Chapter 3 Table and Normal Distribution

Chapter3GraphicalPresentationofDataandNormalDistributionOutline•1.Frequencytable•2.FrequencyDistribution•3.NormalDistribution•SkewandKurtosis•4.Reportingtheresults•5.InterpretingtheresultsIntroductionTwomethodstodescribedata:1)numbers:summaryvalues,alsocalleddescriptivestatistics,mean,SD,modeetc.2)graphs:frequencydistribution1.Frequencytable•Awayoforganizingthedatabylistingeverypossibleobservationasacolumnandthefrequenciesofoccurrenceofeachobservationasanother.•SPSSfor1group:•Analyze---Frequencies---SelectStatisticsforM,SD,Range,Modeetc.---SelectChartsforbarcharts,piechartsorhistograms•Iffrequenciesforthegrouparelow,thenregroup…1.Frequencytable•UsingSPSStoregroupthedataandanalyze1)Transform—Recode—IntoDifferentVariables2)VariableofregroupingtoNumericVariableOutput3)Among“OutVariable”,providinganameofvariableto“Name”,e.g.regroup,click“Change”.4)Definetherangein“OldandNewvalues”---e.g.50—69=1,70-89=2,90-119=3,120-139=4,140-169=5(见SPSS文件描述统计分组）clickRange---fillinginthenumber,e.g.50through69----NewValueforeachnewgroup(1-5)---ClickAdd5)Analyzethenumbersof“regroup”,youwillseethedifference.2.FrequencyDistribution2.1Barchart条形图(for2groupsselectCluster)•Constructedfromafrequencytableof2groups:•Horizontalaxis(X):categories•Verticalaxis(Y):frequencies•SPSS：•Graph----LegacyDialogs---Bar---Cluster---Define---BarRepresent(selectNofcases)---CategoryAxis(adding“regroup”)---DefinedClustersby(adding“group”)---Title(nameatitle)---ClickOK2.FrequencyDistribution2.2LineCharts线图(for2groups)sameasBarCharts•2.3Area面积图,Pie饼图,Histogram直方图Charts•Nogroupschart,onlysimplecharts•Histogramwithnormalcurve（seenextpicture）3.NormalDistribution•Symmetricasbell-shaped•EachmemberofthefamilyisdeterminedbythevaluesofthemeanandSD.•Mean:anypositiveandnegative•SD:anypositiveandnegative•Ameanof0andaSDof1,itiscalledstandardnormaldistribution(seepicture)3.NormalDistribution3.1FeaturesofNormalDistribution•1）只有一个高峰，即只有一个最高点，“中间高，两边低”，类似尖塔或古钟；•2）有一个对称轴。曲线在高峰处有一个对称轴，轴的左右两边是对称的。•3）曲线无论向左或向右延伸，都愈来愈接近轴线，但不会和横轴相交，以横轴为渐近线。•4)中数、众数及平均数必须重叠。（李绍山，2008：59-69；韩宝成，2000：33）3.2TableofNormalDistribution•Z(标准分）=1.00，A（面积）=0.34134•Z=1.96，A=0.47500•Z=2，A=0.47725•Z=2.58，A=0.49506•Z=3.00，A=0.49865•（李绍山，2008：61，•查正态分布表p195）3.3Theapplicationofthetheoryofnormaldistribution对A\B两组学生测试，A组的平均数为20，SD为3，学生得了23分（20+3),比平均数多1个标准分的值，这个值在在正态分布中所占面积为84.1%（50%+34.1%),即，得23分的学生比84.1%的学生好。B组X‘也是20，但SD为14，要比84.1%的学生好，要取得平均分+14的分数（20+14=34)(李绍山，2008：63-66；韩宝成，2000：34)•3.4Methodsfornormaldistribution•1)绘制直方图，可以直观看出；•2）比较理论分布与实际分部中各标准差的面积或概率•3)计算数据分部的偏态值和峰值。•（李绍山，2008：66-67）3.4Skew（偏态值）Kurtosis（峰值）•Ifthedistributionislopsidedratherthansymmetrical,itissaidtobeskewed.（分部不对称，称为“偏态”）•Positivelyskew:(正偏态）--正值,SK0--morescoresaretotherightofthemode--themeanandmedianarebiggerthanthemode—morelowscores(低分偏高）•Negativeskew（负偏态）--负值,SK0--Morescoresaretotheleftofthemode--themeanandmedianaresmallerthanthemode--morehighscores（高分偏多）Normal——Zerovalue,SK=0•(Howitt&Cramer,2000,p.34-35)3.4Skew（偏态值）kurtosis（峰值）Kurtosis:•Thetermusedtoidentifythedegreeofsteepnessorshallownessofadistribution.（分布曲线的顶点尖峭程度）--astepcurve--leptokurtic（K0,正值，尖峰态）--anormalcurve—mesokurtic（0值，正态）--aflatcurve—platykurtic（K0,负值，低峰态）•(Howitt&Cramer,2000,p.34-35)4.Reportingtheresults•Seewordfile“Chapter3ReportingData”5.Interpretingtheresults•Examples•Seepdf“suggestionsandtextbooks”“留学生汉语语用能力调查”•Seewordfile“整体听写有效性”