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RESEARCH DESIGN AND STATISTICAL ANALYSIS.
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Paper Abstract:
Reviews concepts and issues. Background and definitions. Theory in scientific inquiry. Applications of quantitative statistical methods. Descriptive statistics. Statistical inference techniques. Internal validity. Measuring instrument. Reliability of a data collection procedure. Hypothesis testing; the 3 procedures used for testing (ANOVA, linear regression analysis, correlation analysis).
Paper Introduction:
CONCEPTS AND ISSUES INVOLVED IN RESEARCH DESIGN AND STATISTICAL ANALYSIS: DEFINITIONS, DESCRIPTIONS, AND EXPLANATIONS
Abstract
This paper reviewed concepts and issues involved in research design and statistical analysis. The discussions covered definitions, descriptions, and explanations of various concepts and issues. While the concepts and issues tend to be complex, they are logical in application. Further, the application of the concepts and issues allow psychological providers and researchers to generalize findings based on samples to general populations.
Introduction
This paper reviews concepts and issues involved in research design and statistical analysis. The discussions cover d
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New York: W. Assume the following data set: 12, 22, 5, -14, 5, 5, 17, .The median of the data set is as follows: Median = X(n+1)/2 X(7+1)/2 X4.5 -14 5 5 5 12 17 22 [(5-5) / 2] + 5 Median = 5 3. (1998). Thus,to be valid, data provided by an instrument designed to measure a tendencytoward abnormal behavior would have to be consistent with those of otherinstruments of proven reliability in the measurement of tendencies towardabnormal behavior (Lockhart, 1998). Onceagain, consider the desire to measure the height of a group of elementaryschool students in feet and inches. Oehlert, G. In addition to the use of ANOVA, correlation analysis, and regressionanalysis in the testing of hypotheses, several other quantitativeprocedures are also used. Essentially, the choice between probability levels of Type I (Alpha)and Type II (Beta) errors is the basis for assessing the relativeimportance of two alternative types of mistakes in hypothesis testing instatistical inference analysis. Ifthe instrument does not measure the height of the same individual as beingthe same in measurement-after-measurement, it is not a reliable measurementinstrument. W. There are three pervasive applications of quantitative statisticalmethods in the conduct of psychological research. Assume the following data set: 12 -33 6 15 9 19 11 -13 8.The standard deviation of the data set is as follows: SX = 34 _ X = 3.4 _ SD = ? The discussions cover definitions, descriptions, andexplanations of various concepts and issues. Thus, hypothesis testing applied to sampledata in inferential statistical applications can provide valid and reliableinformation about the entire population when the research design assuresthat the sample is representative of the population (Oehlert, 2 ). Yates, D., Moore, D. P. Thus, ifthe objective were to measure the height of a group of elementary schoolstudents in terms of feet and inches, it would be necessary to have ameasuring instrument calibrated in feet and inches. Perhaps the most important use of statistics and statisticalprocedures is the testing hypotheses - one of the procedures that permitthe making of inferences. 2. 3. Belmont, California: Wadsworth Publishing. Hypothesis testing falls in the realm of inferential statistics.The basic theoretical principle underlying inferential statistics isprobability. Myers, J. If, however, this identical time-after-timemeasurement is not in agreement with a previously validated externalstandard, the reliable instrument is not a valid instrument. H. (2 ). L., & Well, A. Internal validity isassociated with causal relationships. , which is an indication of nocorrelation whatever, to 1. Although statistical inference techniques are directly concerned withestimating values or with the testing of hypotheses concerning populationparameters, the results of these procedures relate to alternative coursesof action or to alternative decisions. In almost all cases, the correlation coefficient will be morethan . Background In scientific inquiry, a proposition is a statement about conceptsthat analysis may determine to be true or false if it refers to observablephenomena. External validity is concerned withthe generalizability of the study findings; that is the ability to applythe study findings beyond the research sample. Theory, in scientific inquiry, is, in effect, a descriptiveexplanation of how something works - an explanation of the interrelatedactions within a system. Statistical analysis for decisionmaking. The principal techniques of statisticalinference are interval estimation and hypothesis testing (Moore, McCabe,Duckworth, & Sclove, 2 2). 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. Therefore, the central limit theorem assumes a high-level ofimportance in hypothesis testing. For use in inferential statistics, thisprobability must be statistically independent. S. Theinterval level requirement for measurement of the dependent variable meansthat an equality of interval exists between the points on the scale withwhich the variable is measured (Moore, McCabe, Duckworth, & Sclove, 2 2). J., & Wallnau, L. Nevertheless, correlation analysis does notestablish causal relationships (Gravetter & Wallnau, 2 ) Correlation coefficients range from . Lastly, theory summarizes existingknowledge relating to a problem (Hamburg & Young, 1994). 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 (typically theassumption is that it is the product of an interval level measurement. Descriptive statistics describe the performance oractivity of one group or class, without attempting to generalize or inferbehaviors or characteristics of other groups or classes (Lockhart, 1998). The major threatto the external validity of an experiment or study typically is therepresentativeness of the sample. H. A measurement procedure is,thus, reliable to the extent that it supplies consistent results. The practice ofstatistics. Theory also suggests the most productive approachesto the investigation of a problem. (1995). Introduction This paper reviews concepts and issues involved in research design andstatistical analysis. Thus, the reliability and validity of datacollected for use in statistical analysis is of paramount importance.Validity refers to the extent to which data or a data collection instrumentmeasures what it is actually desired to measure. While one may derive hypotheses from observedfacts, one also may deduce hypotheses from theory. San Diego: Harcourt Brace College Publishers. With respect to internal validity, the experimental researcher isconcerned with matters such as the stability of the sample over time andsubjects' maturation during the course of the experiment. Decision theory used in conjunctionwith statistics provides administrators, managers, professionals,researchers, and others with knowledge about events and relationships thatreduce the level of uncertainty in the data, thereby improving the qualityof decisions (Hamburg & Young, 1994). In thecase of the measurement of tendencies toward abnormal behavior inindividuals, an instrument, to be reliable, would have to provideconsistent scores for the same individuals within a short span of time whenthose individuals were both tested and retested with the instrument (Myers& Well, 1995). (1994). Lockhart, R. Hillsdale, New Jersey: Erlbaum Publishers. (2 2). New York: W. The central limit theorem holds that the distribution of thetotals (and therefore the means) of random samples will be normal no matterwhat the distribution in the population is like, provided only that thesamples are large enough. D. Assume the following data set: 12 -33 6 15 9 19 11 -13 8.The range of the data set is as follows: Range = 19 - (-33) 19 + 33 33 4. Assume the following data set: 12, 22, 5, -14, 5, 5, 17, .The mean of the data set is as follows: Mean = 12+22+5+(-14)+5+5+17+ = 52 / 8 = 6.5 2. As has been stated, the correlationcoefficient represents the strength of a relationship between variables.An r of .25 (a simple coefficient of correlation is represented by thesymbol r, while a multiple coefficient of correlation is represented by thesymbol R) would represent a relatively weak relationship, while an r of .85 would represent a relatively strong relationship. New York: W. In inferential statisticalapplications, probability is largely a function of sampling, as well as ofrelationships, because it is usually not feasible or even possible tomeasure an entire population. Moore, D. H. P., Duckworth, W., & Sclove, S. One application of quantitative statistical methods is todescribe events. There are several statistical procedures used inthe testing of hypotheses. Evaluation ofthe validity of an instrument designed to measure some psychologicalcharacteristic or factor would rely on its ability to yield resultsconsistent with those of another instrument of established validity. (6th ed.). (2 ). To illustratethese points, consider, again, the case of the instrument calibrated infeet and inches used to measure the height of a group of individuals. New York: W. Probability is a number expressing the likelihood ofoccurrence of a specific event. In such analysis, decision procedures restentirely on the analysis of data collected through a random sampling of thetotal population (Yates, Moore, & McCabe, 1999). A proposition formulated for empirical testing is a hypothesis. One result ofthis difference in emphasis is that, in regression analysis, therequirement is that the measurement of both the independent and thedependent variables occur through the use an interval scale, whereas, inanalysis of variance procedures, only the measurement of the dependentvariable must be interval in character (Oehlert, 2 ). Further, aninstrument cannot be valid if it is not also reliable; however, justbecause it is reliable, it is not, of necessity, valid. A study must be internallyvalid for its findings to be generalizable (Gravetter & Wallnau, 2 ). Reliability, as opposed to validity, is concerned with the accuracyand precision of a measurement procedure. Reliability refers to the accuracy and precision of a ofdata collection procedure. On the otherhand, if an instrument does measure the height of the same individual asbeing the same in measurement-after-measurement, the instrument is areliable instrument. The reliability of a data collection procedure is a contributor to thevalidity of that procedure, rather than the other way around. Hypotheses are declarative statements that are both tentative andconjectural in character. The discussions covered definitions,descriptions, and explanations of various concepts and issues. Hypotheses may be both descriptive andrelational in form (Gravetter & Wallnau, 2 ). Research design and statisticalanalysis. Another application of quantitative statistical methods isto infer causes or future events. H. In scientific inquiry,theory provides a basis for the narrowing of the body of facts studied toinvestigate a problem. , which is an indication of a perfectcorrelation. Another application of quantitative statistical is toenhance the decision making process. B. While theconcepts and issues tend to be complex, they are logical in application.Further, the application of the concepts and issues allow psychologicalproviders and researchers to generalize findings based on samples togeneral populations. If the instrument does not measure the height of the sameindividual as being the same in measurement-after-measurement, theinstrument, obviously, does not always yield results which are in agreementwith the external standard, such as a master instrument maintained by theNational Bureau of Standards. Bivariate correlation analysis, however,goes further than does regression analysis. Therefore,reliability in an instrument is required before that instrument can bevalid, but that reliability in an instrument alone cannot guarantee thatsuch instrument will be valid. S., & McCabe, G. . The discussions covered definitions,descriptions, and explanations of various concepts and issues. Conclusion This paper reviewed concepts and issues involved in research designand statistical analysis. The basis forassessing the validity of this measuring instrument calibrated in feet andinches would its ability to accurately measure feet and inches inaccordance with an external standard, such as a master measurementinstrument maintained by the National Bureau of Standards. It is with respect to samples and their characteristics, and their usein hypothesis testing, that the central limit theorem and central tendencymeasures are important. Freeman and Company. Thus, empirical psychologicalresearch attempts to establish cause-and-effect relationships betweendependent and independent variables. 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 unknown.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. To accomplish the objective of validity in measurement, it isnecessary to have some standard that is external to the measurementprocedure, in order to evaluate the validity of the procedure. S(X - X)2 N-1 12 - 3.4 = 8.6 8.62 = 73.96 -33 - 3.4 = - 36.4 - 36.42 = 1324.96 6 - 3.4 = 2.6 2.62 = 6.76 15 - 3.4 = 11.6 11.62 = 134.56 - 3.4 = - 3.4 3.42 = 11.56 9 - 3.4 = 5.6 5.62 = 31.36 19 - 3.4 = 15.6 15.62 = 243.36 11 - 3.4 = 7.6 7.62 = 57.76 -13 - 3.4 = - 16.4 - 16.42 = 268.96 8 - 3.4 = 4.6 4.62 = 21.16 2174.4 / 9 = 241.6 ?241.6 = 15.543 Standard Deviation of Sample 2174.4 /1 - 217.4 ?217.4 = 14.744 Standard Deviation [Simple] Inference is among the most important of the uses made of quantitativemethods. Inferential statistics permit theextension of findings with respect to one set of relationships to otherrelationships and to generalize findings and conclusions to an entirepopulation or group through a process of inference (Myers & Well, 1995). and less than 1. Introduction to statistics and data analysisfor the behavioral sciences. The instrument calibrated in feet andinches would be reliable, if it yielded consistent results in themeasurement time-and-time-again of the same group of individuals. Two of the other statistical procedures that arewidely used are t tests and chi square analysis (Lockhart, 1998). Three procedures that are widely used are (1)analysis of variance (ANOVA), (2) linear regression analysis, and (3)correlation analysis (Hamburg & Young, 1994). Freeman Company. References Gravetter, F. (5th ed.). (1999). In most instances of the application ofinferential statistics in hypothesis testing, population distributions areunknown. While theconcepts and issues tend to be complex, they are logical in application.Further, the application of the concepts and issues allow psychologicalproviders and researchers to generalize findings based on samples togeneral populations. One may enhance the probability ofsample representativeness through the application of random procedures insample selection. S., McCabe, G. Therefore, in this example, because themeasuring instrument is not reliable, it cannot be valid. A first course in design and analysis ofexperiments. The central limit theorem and central tendency areamong the assumptions underlying the validity of the results of statisticalanalysis. Thepractice of business statistics. Freeman Company. Hamburg, M., & Young, P. Freeman Company. The quality of any statistical analysis can be only as good as is thequality of the data analyzed. Correlation analysis is quite similar to regression analysis in majorportions of the calculations. Validity, thus, is the extent to whichdifferences found through a particular data collection procedure reflecttrue differences among the measured variables (Gravetter & Wallnau, 2 ). These three generalapplications are as follows: 1. A major difference between the ANOVA procedure and regression analysisis that, in analysis of variance, the emphasis is on analysis of thevariations in the independent variable, as opposed to the joint interactionof the variations in dependent and independent variables. concepts and issues involved in research design and statistical analysis: definitions, descriptions, and explanations Abstract This paper reviewed concepts and issues involved in research designand statistical analysis. Descriptive statistics involve the determination of basic datacharacteristics, such as mean, median, range, and standard deviation.Examples of these data characteristics are as follows: 1. Correlation analysis providesa single number that summarizes the relationship between two variables.This single number expresses the strength of the relationship between thevariables (Yates, Moore, & McCabe, 1999). Statistics for thebehavioral sciences. As an example, the inability toreject a null hypothesis in statistical inference analysis that indicatedthat patient outcomes associated with a proposed therapy likely would beinferior to those associated with existing therapies typically would beassociated with a decision not to implement the proposed therapy.Rejection of the null hypothesis, however, would provide a basis foracceptance of the alternative hypothesis that adoption of the proposedtherapy would lead to improved patient outcomes (Yates, Moore, & McCabe,1999). The acceptabilityof a specific correlation coefficient as a descriptor of a relationshipdepends, to a great extent, on the past experience and practice within aspecific field of investigation; however, in most social scienceinvestigations, a correlation minimum coefficient of .7 is often requiredbefore the descriptor is considered to be acceptable (Moore, McCabe,Duckworth, & Sclove, 2 2).
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