenth century. Probability theory was a branch of mathematics studied by Blaise Pascal and Pierre de Fermat in the seventeenth century.
Currently; in 21 st century, probabilistic modeling are used to control the flow of traffic through a highway system, a telephone interchange, or a computer processor; find the genetic makeup of individuals or populations; quality control; insurance; investment; and other sectors of business and industry. Professor Bradley Efron expressed this fact nicely During the 20 th Century statistical thinking and methodology have become the scientific framework for literally dozens of fields including education, agriculture, economics, biology, and medicine, and with increasing influence recently on the hard sciences such as astronomy, geology, and physics.
In other words, we have grown from a small obscure field into a big obscure field. New and ever growing diverse fields of human activities are using statistics; however, it seems that this field itself remains obscure to the public. Further Readings Daston L.Classical Probability in the EnlightenmentPrinceton University Press, 1988.
The book points out that early Enlightenment thinkers could not face uncertainty. A mechanistic, deterministic machine, was the Enlightenment view of the world.Philosophical Theories of ProbabilityRoutledge, 2000. Covers the classical, logical, subjective, frequency, and propensity views.The Emergence of ProbabilityCambridge University Press, London, 1975.
A philosophical study of early ideas about probability, induction and statistical inference.Counting for Something Statistical Principles and PersonalitiesSpringer, New York, 1987. It teaches the principles of applied economic and social statistics in a historical context. Featured topics include public opinion polls, industrial quality control, factor analysis, Bayesian methods, program evaluation, non-parametric and robust methods, and exploratory data analysis.The Rise of Statistical Thinking1820-1900, Princeton University Press, 1986.
The author states that statistics has become known in the twentieth century as the mathematical tool for analyzing experimental and observational data. Enshrined by public policy as the only reliable basis for judgments as the efficacy of medical procedures or the safety of chemicals, and adopted by business for such uses as industrial quality control, it is evidently among the products of science whose influence on public and private life has been most pervasive.
This new field of mathematics found so extensive a domain of applications. Statistical analysis has also come to be seen in many scientific disciplines as indispensable for drawing reliable conclusions from empirical results.The History of Statistics The Measurement of Uncertainty Before 1900U. It covers the people, ideas, and events underlying the birth and development of early statistics.
of Chicago Press, 1990.The Statistical PioneersSchenkman Books, New York, 1984. This work provides the detailed lives and times of theorists whose work continues to shape much of the modern statistics. Different Schools of Thought in Statistics. The Birth Process of a New School of Thought. The process of devising a new school of thought in any field has always taken a natural path. Birth of new schools of thought in statistics is not an exception. Given an already established school, one must work within the defined framework.
A crisis appears, i. The birth process is outlined below.some inconsistencies in the framework result from its own laws. Reluctance to consider the crisis. Try to accommodate and explain the crisis within the existing framework. Conversion of some well-known scientists attracts followers in the new school. The perception of a crisis in statistical community calls forth demands for foundation-strengthens.
After the crisis is over, things may look different and historians of statistics may cast the event as one in a series of steps in building upon a foundation. So we can read histories of statistics, as the story of a pyramid built up layer by layer on a firm base over time. Other schools of thought are emerging to extend and soften the existing theory of probability and statistics. Some softening approaches utilize the concepts and techniques developed in the fuzzy set theory, the theory of possibility, and Dempster-Shafer theory.
The arrows in this figure represent some of the main criticisms among Objective, Frequentist, and Subjective schools of thought. To which school do you belong. The following Figure illustrates the three major schools of thought; namely, the Classical attributed to LaplaceRelative Frequency attributed to Fisherand Bayesian attributed to Savage. Read the conclusion in this figure.
What Type of Statistician Are You. Click on the image to enlarge it. Further Readings Plato, Jan von, Creating Modern ProbabilityCambridge University Press, 1994. This book provides a historical point of view on subjectivist and objectivist probability school of thoughts. Tanur, The Subjectivity of Scientists and the Bayesian ApproachWiley, 2001. Comparing and contrasting the reality of subjectivity in the work of history s great scientists and the modern Bayesian approach to statistical analysis.
Weatherson B.Begging the question and Bayesians, Studies in History and Philosophy of Science30 4687-697, 1999. Bruno de Finetti, in the introduction to his two-volume treatise on Bayesian ideas, clearly states that Probabilities Do not Exist. Bayesian, Frequentist, and Classical Methods. By this he means that probabilities are not located in coins or dice; they are not characteristics of things like mass, density, etc. Some Bayesian approaches consider probability theory as an extension of deductive logic including dialogue logic, interrogative logic, informal logic, and artificial intelligence to handle uncertainty.
It purports to deduce from first principles the uniquely correct way of representing your beliefs about the state of things, and updating them in the light of the evidence. The laws of probability have the same status as the laws of logic. These Bayesian approaches are explicitly subjective in the sense that they deal with the plausibility which a rational agent ought to attach to the propositions he she considers, given his her current state of knowledge and experience. However, the Bayesian is better able to quantify the true uncertainty in his analysis, particularly when substantial prior information is available.
Bayesians are willing to assign probability distribution function s to the population s parameter s while frequentists are not. From a scientist s perspective, there are good grounds to reject Bayesian reasoning. The problem is that Bayesian reasoning deals not with objective, but subjective probabilities.
The result is that any reasoning using a Bayesian approach cannot be publicly checked -- something that makes it, in effect, worthless to science, like non replicative experiments. Bayesian perspectives often shed a helpful light on classical procedures. It is necessary to go into a Bayesian framework to give confidence intervals the probabilistic interpretation which practitioners often want to place on them.
This insight is helpful in drawing attention to the point that another prior distribution would lead to a different iq option iniciante. A Bayesian may cheat by basing the prior distribution on the data; a Frequentist can base the hypothesis to be tested on the data. For example, the role of a protocol in clinical trials is to prevent this from happening by requiring the hypothesis to be specified before the data are collected.
In the same way, a Bayesian could be obliged to specify the prior in a public protocol before beginning a study. In a collective scientific study, this would be somewhat more complex than for Frequentist hypotheses because priors must be personal for coherence to hold. A suitable quantity that has been proposed to measure inferential uncertainty; i.to handle the a priori unexpected, is the likelihood function itself. If you perform a series of identical random experiments e.coin tossesthe underlying probability distribution that maximizes the probability of the outcome you observed is the probability distribution proportional to the results of the experiment.
This has the direct interpretation of telling how relatively well each possible explanation modelwhether obtained from the data or not, predicts the observed data. If the data happen to be extreme atypical in some way, so that the likelihood points to a poor set of models, this will soon be picked up in the next rounds of scientific investigation by the scientific community.
No long run frequency guarantee nor personal opinions are required. There is a sense in which the Bayesian approach is oriented toward making decisions and the frequentist hypothesis testing approach is oriented toward science. For example, there may not be enough evidence to show scientifically that agent X is harmful to human beings, but one may be justified in deciding to avoid it in one s diet.
In almost all cases, a point estimate is a continuous random variable. Therefore, the probability that the probability is any specific point estimate is really zero. This means that in a vacuum of information, we can make no guess about the probability. Even if we have information, we can really only guess at a range for the probability. Therefore, in estimating a parameter of a given population, it is necessary that a point estimate accompanied by some measure of possible error of the estimate.
The widely acceptable approach is that a point estimate must be accompanied by some interval about the estimate with some measure of assurance that this interval contains the true value of the population parameter. For example, the reliability assurance processes in manufacturing industries are based on data driven information for making product-design decisions.
Objective Bayesian There is a clear connection between probability and logic both appear to tell us how we should reason. But how, exactly, are the two concepts related. Objective Bayesians offers one answer to this question. According to objective Bayesians, probability generalizes deductive logic deductive logic tells us which conclusions are certain, given a set of premises, while probability tells us the extent to which one should believe a conclusion, given the premises certain conclusions being awarded full degree of belief.
According to objective Bayesians, the premises objectively i. uniquely determine the degree to which one should believe a conclusion. Further Readings Bernardo J. Smith, Bayesian Theory, Wiley, 2000.Bayesian Statistical Modelling, Wiley, 2001. Williamson, Foundations of BayesianismKluwer Academic Publishers, 2001. Contains Logic, Mathematics, Decision Theory, and Criticisms of Bayesianism.Operational Subjective Statistical MethodsWiley, 1996.
Presents a systematic treatment of subjectivist methods along with a good discussion of the historical and philosophical backgrounds of the major approaches to probability and statistics.Subjective and Objective Bayesian Statistics Principles, Models, and ApplicationsWiley, 2002. Zimmerman H.Fuzzy Set TheoryKluwer Academic Publishers, 1991. Fuzzy logic approaches to probability based on L.
Zadeh and his followers present a difference between possibility theory and probability theory. Rumor, Belief, Opinion, and Fact. As a necessity the human rational strategic thinking has evolved to cope with his her environment. The rational strategic thinking which we call reasoning is another means to make the world calculable, predictable, and more manageable for the utilitarian purposes.
In constructing a model of reality, factual information is therefore needed to initiate any rational strategic thinking in the form of reasoning. However, we should not confuse facts with beliefs, opinions, or rumors. The following table helps to clarify the distinctions. Rumor, Belief, Opinion, and Fact Rumor Belief Opinion Fact One says to oneself I need to use it anyway This is the truth. I m right This is my view This is a fact One says to others It could be true.
You re wrong That is yours I can explain it to you. Beliefs are defined as someone s own understanding. In belief, I am always right and you are wrong. There is nothing that can be done to convince the person that what they believe is wrong. With respect to belief, Henri Poincarй said, Doubt everything or believe everything these are two equally convenient strategies.
With either, we dispense with the need to think. Believing means not wanting to know what is fact. Human beings are most apt to believe what they least understand. Therefore, you may rather have a mind opened by wonder than one closed by belief. The greatest derangement of the mind is to believe in something because one wishes it to be so.
The history of mankind is filled with unsettling normative perspectives reflected in, for example, inquisitions, witch hunts, denunciations, and brainwashing techniques. The sacred beliefs are not only within religion, but also within ideologies, and could even include science. In much the same way many scientists trying to save the theory.
For example, the Freudian treatment is iq option iniciante kind of brainwashing by the therapist where the patient is in a suggestive mood completely and religiously believing in whatever the therapist is making of him her and blaming himself herself in all cases. There is this huge lumbering momentum from the Cold War where thinking is still not appreciated.
Nothing is so firmly believed as that which is least known. The history of humanity is also littered with discarded belief-models. However, this does not mean that someone who didn t understand what was going on invented the model nor had no utility or practical value. The main idea was the cultural values of any wrong model. The falseness of a belief is not necessarily an objection to a belief.
The question is, to what extent is it life-promoting, and life enhancing for the believer. Opinions or feelings are slightly less extreme than beliefs however, they are dogmatic. An opinion means that a person has certain views that they think are right. Also, they know that others are entitled to their own opinions. People respect others opinions and in turn expect the same. In forming one s opinion, the empirical observations are obviously strongly affected by attitude and perception.
However, opinions that are well rooted should grow and change like a healthy tree. Fact is the only instructional material that can be presented in an entirely non-dogmatic way. Everyone has a right to his her own opinion, but no one has a right to be wrong in his her facts. Public opinion is often a sort of religion, with the majority as its prophet.
Moreover, the profit has a short memory and does not provide consistent opinions over time. Rumors and gossip are even weaker than opinion. Now the question is who will believe these. For example, rumors and gossip about a person are those when you hear something you like, about someone you do not. Here is an example you might be familiar with Why is there no Nobel Prize for mathematics. It is the opinion of many that Alfred Nobel caught his wife in an amorous situation with Mittag-Leffler, the foremost Swedish mathematician at the time.
Therefore, Nobel was afraid that if he were to establish a mathematics prize, the first to get it would be M-L. The story persists, no matter how often one repeats the plain fact that Nobel was not married. To understand the difference between feeling and strategic thinkingconsider carefully the following true statement He that thinks himself the happiest man really is so; but he that thinks himself the wisest is generally the greatest fool.
Most people do not ask for facts in making up their decisions. They would rather have one good, soul-satisfying emotion than a dozen facts. This does not mean that you should not feel anything. Notice your feelings. But do not think with them. Facts are different than beliefs, rumors, and opinions. By contrast, at least some non-Bayesian approaches consider probabilities as objective attributes of things or situations which are really out there availability of data. Facts are the basis of decisions.
A fact is something that is right and one can prove to be true based on evidence and logical arguments. Facts are always subject to change. A fact can be used to convince yourself, your friends, and your enemies. Data becomes information when it becomes relevant to your decision problem. Information becomes fact when the data can support it. Fact becomes knowledge when it is used in the successful completion of a structured decision process.
However, a fact becomes an opinion if it allows for different interpretations, i.different perspectives. Note that what happened in the past is fact, not truth. Truth is what we think about, what happened i. Business Statistics is built up with facts, as a house is with stones. But a collection of facts is no more a useful and instrumental science for the manager than a heap of stones is a house. Science and religion are profoundly different. Religion asks us to believe without question, even or especially in the absence of hard evidence.
Indeed, this is essential for having a faith. Science asks us to take nothing on faith, to be wary of our penchant for self-deception, to reject anecdotal evidence. Science considers deep but healthy skepticism a prime feature. One of the reasons for its success is that science has built-in, error-correcting machinery at its very heart. Learn how to approach information critically and discriminate in a principled way between beliefs, opinions, and facts.
Critical thinking is needed to produce well-reasoned representation of reality in your modeling process. Analytical thinking demands clarity, consistency, evidence, and above all, a consecutive, focused-thinking. Further Readings Boudon R.The Origin of Values Sociology and Philosophy of BeliefTransaction Publishers, London, 2001. Castaneda C.The Active Side of InfinityHarperperennial Library, 2000. Wright, Decision Analysis for Management JudgmentWiley, 1998.The Hoax of Freudism A Study of Brainwashing the American Professionals and LaymenPhiladelphia, Dorrance, 1974.Religions in Four Dimensions Existential and Aesthetic, Historical and ComparativeReader s Digest Press, 1976.
What is Statistical Data Analysis. Data are not Information. Vast amounts of statistical information are available in today s global and economic environment because of continual improvements in computer technology. To compete successfully globally, managers and decision makers must be able to understand the information and use it effectively. A Bayesian and a classical statistician analyzing the same data will generally reach the same conclusion.
Jurjevich R. Statistical data analysis provides hands on experience to promote the use of statistical thinking and techniques to apply in order to make educated decisions in the business world. The statistical software package, SPSS, which is used in this course, offers extensive data-handling capabilities and numerous statistical analysis routines that can analyze small to very large data statistics.
Computers play a very important role in statistical data analysis. The computer will assist in the summarization of data, but statistical data analysis focuses on the interpretation of the output to make inferences and predictions. Collecting the data 3. Defining the problem 2. Analyzing the data 4. Defining the Problem. Reporting the results.
An exact definition of the problem is imperative in order to obtain accurate data about it. It is extremely difficult to gather data without a clear definition of the problem. Collecting the Data. We live and work at a time when data collection and statistical computations have become easy almost to the point of triviality. Studying a problem through the use of statistical data analysis usually involves four basic steps. Paradoxically, the design of data collection, never sufficiently emphasized in the statistical data analysis textbook, have been weakened by an apparent belief that extensive computation can make up for any deficiencies in the design of data collection.
One must start with an emphasis on the importance of defining the population about which we are seeking to make inferences, all the requirements of sampling and experimental design must be met. Two important aspects of a statistical study are Population - a set of all the elements of interest in a study Sample - a subset of the population Statistical inference is refer to extending your knowledge obtain from a random sample from a population to the whole population.
Designing ways to collect data is an important job in statistical data analysis. This is known in mathematics as an Inductive Reasoning. That is, knowledge of whole from a particular. Its main application is in hypotheses testing about a given population. The purpose of statistical inference is to obtain information about a population form information contained in a sample. It is just not feasible to test the entire population, so a sample is the only realistic way to obtain data because of the time and cost constraints.
Data can be either quantitative or qualitative. Qualitative data are labels or names used to identify an attribute of each element. For the purpose of statistical data analysis, distinguishing between cross-sectional and time series data is important. Cross-sectional data re data collected at the same or approximately the same point in time. Time series data are data collected over several time periods. Data can be collected from existing sources or obtained through observation and experimental studies designed to obtain new data.
In an experimental study, the variable of interest is identified. Then one or more factors in the study are controlled so that data can be obtained about how the factors influence the variables. Quantitative data are always numeric and indicate either how much or how many. A survey is perhaps the most common type of observational study. Analyzing the Data. Statistical data analysis divides the methods for analyzing data into two categories exploratory methods and confirmatory methods.
Exploratory methods are used to discover what the data seems to be saying by using simple arithmetic and easy-to-draw pictures to summarize data. In observational studies, no attempt is made to control or influence the variables of interest. Confirmatory methods use ideas from probability theory in the attempt to answer specific questions. Probability is important in decision making because it provides a mechanism for measuring, expressing, and analyzing the uncertainties associated with future events.
The majority of the topics addressed in this course fall under this heading. Through inferences, an estimate or test claims about the characteristics of a population can be obtained from a sample. The results may be reported in the form of a table, a graph or a set of percentages. Because only a small collection sample has been examined and not an entire population, the reported results must reflect the uncertainty through the use of probability statements and intervals of values.
To conclude, a critical aspect of managing any organization is planning for the future. Good judgment, intuition, and an awareness of the state of the economy may give a manager a rough idea or feeling of what is likely to happen in the future. Statistical data analysis helps managers forecast and predict future aspects of a business operation. However, converting that feeling into a number that can be used effectively is difficult. The most successful managers and decision makers are the ones who can understand the information and use it effectively.
Data Processing Coding, Typing, and Editing. Coding the iq option iniciante are transferred, if necessary to coded sheets. Typing the data are typed and stored by at least two independent data entry persons. For example, when the Current Population Survey and other monthly surveys were taken using paper questionnaires, the U.
Census Bureau used double key data entry. Editing the data are checked by comparing the two independent typed data. The standard practice for key-entering data from paper questionnaires is to key in all the data twice. Ideally, the second time should be done by a different key entry operator whose job specifically includes verifying mismatches between the original and second entries.
It is believed that this double-key verification method produces a 99. 8 accuracy rate for total keystrokes. Types of error Recording error, typing error, transcription error incorrect copyingInversion e. 45 is typed as 123. 54Repetition when a number is repeatedDeliberate error. Type of Data and Levels of Measurement. Qualitative data, such as eye color of a group of individuals, is not computable by arithmetic relations. They are labels that advise in which category or class an individual, object, or process fall.
They are called categorical variables. Quantitative data sets consist of measures that take numerical values for which descriptions such as means and standard deviations are meaningful. They can be put into an order and further divided into two groups discrete data or continuous data. Discrete data are countable data, for example, the number of defective items produced during a day s production.
For example, measuring the height of a person. The first activity in statistics is to measure or count. Continuous data, when the parameters variables are measurable, are expressed on a continuous scale. Measurement counting theory is concerned with the connection between data and reality. A set of data is a representation i.a model of the reality based on a numerical and mensurable scales. Data are called primary type data if the analyst has been involved in collecting the data relevant to his her investigation.
Otherwise, it is called secondary type data. Data come in the forms of Nominal, Ordinal, Interval and Ratio remember the French word NOIR for color black. Data can be either continuous or discrete. While the unit of measurement is arbitrary in Ratio scale, its zero point is a natural attribute. Both zero and unit of measurements are arbitrary in the Interval scale. The categorical variable is measured on an ordinal or nominal scale. Measurement theory is concerned with the connection between data and reality.
Both statistical theory and measurement theory are necessary to make inferences about reality.
Coments:30.03.2020 : 19:54 Vizuru:
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Integration of multi-format and multi-type data from heterogeneous databases. Information and knowledge visualization techniques for biological systems.
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29.03.2020 : 12:02 Gozshura:
The war on drugs was iq option iniciante about the drugs it was a way to create an excuse to attack people whose ideology was suspect. The poor, the pigmented, the anti-war activist, the politically active young folk.
27.03.2020 : 02:21 Zulubei:
I ve managed to get the XP64 drivers working in W7 by disabling driver signing. I tried the NGOHQ iq option iniciante first, and that seemed to work okay.