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UNL PSYC 971 - Lecture notes

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Univariate Parametric & Nonparametric Statistics & Statistical TestsSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Univariate Parametric & Nonparametric Statistics & Statistical Tests•Kinds of variables & why we care•Univariate stats–qualitative variables–parametric stats for ND/Int variables–nonparametric stats for ~ND/~Int variables•Univariate statistical tests–tests qualitative variables–parametric tests for ND/Int variables–nonparametric tests for ~ND/~Int variables–of normal distribution shape for quantitative variablesKinds of variable  The “classics” & some others …Labels• aka  identifiers• values may be alphabetic, numeric or symbolic• different data values represent unique vs. duplicate cases, trials, or events• e.g., UNL ID#Nominal• aka  categorical, qualitative• values may be alphabetic, numeric or symbolic• different data values represent different “kinds”• e.g., speciesOrdinal• aka  rank order data, ordered, seriated data• values may be alphabetic or numeric • different data values represent different “amounts”• only “trust” the ordinal information in the value • don’t “trust” the spacing or relative difference information• has no meaningful “0”• don’t “trust” ratio or proportional information• e.g., 10 best cities to live in• has ordinal info  1st is better than 3rd• no interval info  1st & 3rd not “as different” as 5th & 7th• no ratio info  no “0th place”• no prop info  2nd not “twice as good” as 4th • no prop dif info 1st & 5th not “twice as different” as 1st & 3rdInterval• aka  numerical, equidistant points• values are numeric • different data values represent different “amounts”• all intervals of a given extent represent the same difference anywhere along the continuum• “trust” the ordinal information in the value • “trust” the spacing or relative difference information• has no meaningful “0” (0 value is arbitrary)• don’t “trust” ratio or proportional information• e.g., # correct on a 10-item spelling test of 20 study words• has ordinal info  8 is better than 6• has interval info  8 & 6 are “as different” as 5 & 3• has prop dif info 2 & 6 are “twice as different” as 3 & 5• no ratio info  0 not mean “can’t spell any of 20 words”• no proportional info  8 not “twice as good” as 4| | | | | | | | |Represented Construct20 30 40 50 60Measured VariableOrdinal MeasurePositive monotonic trace“more means more but doesn’t tell how much more”| | | | | | | | |Represented Construct20 30 40 50 60Measured VariableInterval MeasureLinear trace“more how much more”y = mx + c“Limited” Interval Scale• provided interval data only over part of the possible range of the scale values / construct• summative/aggregated scales| | | | | | | | |Represented Construct20 30 40 50 60Measured Variable| | | | | | | | |Represented Construct20 30 40 50 60Measured Variable“Nearly” Interval Scale• “good” summative scales• how close is “close enough”Binary ItemsNominal • for some constructs different values mean different kinds• e.g., male = 1 famale = 2Ordinal• for some constructs can rank-order the categories• e.g., fail = 0 pass = 1Interval• only one interval, so “all intervals of a given extent represent the same difference anywhere along the continuum”So, you will see binary variables treated as categorical or numeric, depending on the research question and statistical model.Ratio• aka  numerical, “real numbers”• values are numeric • different data values represent different “amounts”• “trust” the ordinal information in the value • “trust” the spacing or relative difference information• has a meaningful “0”• “trust” ratio or proportional information• e.g., number of treatment visits• has ordinal info  9 is better than 7• has interval info  9 & 6 are “as different” as 5 & 2• has prop dif info 2 & 6 are “twice as different” as 3 & 5• has ratio info  0 does mean “didn’t visit”• has proportional info  8 is “twice as many” as 40 10 20 30 40 50 60 Represented Construct0 20 40Measured VariableRatio MeasureLinear trace w/ 0“more how much more”y = mx + cPretty uncommon in Psyc & social sciences• tend to use arbitrary scales• usually without a zero• 20 5-point items  20-100Linear scale & “0 means none”Kinds of variables  Why we care …Reasonable mathematical operationsNominal  ≠ =Ordinal  ≠ < = >Interval  ≠ < = > + - (see note below about * / )Ratio  ≠ < = > + - * / Note: For interval data we cannot * or / numbers, but can do so with differences. E.g., while 4 can not be said to be twice 2, 8 & 4 are twice as different as are 5 & 3.Data DistributionsWe often want to know the “shape” of a data distribution.Nominal  can’t do  no prescribed value orderOrdinal  can’t do well  prescribed order but not spacingdogs cats fish rats fish cats dogs ratsInterval & Ratio  prescribed order and spacingvs.10 20 30 40 50 60 10 20 30 40 50 6010 20 30 40 50 60Univariate Statistics for qualitative variables Central Tendency – “best guess of next case’s value”• Mode -- the most common score(s) • uni-, bi, multi-modal distributions are all possibleVariability – “index of accuracy of next guess”• # categories• modal gender is more likely to be correct guess of next person than is modal type of pet – more categories of the latterShape – symmetry & proportional distribution• doesn’t make sense for qualitative variables • no prescribed value orderParametric Univariate Statistics for ND/Int variablesCentral Tendency – “best guess of next case’s value”• mean or arithmetic average  M = ΣX / N • 1st


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