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Uses of statistics.... More...
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Paper Abstract:
Uses of statistics. Collecting, organization, analyzing and presenting data. Two basic types of data: categorical and Quantitative. Various approaches to organizing data and approaches to other tasks. Averages and variations. Theory of probability. Normal and Binomial distribution. Sampling distribution. Estimation. Hypothesis testing. Chi Square & ANOVA. Regression and correlation. Non-paramatric statistics.
Paper Introduction:
INTRODUCTION TO STATISTICS
Introduction
The term “statistics” to many (perhaps most) people implies a collection of numerical data about a topic. The extent to which most people have confidence in the validity of such a collection of data depends upon the topic, the source of the data, and the extent to which they think the data are measurable. As an example, most people are more likely to accept the accuracy of major league baseball statistics than are likely to express confidence in the accuracy of the failure rate of Firestone tires on Ford Explorers.
The term “statistics” to a smaller proportion of the population refers to the processes of collecting, organizing, analyzing, and presenting data is forms usable for policy analysis, decision-m
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If several values share the greatest frequency of occurrence,each of them is a mode (Summers, Peters, & Armstrong, 2 ). This theorem isthe main justification for the widespread use of confidence intervals basedon the normal distribution and for t tests when estimating the mean andcomparing two means by the Polk Company. The Polk Company makes estimates of population parameters in relationto the various populations sampled. From such data,determinations could be made that the mean (average) age in the censustract was 37.24; that the median age was 37; and that the mode was 4 .|Table 1 - Date of Birth || | |Frequen|Percent|Valid |Cumulative|| | |cy | |Percent|Percent | ||Valid |1944 |1 |2. Asan example, the standard error of the mean is the standard deviation of thesample means. The test statistic is based on the ranks of the absolutevalues of the differences between the two variables (Pfaffenberger &Patterson, 1997). | || |1977 |1 |2. |2. The standard erroris a measure of how much the value of a test statistic varies from sampleto sample. Convergers tend to rely most heavily on the AC and AE learning modesin the application of the type 3 learning style. The cross-tabulation wouldestablish the frequency of men and women in each compensation category.The distribution of men and women in each compensation category would beexpected to be proportionately the same. | || |1974 |2 |4. Kolb, D. The test takes into accountinformation about the magnitude of differences within pairs and gives moreweight to pairs that show large differences than to pairs that show smalldifferences. Type 3 learners would develop theoretical models designed to attainthe objectives, and then experiment with those models to determine modelbest attained the objectives. Convergers are best atfocusing on specific problems, which are best solved by a single bestanswer. |6 . It is the SD of the sampling distribution for a statistic. Tossing a fair 1 times and counting the number of heads gives a valuefrom a binomial distribution with 1 trials and p = 1/2. The CumulativeBinomial distribution represents the probability that an event having aprobability p of occurring in a single trial will occur n or fewer (lowertail) or n or more (upper tail) times in m independent trials. In fact, the correlation coefficients areoften used in conjunction with the regression coefficients in predictiveanalysis. Elementary Probability Theory The theory of probability is the science of making decisions based onincomplete information. The distribution is uniquely determined by thevalues of N and p (Pfaffenberger & Patterson, 1997). Both the dependent and the independent variables are measured asfrequencies. Type 3 learners wouldapproach the task by developing theoretical models upon which to basehypotheses, and then experiment with alternative hypotheses to determinehow best to achieve analytical objectives. With imaginative capacity asa major strength, the diverger is able to reflect on concrete experiencesfrom a variety of perspectives. Rolling a die 1 times and counting the number of times it comes up six gives a value from abinomial distribution with 1 trials and p = 1/6 (Pfaffenberger &Patterson, 1997). |2. The Normal distribution is the mostcommonly used distribution for modeling experimental data. The learner types are divergers, assimilators, convergers, andaccommodators. C., & Patterson, J. | || |Total |5 |1 . Regression analysis is seldom used by the Polk Company. Type 4 learners would accept the data available,assess the data without bias, and then experiment with those models todetermine the best way to assess the estimated parameters. Divergers are typically idea, orbrainstorming, people, who are interested in people, and who have a broadrange of cultural interests (Kolb, 1989). | || |1955 |2 |4. |44. Type 4 learners would reviewavailable data without bias, and then experiment with alternativehypotheses to determine how best to achieve analytical objectives. VII. | || |1954 |2 |4. The term "statistics" to a smaller proportion of the population refersto the processes of collecting, organizing, analyzing, and presenting datais forms usable for policy analysis, decision-making, and other importanttasks confronting people and organizations in contemporary society. Data may be organized tofacilitate specific analytical objectives, or data may be organized to makeit easily accessible to a variety of users with divergent analyticalobjectives. Basic statistical concepts. The test requires an ordinal level of measurement."U" is the number of times a value in the first group precedes a value inthe second group, when values are sorted in ascending order (Pfaffenberger& Patterson, 1997). I. The Normaldistribution is a limiting case of the Binomial distribution when n, thenumber of trials, becomes very large and p does not differ by substantiallyfrom .5. The Chi-Square Test computes a chi-square statistic based onthe distributions in the cross-tabulation table. introduction to statistics Introduction The term "statistics" to many (perhaps most) people implies acollection of numerical data about a topic. Therefore, the central limit theorem assumes a high-level ofimportance in hypothesis testing (Pfaffenberger & Patterson, 1997). The choice among these techniques depends inpart on the focus of the statistical analysis-dependence or independence.Multivariate tests of dependence include multiple regression, discriminateanalysis, canonical analysis, multiple classification analysis, automaticinteraction detection, and multivariate analysis of variance. The Polk Company works with data models incorporating differentdistribution curves. Approaching a task involving the consideration of data distributions,the Type 1 learner would accept the data available, assess the data withoutbias, and study and consider the data from a variety of perspectives indetermining which distribution curve is most appropriate for use inanalysis. & Armstrong, C. The ANOVAprocedures is not widely used by the Polk Company. The test makes no assumptions about the shapes ofthe distributions of the two variables. IV. The Polk Company applies all of the above concepts in theorganization, analysis, and presentation of data. |2. Type 2 learners would approach the task by developingtheoretical models upon which to base hypotheses, and then study andconsider the data from a variety of perspectives in which model bestsupports the development of workable hypotheses. The median is the valueabove and below which half the cases in a data set fall, i.e., the 5 thpercentile. The probability statistic is a number expressing thelikelihood of occurrence of a specific event. |24. The Spearman Correlation is a non-parametric version of the Pearsoncorrelation coefficient. TheCentral Limit Theorem states that, for a random sample of observations fromany distribution with a finite mean and a finite variance, the average willtend to follow a normal distribution for large samples. |2. As stated above, within a data set, each data element deviates fromthe value of the mean by an amount equal to the difference between thevalue of the data element and the value of the data mean. Sample sizes are designed to provide confidence in thesample at a specified level of statistical significance, which is astatement of probability or sampling error. |2. If an advertising manager wanted to test the effectiveness of threedifferent proposed advertising campaigns, the three different approachescould be tries in three different test markets with similar populations.The sales generated on each of 2 days of a test period then could becompared through the application of analysis of variance procedures.Analysis of variance could provide the advertising manager with adetermination of the statistical significance of any differences in thesales generated by the three proposed advertising campaigns. Type 2 learnerswould approach the task by developing theoretical models upon which to basethe assessment of the appropriateness of competing statistical procedures,and then study and consider the data from a variety of perspectives indetermining which statistical procedures were most appropriate forapplication in the specific case at hand. The extent to which mostpeople have confidence in the validity of such a collection of data dependsupon the topic, the source of the data, and the extent to which they thinkthe data are measurable. |4. The Polk Company applies random selection procedures in an effort toassure that sample data are representative of the populations from whichthey are drawn. The data for the dependent variables in an analysis of variance mustbe interval or ratio in character. | || |1968 |2 |4. |1 . |12. The test is more powerful than the t-test, because isrelies on ranks as opposed to means. |2. Type 3 learnerswould approach the task by developing theoretical models upon which to basethe assessment of the appropriateness of competing statistical procedures,and then experiment with those models to determine the most appropriatestatistical procedure for the task at hand. Polk Company employees also must be able todetermine how problems must be approached and then develop effective anefficient strategies to solve those problems. P. Probability theory is applied in those situationswherein it is impossible to gather enough information to be absolutelycertain about outcomes. If there is an even number of cases, the median is the averageof the two middle cases when they are sorted in ascending or descendingorder. Type 2 learners would develop theoretical models upon which toaccount for data distribution, and then study and consider the data from avariety of perspectives in determining distribution curve is mostappropriate. In most instances where inferentialstatistics are applied in hypothesis testing, population distributions areunknown. |6. | || |1958 |2 |4. The Polk Company works with data models incorporating differentprobability distribution curves. (1989). Data may be organized in several ways. The Mann-Whitney U test is non-parametric equivalent to the t test.The Mann-Whitney U tests whether two independent samples are from the samepopulation. |16. |4. The standard deviation (SD)is a measure of dispersion around the mean in a data set. As an example, assume that an analytical objective was toknow if significant differences in compensation existed between men andwomen in a specific metropolitan area or in a specific job market. | || |196 |4 |8. Values of the coefficient range from -1 to +1. H. Assimilators tend to rely most heavily on the AC and RO learning modesin the application of the Type 2 learning style. The Polk Company organizes vast arrays of disparate data. |6. The variance forthe data set is the sum of these individual variances. Other than the cross-tabulation chi square procedure, non-parametricstatistical procedures are seldom used at the Polk Company. A point estimator is a formula or expression producing a singlevalue estimate of a population parameter. II. The mode is the most frequently occurring value in adata set. The experiential modes of learning are concrete experience(CE), reflective observation (RO), abstract conceptualization (AC), andactive experimentation (AE). Type 3 learners develop theoretical models uponwhich to base evaluations of the reliability and validity the data, andthen experiment with those models to determine the best way to assess theestimated parameters. As an example, one cancategorize human beings by eye color. |4. | || |1965 |2 |4. As an example, the acceptance of a null hypothesis(or the inability to reject a null hypothesis) in statistical inferenceanalysis which indicated that the sales level for a product will be belowthe breakeven point for that product would, also, typically be associatedwith a decision not to market the product. |96. Basicstatistics in business and economics. The Mann-Whitney test may be used with sample groups that aredissimilar in size. Type 4 learners would assess the data aspresented, and then experiment with those models to determine model bestattained the objectives. Type 4learners would approach the task of organizing data by accepting the dataavailable, assessing the data without bias, and then experiment with thosemodels to determine which distribution model of most appropriate. | || |1971 |3 |6. |6. Type 3 learners tend to apply a combination of the AC and AE learningmodes. Type 4 learnerswould approach the task of organizing data by accepting the data available,assessing the data without bias, and then experiment with those models todetermine which distribution model of most appropriate. When the Normal distribution is used as an approximation to theBinomial distribution there is a correction term that may be applied whenthese conditions are not strictly met. A strength of regression analysis is that a causal relationship may beestablished between dependent and independent variable. Thus,hypothesis testing is applied to sample data in inferential statisticalapplications (Pfaffenberger & Patterson, 1997). The company's databases hold informationon more than 1 million households in the United States and geographicdata covering 12 million addressed streets in the country. The interval levelrequirement for measurement of the dependent variable means that anequality of interval exists between the points on the scale with which thevariable is measured. | || |1975 |3 |6. The PolkCompany operates across the United States and in several Europeancountries. Type 1 learners, when applying chi square or ANOVA procedures to thepursuit of analytical objectives, would accept the data available, assessthe data without bias, and study and consider the data from a variety ofperspectives in determining which statistical procedures were mostappropriate for application in the specific case at hand. (1997). | || |197 |2 |4. New York:Macmillan Publishing Company. The CE learning mode implies that an individual is able to becomefully and openly involved, without bias, in new experiences, while the ROlearning mode implies that the individual is capable of observing andreflecting upon such experiences from a multiplicity of perspectives, andthe AC learning mode implies that an individual can create concepts whichintegrate their observations into logical and sound theories. | || |1956 |1 |2. If variations occurred, however,the chi-square test could determine if these variations were statisticallysignificant or just mathematical accidents. |3 . Bivariate correlation analysis, however, goes further than doesregression analysis. The independent variables in ananalysis of variance are nominal in character. Categorical and quantitative data may be combined inanalyses and presentations to provide greater insight into phenomena orproblems, or to provide stronger based for decision-making. |4. | | | III. |2. Normal Distribution Normal distribution is defined mathematically. |52. Conclusion A wide variety of statistical procedures are available to a firm suchas the Polk Company. The Modelposits that people may be categorized into four types of learners who learnthrough four experiential modes of learning. The Binomial distribution represents theprobability that an event having a probability p of occurring in a singletrial will occur exactly n times in m independent trials. The probability of the occurrence ofspecific distributions is used to determine the statistical significance ofdata analyses. |1 . Non-Parametric Statistics There are many non-parametric statistical procedures. Regression and Correlation A major difference between the analysis of variance procedure andregression analysis is that, in analysis of variance, the emphasis is onanalysis of the variations in the independent variable, as opposed to thejoint interaction of the variations in dependent and independent variables. An interval estimator provides aconfidence interval estimate of the reliability of an estimated populationparameter. Approaching the task of organizing data, thus, a Type 3 learnerwould develop theoretical models upon which to base the organization of thedata, and then experiment with those models to determine the best way tocomplete the organizing task. This goodness-of-fit testcompares the observed and expected frequencies in each category to testeither that all categories contain the same proportion of values or thateach category contains values specified in a null hypothesis (Summers,Peters, & Armstrong, 2 ). |4. | || |1978 |1 |2. Homewood, Illinois: Richard D. Correlationanalysis is used somewhat more than regression analysis by the company.Neither approach, however, is used to the extent that chi square analysisis used. |4. |2. Approaching a task involving the determination and application ofaverage and variations, the Type 1 learner would assess the data aspresented, and then would consider the results from a variety ofperspectives to weigh their validity within the context of the objective.Type 2 learners would develop theoretical models designed to attain theobjectives, and then would consider the results from a variety ofperspectives to weight their validity within the context of the objectives. The Type 1 learner, when estimating population parameters, wouldaccept the data available, assess the data without bias, and study andconsider the data from a variety of perspectives in determining how best toevaluate the reliability and validity of the parameter. Englewood Cliffs, New Jersey: Prentice-Hall, Inc. Thus, if the mean in a data set is 45with a standard deviation of 1 , 95 percent of the cases would be between25 and 65 in a normal distribution (Summers, Peters, & Armstrong, 2 ). | || |1951 |1 |2. Probability theory is applied in statistically analysis in relation tothe distribution of values in data sets. The coefficient ofvariation relates a measure of dispersion to its average deviation andconverts the relationship to a percentage. In other words, an attempt ismade to explain the movement in a dependent variable through the analysisof movements in independent, or explanatory, variables. |66. The Spearman Correlation is based on the ranks ofthe data rather than the actual values. Approaching the taskof organizing data, therefore, the Type 1 learner would accept the dataavailable, assess the data without bias, and study and consider the datafrom a variety of perspectives in determining how best to organize it.Type 2 learners, who tend to apply a combination of the AC and RO learningmodes, would approach the task of organizing data by developing theoreticalmodels upon which to base the organization of the data, and then study andconsider the data from a variety of perspectives in determining how best tocomplete its organization. |54. The test is appropriate forordinal data, or for interval data that do not satisfy the normalityassumption. It is with respect to samples and their characteristics, and their usein hypothesis testing, that the central theorem and central tendencymeasures are important. Hypothesis testing falls in the realm of inferential statistics.The basic theoretical principle upon which inferential statistics are basedis probability. Correlation analysis is quite similar to regression analysis in majorportions of the calculations. As an example, most people are more likely toaccept the accuracy of major league baseball statistics than are likely toexpress confidence in the accuracy of the failure rate of Firestone tireson Ford Explorers. Type 2learners would approach the task by developing theoretical models uponwhich to base the assessment of the appropriateness of competingstatistical procedures, and then study and consider the data from a varietyof perspectives in determining which statistical procedures were mostappropriate for application in the specific case at hand. The coefficient of variation isdetermined by dividing the SD of a data set by the mean (average) deviationof the data set (Summers, Peters, & Armstrong, 2 ). Binomial distribution curves may be skewed to eitherthe right or the left of the normal distribution. The number of persons in each eyecolor category can be determined; however, such data cannot be used todetermine an average eye color. Pfaffenberger, R. The concept of experiential learning is best understood within thecontext of the Kolb (1989) Model of Experiential Learning. Frequency in the cross-tabulation table means how many casesare defined at the intersection (cell) of a category of the dependentvariable and a category of the independent variable (Summers, Peters, &Armstrong, 2 ). IX. |2. Type 2 learnersdevelop theoretical models upon which to base evaluations of thereliability and validity the data, and then study and consider the datafrom a variety of perspectives in determining how best to assess estimatedpopulation parameters. |82. The chi-square test could notbe used to state, however, that compensation was higher for one gender oranother because of a person's gender. It is more powerful than the median test since it uses theranks of the cases. Multivariatetests of independence include multidimensional scaling, latent structureanalysis, latent class analysis, cluster analysis, and two variants offactor analysis. Type 4 learners would acceptthe data available, assess the data without bias, and then experiment withthose models to determine the most appropriate statistical procedure forthe task at hand. (5th ed.). Type 1 learners, when applying regression or correlation procedures tothe pursuit of analytical objectives, would accept the data available,assess the data without bias, and study and consider the data from avariety of perspectives in determining which statistical procedures weremost appropriate for application in the specific case at hand. The company almost exclusively reliesin interval estimators to produce confidence interval estimates. In the normaldistribution, 5 percent of the cases fall within .6745 SD on either sideof the data mean, 68.26 percent of cases fall within one SD on either sideof the data mean, 95 percent of the cases fall within 1.96 SD on eitherside of the data mean, 99 percent of the cases fall within 2.58 SD oneither side of the data mean, and 99.73 percent of the cases fall withinthree SD on either side of the data mean (Bartz, 1998). Type 1 learners tend toapply a combination of the CE and RO learning modes. The Wilcoxen Signed-Ranks Test is a non-parametric procedure used withtwo related variables to test the hypothesis that the two variables havethe same distribution. The median is a measure of central tendency not sensitive tooutlying values, unlike the mean, which can be affected by a few extremelyhigh or low values. In this latter context, theyare required to apply to concepts of experiential learning. Quantitative data (further subdivided as interval and ratio) are datarelated to entities or phenomena that can be identified by numbers. VIII. |4. Date of birth data for aspecific census tract, as an example, might be organized as illustrated inTable 1, which may be found below on this page. With respect to multivariate procedures, a wide variety isavailable to the researcher. In is within the framework of the second perception of statisticsdiscussed above that commercial organizations such as the Polk Companybased in Southfield, Michigan collect, organize, analyze, and provide datato a wide variety of users and on equally wide variety of topics,activities, and phenomena. |86. Type 1 learners, when working with hypotheses, tend to reviewavailable data without bias and study and consider the data from a varietyof perspectives to develop workable hypotheses related to analyticalobjectives. Variables must be interval (Summers, Peters, & Armstrong,2 ). Organizing Data The two basic types of data are categorical and quantitative.Categorical data (frequently referred to as qualitative, and furthersubdivided as nominal or ordinal) are data related to entities or phenomenathat cannot be readily identified with numbers. Type 3 learnerswould approach the task by developing theoretical models upon which to basethe assessment of the appropriateness of competing statistical procedures,and then experiment with those models to determine the most appropriatestatistical procedure for the task at hand. The Polk Company works with data models incorporating differentdistribution curves. Type 4 learners would acceptthe data available, assess the data without bias, and then experiment withthose models to determine the most appropriate statistical procedure forthe task at hand. | || |1953 |2 |4. Correlation analysis provides a single number thatsummarizes the relationship between two variables. |2. Organizational psychology: An experimental approach.(3rd ed.). An illustration of thebinomial distribution curve variations and the normal distribution curve ispresented in Figure 2, which may be found below on this page.Figure 2 - Binomial Distribution Curve Variations & the Normal Distribution Curve[pic] VI. The principal techniques of statistical inference are intervalestimation and hypothesis testing. |72. For use in inferentialstatistics, this probability statistic must be statistically independent.In inferential statistical applications, probability is largely a functionof sampling, as well as of relationships, because it is usually notfeasible, or even possible, to measure an entire population. Hypothesis Testing Inference is among the most important of the uses made of quantitativemethods. The people who work at the Polk Company, such as the author of thispaper, are required to apply more than simply knowledge of valid andreliable data collection and statistical analysis procedures in thedischarge of their duties. Irwin,Inc. The central limit theorem holds that the totals(and therefore the means) of random samples will be normally distributed nomatter what the distribution in the population is like, provided only thatthe samples are large enough. Statistical methodsfor business ad economics. |84. As anexample, one can categorize human beings by age. Multivariate analysis procedures include those techniques that focuson the structure of simultaneous relationships among three or morevariables. Averages and Variations The mean is the average value of a data set. |2. A Type 3 learner would develop theoretical models uponwhich to account for data distribution, and then experiment with thosemodels to determine which distribution model of most appropriate. Type 2 learners would develop theoretical models uponwhich to account for data distribution, and then study and consider thedata from a variety of perspectives in determining distribution curve ismost appropriate. Analysis of variance is a statistical technique that assesses theeffects of one or more categorical independent variables (factors),measured at any level upon a continuous dependent variable that usually isassumed to be measured at an interval level. (5th ed.). (1998). Adaptation is a major characteristic of theaccommodators' behavior, and, while accommodators tend to like people, theyalso tend to be impatient with them (Kolb, 1989). The Polk Company uses cross-tabulation chi-square testing to determineif significant differences are present in a specified characteristic insample groups in relation to the frequency of occurrence of the specifiedcharacteristic. |7 . Theextent to this smaller proportion of the population have confidence in thevalidity of such organized and analyzed collections of data tend to dependupon the integrity and reliability of the data collection process, theappropriateness and validity of the analytical processes, and the qualityof the output of these processes. Assimilators are typically more interested in abstractconcepts than they are in people, and they tend to be less interested inthe practical usefulness of a theoretical model than they are with itsconceptual validity (Kolb, 1989). Approaching a task involving the consideration of data distributions,the Type 1 learner would accept the data that were available, assess thedata without bias, and study and consider the data from a variety ofperspectives in determining which distribution curve is most appropriatefor use in analysis. A Type 3 learner would developtheoretical models upon which to account for data distribution, and thenexperiment with those models to determine which distribution model of mostappropriate. Type 4 learners would accept the dataavailable, assess the data without bias, and then experiment with thosemodels to determine the most appropriate statistical procedure for the taskat hand. |4. Within a data set, each data element deviates (varies) from the valueof the mean by an amount equal to the difference between the value of thedata element and the value of the data mean. (2 ). |4. The range of probability statednumerically is from zero ( ) to one (1), which means that the range ofprobability is from no chance to 1 percent certain (Bartz, 1998). S. | || |1972 |1 |2. If an educator had two sets of scores on a standardized test, thescores could be subjected to analysis by the Mann-Whitney test to determineif the subjects in the two groups were from the same population (or fromtwo populations with the same characteristics) or from differentpopulations. Type 1 learners, when applying non-parametric statistical proceduresto the pursuit of analytical objectives, would accept the data available,assess the data without bias, and study and consider the data from avariety of perspectives in determining which statistical procedures weremost appropriate for application in the specific case at hand. Correlation analysis can provide a powerful measure of the degree ofassociation between two variables. XI. |26. Type 4 learners would approach the task of organizing data byaccepting the data available, assessing the data without bias, and thenexperiment with those models to determine which distribution model of mostappropriate. The potential for a researcherto be misled by a non-experimental data set, thus, is high (Summers,Peters, & Armstrong, 2 ). Type 2 learners would develop theoreticalmodels upon which to account for data distribution, and then study andconsider the data from a variety of perspectives in determiningdistribution curve is most appropriate. An example of the normal distribution curve ispresented in Figure 1, which may be found below on this page.Figure 1 - Normal Distribution curve[pic] V. |8. Analysis of variance is measured by the F Test(Summers, Peters, & Armstrong, 2 ). Type 2learners would approach the task by developing theoretical models uponwhich to base the assessment of the appropriateness of competingstatistical procedures, and then study and consider the data from a varietyof perspectives in determining which statistical procedures were mostappropriate for application in the specific case at hand. |2 . |34. The remainder ofthis study considers the application at the Polk Company of 11 tasksassociated with the processes of collecting, organizing, analyzing, andpresenting data. Genderwould be the independent variable in a chi-square test, and the categoriesof the independent variable would be men and women. Accommodators tend to rely most heavily on the CE and AE learningmodes in the application of the Type 4 learning style. | || |1963 |2 |4. The Type 1 learner, when working with sampling distributions, wouldaccept the data available, assess the data without bias, and study andconsider the data from a variety of perspectives in determining how best toevaluate the reliability and validity of the data. |4. | || |1964 |1 |2. W., Peters, W. |6. Data may be organized to emphasize specific issues in itspresentation, or data may be organized to present a broad picture in apresentation. X. A probability variable is an algebraic statementthat expresses a degree of confidence in the existence of something or inthe truth of some statement or concept. Binomial Distribution The binomial distribution is the discrete distribution of the numberof events (successes) in N independent trials with the probability ofsuccess p in each trial. At the Polk Company, hypotheses are tested in their null forms. |4. E. Internal estimators are used more frequently than are pointestimators. A Type 3 learner would develop theoretical models upon whichto account for data distribution, and then experiment with those models todetermine which distribution model of most appropriate. This single numberexpresses the strength of the relationship between the variables.Variables must be interval in character (Summers, Peters, & Armstrong,2 ). In each instance, the data management or statisticalanalysis function is defined, the learning process is explained within thecontext of the Kolb Model, and an illustration of the application of thedata management or statistical analysis function is presented. Convergers tend to prefer things to people, and to focus on arelatively narrow range of technical interests (Kolb, 1989). Type 2 learners developtheoretical models upon which to base evaluations of the reliability andvalidity the data, and then study and consider the data from a variety ofperspectives in determining how best to assess the sampling distributions.Type 3 learners develop theoretical models upon which to base evaluationsof the reliability and validity the data, and then experiment with thosemodels to determine the best way to assess the sampling distributions.Type 4 learners would accept the data available, assess the data withoutbias, and then experiment with those models to determine the best way toassess the sampling distributions. Standard multiple regression works best under experimental conditions,wherein substantial correlation between the independent variables can beprecluded. In non-experimental research some degree of correlation existsbetween the several independent variables. Thesampling statistic is a measure of the standard error. Belmont, California:Wadsworth Publishing Company. Lastly, theAE learning mode implies that an individual is capable of effectivelyapplying the theories developed to decision-making and problem-solvingprocesses (Kolb, 1989). The sign ofthe coefficient indicates the direction of the relationship, and itsabsolute value indicates the strength, with larger absolute valuesindicating stronger relationships (Pfaffenberger & Patterson, 1997). The learner types and theexperiential modes of learning are combined to create four learning stylesthat are described through the Learning Style Inventory (LSI). | || |1966 |1 |2. |1 . Estimation Estimation is the process of estimating a population parameter insituations where it is not possible to directly determine the populationparameter. Type 4 learners, who tend to apply the CEand AE learning modes, would approach the task of organizing data byaccepting the data available, assessing the data without bias, and thenexperiment with a variety of approaches to determine the best way toorganize the data. Chi Square and ANOVA (F Statistic) A cross-tabulation is a table displaying the number of cases fallinginto each combination of the categories of two or more categoricalvariables. Additional non-parametricprocedures are discussed in this section. | || |1959 |1 |2. Education, training, and a host ofother factors could be the causes of such variations. (7th ed.). | || |1969 |1 |2. Type 3 learners would approachthe task by developing theoretical models upon which to base the assessmentof the appropriateness of competing statistical procedures, and thenexperiment with those models to determine the most appropriate statisticalprocedure for the task at hand. |9 . The 11 datamanagement or statistical analysis functions are (1) organizing data, (2)averages and variations, (3) elementary probability theory, (4) normaldistribution, (5) binomial distribution, (6) sampling distribution, (7)estimation, (8) hypothesis testing, (9) regression and correlation, (1 )chi square and analysis of variance (ANOVA) which is based on the Fstatistic, and (11) non-parametric statistics. Divergers tend to rely most heavily on the CE and RO learning modes inthe application of the Type 1 learning style. |4. Accommodators arethe doers of the world, who excel in carrying out plans, and who thrive onnew experiences. The more causal variables that are included in a regressionequation to be used in causal analysis, the simpler assumptions must beconcerning the manner in which the variables are combined in their effecton the dependent variable in the equation (Summers, Peters, & Armstrong,2 ). |4. Sampling Distributions The sampling distribution of a statistic is the set of values thatwould be obtained if an infinite number of random samples were drawn from agiven population and the statistic for each sample was determined. The Poissondistribution is a limiting case of the Binomial distribution when thenumber of trials becomes very large and p is very small (Bartz, 1998) Approaching a task involving the consideration of the probability ofdata distributions, the Type 1 learner would accept the data available,assess the data without bias, and study and consider the data from avariety of perspectives in determining which distribution curve is mostappropriate for use in analysis. |58. Individuals approach the task of organizing data differently,depending upon the Kolb Learning Style applied. The number of persons ineach age category can be determined, and such data can be used to determinean average age. The companyprovides demographic surveys and direct marketing services for more than1 top consumer goods companies. |76. Correlation analysis cannot determine acausal relationship between two variables (Summers, Peters, & Armstrong,2 ). The wide variation in learning styles implies that different peoplewill approach organizational tasks in different ways. Summers, G. An estimator is a mathematical formula or expression used tocalculate an estimate of the actual numerical value of a populationparameter. | || |1957 |2 |4. |48. | || |1947 |2 |4. |98. Although statistical inferencetechniques are directly concerned with estimating values or with thetesting of hypotheses concerning population parameters, the results ofthese procedures are related to alternative courses of action or toalternative decisions. It is held thatbefore a regression equation can be used for causal analysis, a theoreticalbasis for a causal relationship between the variables concerned must beestablished. The chi squareprocedure, however, is used frequently. Thehypothesized assumption in this approach is that the data distribution doesnot deviate from the normal distribution. The Mann-Whitney test is difficult touse with sample groups of more than 2 subjects (Pfaffenberger & Patterson,1997). References Bartz, A. A strength of the analysisof variance procedure when compared with chi-square or t-test is thatanalysis of variance can measure the interactive effects of more than oneindependent variable on a dependent variable (Summers, Peters, & Armstrong,2 ). |36. One result of this difference in emphasis is that, in regression analysis,both the independent and the dependent variables must be measured on aninterval scale, whereas, in analysis of variance procedures, only thedependent variable is required to be measured on an interval scale(Summers, Peters, & Armstrong, 2 ). The salesof new automobiles, as an example, are organized and stored in a databasethat allows users to search and extract the data from multiple perspectivesin a variety of presentation formats. The Polk Company is the oldest and one of thelargest consumer marketing firms in the United States. In a normaldistribution, 68 percent of cases fall within one SD of the mean and 95percent of cases fall within two SD. With an excellentcapacity for indicative reasoning, the assimilator is able create validtheoretical models. |2. | || |1962 |2 |4. The cross-tabulation chi square analysis discussed earlier in this investigation isitself a non-parametric statistical procedure. Binomial distribution, normaldistribution, and Poisson distribution are among the more prevalent ofthese probability distributions. | || |1973 |1 |2. | || |1967 |3 |6. Compensation levelswould be the dependent variable, and compensation brackets would be definedas the categories of the dependent variable. | || |1949 |2 |4. The company, however, is selective in its applicationof these procedures, using only those that best meet the demands of thecompany's analytical objectives.
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