Y học - Chapter 13: Descriptive data analysis

Chapter 13 Descriptive Data AnalysisStatisticsScience is empirical in that knowledge is acquired by observation Data collection requires that we make measurements of our observationsMeasurements then yield dataStatistics are used for analyzing data3 Basic Steps in Data AnalysisSelect the appropriate statistical techniqueApply the techniqueInterpret the resultDescriptive statisticsUsed to organize, simplify, and summarize the collected data Data typically consist of a set of scores called a distribution. These scores result from the measurements taken The original measurements or values in a distribution are called raw scoresTypes of ScoresContinuousa continuous progression from the smallest possible amount to the largest possible amount, with measurement theoretically possible at any point along the continuum; may be expressed as a fraction (e.g., height, weight, temperature, strength)Discretemeasurement and classification are possible only in whole units; no fractional units (e.g., size of family, number of schools in country)Dichotomous – 2 category variable (yes/no; alive/dead)Scales of MeasurementNominalOrdinalIntervalRatioNominalMerely classifies objects in accordance with similarities and differences with respect to some property; no hierarchy of scores Examples color of hairgenderresponse to a yes/no questionshoe preferenceOrdinalType of data that is characterized by the ability to rank order on the basis of an underlying continuum No common unit of measurementExamplesclass ranksplace of finish in a raceIntervalData having known and equal distances between score units, but having an arbitrary zero point Exampletemperature on Fahrenheit scaleRatioPossesses same properties of interval data, but does have a true zero point Examplesheight or weightdistance measurementComputer AnalysisVariety of computer programs for statistical computations; mainframe and desktopSPSS See Appendix A in textbook for more informationSASStatviewExcelFast, easy to use, widely availableOrganizing and Graphing ScoresFrequency distributionsSimple frequency distributionGroup frequency distributionGraphing techniquesHistogramFrequency polygonNormal curveBell-shaped curveSkewed distributionSimple Frequency DistributionScore Frequency Cumulative Freq.X f cf22 1 1519 2 1418 3 1217 5 916 2 413 1 211 1 1Group Frequency DistributionClass Interval f cf66 – 68 2 3063 – 65 4 2860 – 62 2 2457 – 59 2 2254 – 56 2 2051 – 53 3 1848 – 50 2 1545 – 47 1 13HistogramFrequency PolygonNormal CurveSymmetrical CurvesDistribution ShapesTypes of Descriptive StatisticsMeasures of Central TendencymeanmedianmodeMeasures of Variabilitystandard deviationvariancerangeminimum/maximumMeasuring Group PositionPercentile ranks and percentileStandard scoresz scoreT scoreRelationships Among VariablesCorrelational StatisticsCorrelation is a family of statistical techniques that is used to determine the relationship between 2 or more variablescorrelation coefficient ranges from -1.0 to +1.0scatterplot is a graphic illustration of the relationship between 2 variablescorrelation provides information about the magnitude and direction of a relationship, but does not imply a cause-and-effect relationship between the variablesCorrelational TechniquesPearson product-moment correlation (r)requires interval or ratio scoresevery subject has scores on two variablesmost frequently usedSpearman rank-order correlation (rs)nonparametric technique for use with ordinal scoresevery subject has scores on two variablesInterpretation of CorrelationCoefficient of determination (r2)Portion of the total variance in a variable that can be explained or accounted for by the variance of the other variableSquare of the correlation coefficient If r = .70 then r2 = .49Question of AccuracyLinear relationshipCurvilinear relationshipReliability of test scoresLow reliability reduces correlationRange of scoresCorrelation will be smaller for a homogeneous group than a heterogeneous group