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STATISTICAL ANALYSIS.
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Examines statistical theory & procedures in general & applied to U.S. unemployment problem.... More...
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Paper Abstract:
Examines statistical theory & procedures in general & applied to U.S. unemployment problem.
Paper Introduction:
INTRODUCTION
The purpose of this research is to explain the application of statistical procedures to the solution of a realistic problem. In this instance, the problem is related to the domestic economy of the United States.
THE PROBLEM
The level of unemployment is a matter of significant concern to both the general public and political leaders. In order to develop effective policies to address the unemployment issue, it is necessary to understand how the unemployment rate is related to other factors. It is this problem which is addressed in this research.
HYPOTHESES
A total of six hypotheses were formulated for, and tested in
Text of the Paper:
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THE PROBLEM The level of unemployment is a matter of significant concern to boththe general public and political leaders. 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.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 (Nie,Hull, Jenkins, Steinbrenner & Bent, 1975). EnglewoodCliffs: Prentice-Hall. When correlation analysis wasapplied to these two sets of data, it was found that the correlation was r= - .9824, and that the t statistic for the correlation was 22.1698. Correlation analysis is quite similar to regression analysis in majorportions of the calculations. A ttest was employed to test the statistical significance of the correlationcoefficient at the p<. Year-to-year changes in these unemployment rates were then calculated forthe nine annual intervals. It is hypothesized that changes in the unemployment rate are moreextreme for inexperienced workers than for experienced workers. Homewood, IL: R.D. It is this problemwhich is addressed in this research. References Council of Economic Advisers. 217). In other words, an attempt is made toexplain the movement in a.dependent variable through the analysis ofmovements in independent, or explanatory, variables. Simple regression analysis involves the analysis of the relationshipbetween one dependent variable and one explanatory, or independent,variable. It is hypothesized that changes in the unemployment rate are moreextreme for persons under the age of 2 years old in the economy than forthose persons aged 2 years old and older. 276). This procedure is one which permits the making of inferences(Levin, 1984). 5 (critical value of t= 2.26, df: 9). 3. 9). Nie, N.H., Hull, C.H., Jenkins, J.G., Steinbrenner, K., & Bent, D.H.(1975). Perhaps the most important use of statistics and statisticalprocedures to the manager and the administrator is that of testinghypotheses. Homewood,IL: R.D. 6. . (1984). Similarly, datapertaining to changes in the overall civilian unemployment rate werecollected for the same 1 -year time period. Statistical methodsfor business and economics (3rd ed.). Multiple regression may be viewed either as a descriptive tool by which the linear dependence of one variable on others is summarized and decomposed, or as an inferential tool by which the relationships in the population are evaluated from the examination of sample data (Nie, Hull, Jenkins, Steinbrenner & Bent, 1975, p. Multiple regression isused as an inferential tool in hypothesis testing. (1987). High levels of correlation were found to existbetween the movements in the several data set pairs; however, in eachinstance, the mean annual change was found to be greater in thehypothesized data set, and, in each instance, the correlation was found tobe statistically significant at p<. Correlation coefficientsestablish both the strength of relationships between variables and thenature of such relationships--positive or negative. These hypotheses were stated as follows: 1. For minority groups, increases inunemployment tend to be greater, and decreases in unemployment tend to begreater. In thisinstance, the problem is related to the domestic economy of the UnitedStates. DATA SOURCE The required data required for the performance of this research @Ye-collected and published by the United States government. Emory, C.W. 5 (critical value of t = 2.31; df: 8). Probability is "a numberexpressing the likelihood of occurrence of a specific event" (Shao, 1986,p. Thecorrelation coefficient indicated an exceptionally strong inverserelationship between changes in the gross national product, and changes inthe overall rate of civilian unemployment. Irwin. The differences between the means ofthese categories are then tested for statistical significance. There are several statistical procedures which are used in thetesting of hypotheses. In order to develop effectivepolicies to address the unemployment issue, it is necessary to understandhow the unemployment rate is related to other factors. New York:McGraw-Hill. The t statistic indicated thatthe correlation was statistically significant at p<. This single number expresses thestrength of the relationship between the variables. (1985). 2. Irwin. Government Printing Office. 5 level. Economic indicators. general statistical technique through which one can analyze the relationship between a dependent or criterion variable and a set of independent or predictor variables. It is hypothesized that the rate of civilian unemployment in theUnited States changes linearly and inversely to changes in the grossnational product. Multiple regression is used as a descriptive tool in three types ofsituations: (a) to develop a self-weighting estimating equation by whichto predict values for a dependent variable; (b) to control for confoundingvariables so as to better evaluate the contribution of other variables; and(c) to test explicit causal theories (Emory, 1985). Three procedures which are widely used by managersand administrators are (a) analysis of variance (ANOVA), (b) regressionanalysis, and (c) correlation analysis (Pfaffenberger & Patterson, 1987). It is hypothesized that changes in the unemployment rate are moreextreme for females than for males. The basic theoretical principle upon which inferential statistics arebased is that of probability (Levin, 1984). Inferentialstatistics permit the findings with respect to one set of relationships tobe extended to other relationships, and to generalize findings andconclusions on the basis of statistical inference (Levin, 1984). For use in inferential statistics, this probability must bestatistically independent (Levin, 1984). In the testing ofhypotheses, multiple regression provides the data by which researchers mayeither reject or not reject the null forms of the hypotheses being tested.If the null form of an hypothesis is rejected, then, by inference, thehypothesis may be accepted; and, conversely, if the null form of anhypothesis cannot be rejected, then, by inference, the hypothesis may berejected. Bivariate correlation analysis, however, goes further than doesregression analysis. Thisgeneral procedure permits the assessing of the relative effect upon thedependent variable of each of the independent variables; an assessing ofthe combined effects of the independent variables on the dependentvariable; and an assessment of the interactions between all of thevariables. Washington: U.S. Regression coefficients permit theprojection of movements in one variable based on movement in anothervariable or in a set of other variables. Statistics for management (3rd ed.). Thecorrelation coefficients provided an inferential analysis of movements inthe unemployment rate in the United States. STATISTICAL PROCEDURE APPLIED The data were analyzed and the hypotheses tested through theapplication of correlation analysis to the appropriate sets of data. Correlation analysis provides "a single number whichsummarizes the relationship between two variables" (Nie, Hull, Jenkins,Steinbrenner & Bent, 1975, p. Multiple regression, on the other hand, is a . Mathematics and quantitative methods (3rd ed.).Cincinnati: South-Western.----------------------- 9 Statistical package for the social sciences (2nd ed.). The statistical concepts of both regression and correlation arevaluable tools for the manager. (1986). HYPOTHESES A total of six hypotheses were formulated for, and tested in theperformance of this research. Pfaffenberger, R.C., & Patterson, J.H. In concept, all of the cases in a setare divided into categories, which are based upon their values in relationto each of the independent variables. 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 is usuallyassumed to be measured at an interval level" (Nie, Hull, Jenkins,Steinbrenner & Bent, 1975, p. POPULATION The population for which the data were collected was the entireworking-age, non-institutionalized segment of the American population.This population was not sampled. It is hypothesized that changes in the unemployment rate are moreextreme for nonwhites than for whites. CONCLUSION Based on the findings of the research performed, it may be concludedthat the overall civilian unemployment rate in the United States does moveinversely and linearly to changes in the gross national product. The unemployment rate data for the various classifications (racial,gender, age, employment status, and work experience) provided a descriptiveanalysis of the unemployment situation in the United States. Rather, data applicable to the entirepopulation were used in this research. Descriptive statistics describe the performance or activity of onegroup or class, without attempting to make generalizations about othergroups or classes (Pfaffenberger & Patterson, 1987). Shao, S.P. 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 (Emory, 1985). 5. SOLUTION The data pertaining to changes in the gross national product werecollected for the 1 -year time period 198 -1989. As is true for regression analysis, correlation analysis requires adependent variable and at least one independent variable for the structureof the calculations, although the variable labeled as the dependentvariable may not actually be dependent upon the actions of the variablesincluded in the calculations as independent variables. In fact, the correlation coefficients areoften used in conjunction with the regression coefficients in predictiveanalysis. It mayalso be concluded that minority group employment levels are less stablethan are those for majority groups. . Business research methods (3rd ed.). These data wereobtained from Economic Indicators, a statistical publication covering macroeconomic data (Council of Economic Advisers, 199 ). INTRODUCTION The purpose of this research is to explain the application ofstatistical procedures to the solution of a realistic problem. What a simplecorrelation coefficient does not do for the manager or administrator,however, is to establish a causal relationship between the variables. It is hypothesized that changes in the unemployment rate are moreextreme for part-time workers than for full-time workers. Unemployment data for the various groups represented in thequalitative variables were collected for the 1 -year time period 198 -1989. 321). 4. (199 , January). Levin, R.I. Indeed, in someinstances, the purpose of a correlation analysis is not to determine thestrength of the association between a dependent and an independentvariable, but, rather, to determine the strength of the relationshipbetween two variables for which dependency characteristics are not known.More often than not, however, the researcher will have strong support forlabeling one or other of the variables as the dependent variable in thecorrelation analysis.
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