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Introduction to Statistics inPsychologyPSY 201Professor Greg FrancisLecture 02measurement scalesdescriptive statisticsWhat is our national securitythreat?VARIABLESfactors that affect data e.g.study the effect viewing violent videogames on childhood aggressionYou might want to measure manydifferent variables2DEPENDENT VARIABLESvariables might include• number of violent acts in game• age of child• time spent playing the game• time sense last played the game• frequency of play• other activities• gender of child• number of friends• aggressive acts by the child3DEPENDENT VARIABLESthese are the variables that measurethe effect you are interested in• number of violent acts in game• age of child• time spent playing the game• time sense last played the game• frequency of play• other activities• gender of child• number of friends• aggressive acts by the childthese measurements are not alwayseasy to get!4VARIABLESresearchers are interested in howdependent variables change as othervariables change(see how the dependent variablesdepend on other variables)other variables are calledindependent variablesresearcher either keeps track of orcontrols the values of independentvariables5INDEPENDENT VARIABLEStwo types1. researcher manipulates variablee.g. have children play a video gamefor various durations and measure theeffect on aggression2. variable classifiese.g. gender, age of childstudy wants to know how thedependent variable changes withchanges in the independent variables6LEVELS OF VARIABLESindependent variables can havedifferent levelse.g.gender of child1. male.2. female.time spent playing video games1. 0-1 hours per week.2. 2-5 hours per week.3. 6-10 hours per week.4. 11-20 hours per week.5. more than 20 hours per week.7CONFOUNDINGVARIABLESsome types of independent variablesare present but not really related to astudyFor example a child’s tendency to playa violent video game may be related to:• aggression in the family• socioeconomic status• weather• availability of counselinga researcher often cannot manipulatethese variables (ethics!)a researcher can sometimes control forthese variables by measuring them andinsuring effects do not depend on them8EXAMPLElet’s identify the dependent variable,independent variable, and possibleconfounding variablesA researcher wants to know the effectof sweetener (sweetened, unsweetened)added to drinking fluid on the amountof fluid drunk by subjects.A researcher wants to know the effectof type of counseling (group,individual) on clients’ level ofemotional adjustment.9MEASUREMENTstudies need to identify variables andmeasure themdifferent variables have different scalesof measurementfour scales of measurement:least precise to most precise• nominal• ordinal• interval• ratio10NOMINAL SCALEclassification of objects into categoriese.g.nationalitycolor of eyesgendernames of objectsno order to the categories!11NOMINAL SCALEtwo key properties1. data categories are mutually exclu-sive.2. data categories have no logical order.numbers can designate categories1–blue eyes2–brown eyes3–green eyesbut the order of numbers does notimply order of categories, becausethere really is no order12ORDINAL SCALEordered classificatione.g.grading system A,B,C,D,Fwarmth: cold, cool, warm, hotfinish in a raceorder is important and meanssomething13ORDINAL SCALEnumbers can be used to designatecategoriese.g. finish in a race1. first place2. second place3. third place4. fourth placeorder of numbers agrees with order ofcategories14ORDINAL SCALEbut size of number does not correspondto amount of relevant characteristicthe difference between fourth and fifthmight be much larger than thedifference between first and secondOlympic Men’s 100m Butterfly Finals15ORDINAL SCALEbut size of number does not correspondto amount of relevant characteristicthe difference between fourth and fifthmight be much larger than thedifference between first and secondOlympic Men’s 100m Butterfly Finals1. Michael Phelps: 50.58 s2. Milorad Cavic: 50.59 s3. Andrew Lauterstein: 51.12 s4. Ian Crocker: 51.13 s5. Jason Dunford: 51.47 s6. Takuro Fujii: 51.50 s7. Andrii Serdinov: 51.59 s8. Ryan Pini: 51.86 s16ORDINAL SCALEcharacteristics1. data categories are mutually exclu-sive.2. data categories have some logical or-der.3. data categories are scaled accordingto the amount of the particular char-acteristic they posses.17USING SCALESOne needs to pick items that have a“natural” scale to convey certain typesof informationThus, for example, colors are typicallyat the nominal scale of measurementthis makes them a poor choice forlabeling of ordinal data because p eopledo not automatically know what thedifferent colors meanthis is a problem for the Nationalsecurity warning system, which usescolors to indicate different terroristthreat levelsWhich is more severe: green threat orblue threat?18MATCHING SCALESthe problem is that the scales of terrorist threat (ordinalscale) and color (nominal scale) do not match. Thus,news reports of the terrorist threat level invariably donot list only the color but also the associated phrasewith each report. The color scale is of no use at all.19INTERVAL SCALEequal unit scalee.g.• temperature (Fahrenheit or Celsius)• IQ scores (try to be)• most testsno beginning to scalezero point is just another category20INTERVAL SCALEnumbers can be used to designatecategoriese.g.• 22◦F → level of heat• 25◦F → level of heat• 28◦F → level of heatorder of numbers agrees with order ofcategoriesnumber differences agree withcharacteristic differences (e.g., 3◦F)21INTERVAL SCALE• 50 IQ• 100 IQ• 150 IQan adult with a 50 IQ should have 50fewer units of intelligence than aperson with a 100 IQa person with a 100 IQ should have 50fewer units of intelligence than aperson with a 150 IQhowever, you cannot say that a genius(150 IQ) is 1.5 times as intelligent asan average (100 IQ)22INTERVAL SCALEzero point0 temperature does not mean no heat(in F and C)0 IQ does not mean no intelligence50◦F IS not twice as hot as 25◦F.an IQ of 100 is not twice as smart asan IQ of 5023WHY ZERO MATTERSI can create an equivalent interval scalethat preserves all the differencesNEWIQ= OLDIQ+ 20differences are still the same• 150 → 170• 100 → 120• 50 → 70but the ratios are all different 170 isnot 1.5 times 120! Multiplicationmakes no sense!if zero meant absence of trait, I couldnot create an equivalent interval scale,zero would have to


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Purdue PSY 20100 - Lecture Notes

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