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
View Full Document