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Understanding Frequency Tables: A Guide to Data Analysis

School
Oakland University**We aren't endorsed by this school
Course
PSY 2510
Subject
Statistics
Date
Dec 11, 2024
Pages
19
Uploaded by AmbassadorFlamingoPerson1299
Frequency tablesSteps:(1) make list down page of each possible value.(2) go one by one through scores making a mark for each next to its value on the list(3) make table showing now many times each was used.(4) figure % of scores for each value•Take frequency of score/value and divide by total number of scores. And multiply by 100 for the percentage.Uses:Describe the dataShows how many scores for each value Makes pattern of data clearerGrouped frequency tablesUsing intervals based on valuesUse when there are many possible valuesGoal: makes it easier for readers to understand.Intervals must be equivalent across the range of scores
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Types of frequency tablesHistograms:Numerical sequence, particular orderContinuity= bars touchNumerical sequence, nominal or categoricalDiscontinuous: ' bars don't touchFrequency polygon: Used for comparing sets Of dataA line moves from point to pointCreates a mountain peak skyline.
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Shapes of frequency graphs.Modality:Unimodal: one high areaBimodal: two high areasMultimodal: over 2 high areasRectangular: similar frequenciesUnimodal: grades of students in a classAppox/ bimodal: uses of people in toddler area in the morning Appox/ rectangular: tossing a die orAges in a 4th grade class
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Skewed distributionsSkewed to the left= negativeSkewed to the right = positiveE.g., on easy examEg. Number of childrenNormal and kurtotic distributions:Normal curve: specific and mathematically defined bell shaped frequency distribution that is symmetrical and unimodalKurtosis: extent to which a . frequency distribution deviates from a normal curve:
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Chapter 2: measures of Central tendency and variability.How to further summarize data to facilitate comparisons?•Measures of Central tendency.•Measures of variabilityCentral tend/Most typical or most representative value of A group of scores→mean→mode→medianMean:Sum of all scores divided by the # of scoresGreek letter sigma stands for "sum of"
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Mode:Most representative, common single value score (score, category) in a distributionUsually not a good way of describing the central tendency of the scores.•You can change some scores w/o changing mode.Some researchers compare mode to mean to show that distribution is not perfectly symmetrical.Ex:Mean = modeMean < modeUsually a measure of Central tendency for nominal variables.Which religion has the most people in itWhat time of day people prefer to go for dinnerThere can be more than on mode: bimodal or multimodal distributionsMedian:Score that divides distribution exactly in half.Exactly 50% of individ in a distribution have scores above the median.Middle score when all are arranged from low to high = 3Median = 2.5Sometimes, the median is better than the mean or mode as a rep/ value for a group of scoresWith extreme scores, annual income.Rank ordered variablesAnnual income, reaction times, price of houses, etc.--rarelyuseresearch!!123Semina↑1234Trarelyused!
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In a normal distribution, (normal curve), mean, median, and mode coincideMean = mode = medianMean is most stable measure of central tendency b/c all scores are included.Exam gradesAge of deathBuilt in obsolescenceHeightWeightIQ# of recalled wordsPrice of housesAnnual incomeGrades on difficult examNumber of kids in householdMeasures of variability:Measures of CT are not enough to describe/compare dataSo, we need measures of variabilityGoal: know how spread out the scores are in a distribution.How close/far from the mean are the scores in distribution?Variance and deviationCompare means: how far apart are means from each other?Compare variability: now much scores vary?You need both..-⑪meanmeanmeanneedde2->negdirectaperfectly~pos/directionsymmetricaluskewright---
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The normal curve table and Z scoresFiguring out z or raw scores from percentagesHours worked in a weekHow many hours a person has to work to be in the top 5?Hours/week scores①DrawapicoftheM=28normalcurve,andshade20areaforyourpercentageSD=5.83usingthe50%-39%-14%16percentages.282525%--as202%14%34%34%14%2%17-3-2+10+1+2+31-2scres1083414.1720258331.662)makearoughestimateoftheZscoreswheretheshadedareaStops(5%).~AppoxIscre:1.73)Findtheexact2scoreusingnormalcurvetable(subtracting58)frompercentageifnecessary,Ontable:%intail=5.05%=IscoreisKe4)checkifexactIscoreisclosetoestimate5)changeItoraw:(164)(583)+20=X=(2)(SD)+M=9.56+20=29.56hours
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Samples and populationPopulation:Entire group of people to which a researcher intends the results of a study to apples.Example: all students in this class.Larger group to which inferences are made on the basis of the particular set of people (sample) studied.Sample:Scores of the particular group of people studied.Considered to be representative of the scores in some larger populationSome students at Oakland University randomly selected.We made inferences about populations based on info from samples.Basis:Symbols:Mean:Standard deviation:Variance:Population parameter (usually unknown)Greek lettersSample statistic (figured from known data)Roman lettersProbability•p•p < 0.5Normal distribution as a probability distribution:Range of probabilities:Proportion: 0 to 1%: from 0% to 100% (proportion * 100)↑M5SD22SD?possiblesuccessfulcutcomesAllpossibleoutcomes~014634%34%(4%20%
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Psychologist is most likely to calculate Z scores in order to compareScores obtained from two scales!Symbol for sample stats: RamanPopulation stats: Greek40 workers at a large factory: samplePopulation is all workers (not just 40).Probability:HomeworkNotesChapter3successfuloutsomes-possible58+108=150=.3or30%350+50+180sajYallpossibleoutcomes
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Cohen's effect size conventions.•Small: d = .2•Med: d = .5•Large: d = .8Effect size and statistical significance:•In general, the larger the effect size, the more likely the result is significant.•However, a result can have a large effect size and not be significant•Probably b/c sample is too small•A result can have a small effect size and be significant•Probably b/c sample is too large.Effect size indicates practical significance.Example:Pop l: students told positive personality qualities.Pop 2: students in general.If =Effect size?Research hypothesis; Pop 1 would give on average a higher attractiveness rating to person in photo than population 2.If =Effect size?d=4,Mzo#208,2=48;N=64,M=220,Om=b;2=3.33>1.64->rejectnull(p=.0S)d=M,M3=220- 288=.42548M=200,8=48;N=64,M=210,um=6;2=167>1.64->rejectnull(py.0S)d=M=2020-
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Step5:gathercharacteristicsofCD(nulldistrp&um=M=5.13Populationvariancefromsamplescores:M=x=7+k5+65+S+8+2.5+0+6+45+18=410=n9=M->DeviationScoreScoreMean(score-mean)SaDeviationScare76.90.100.8/6.S69-0.48216n90400.16l691983.Le686.91.181.217.56.90.600.3686.91-181.214.9-8.90081us69=248S7 b184.93.189.Let5:696.9O22.9S2=z(xMy=229=29=2--N1
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Stder.ofthedist.ofmeans:=F·=as=theshapeofthecomparisondistributionwillbeadistributionw9degreesoffreedom(df=u-1=101=9).
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Step3:determinecutoffsample+scoreonCDwherenullisrejectedlevelofSig:a=0.05(p1.05).non-directional,two-tailedhypothesis.cutoff+score=-2.262and+2.262Step4:determineSample'sScoreonCD.Mm=5.7Sm=0.5M=6.9=>M-Mm=69 - 57==2SM0.SStep5:rejectthenulk?The+scoreoftheSample'smean(G.4)ismoreextremethanthemaximumcutoff+scoreintheCD(+2.262)So,werejectthewullwhasigllevelof5%(p-.05).Thus,wecanconcludethescoresfrompopulation (andpop2comefromdiffpopulations,supportingtheresearchhypoth4T2:figureeffectsize,Pop1:M=6.9⑤d=Mon=6.90.514Pro2:M=0.5,52=2.541.591.59&st=1=03=VERGE
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Exam3NotesStep1:-identifypopulations-stateresearch/fullhypothesisStep2:DeterminecharacteristicsofCDIfBetweendfwithinTheCDwillbeaFdistributionwith?and?degreesoffreedinStep3:DeterminecutoffsampleScoreofCDidentifylevelofsig.-Between-groups(numerator)degreesoffreedom-?-Within-groups(denominator)degreesofFreedom=?-LookatFtableforcutoffFscore.Step4:DetermineSample'sscore1figurewithingroupsestimateofpopulationvarianceatableforeachgroupwith~scorelrating,Mean,DealfromMean,Sq.DerfromM.visiblycalculateMandS2foreachtable.2.Averagethevariances-Calculatewithin:S+SNaroups
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FiguringtheBetween-GroupsEstimateofthePopulationVariance.1.estimatevarianceofdistributionofmeans-tableSampleMeansGrandMeanDerfromGMSq,Dev,fromGroupMeans(M)CGM)(M-GM)GMCM-GM)2GlMlG2M2G3MEE:total8total-calculateoutGMandSim2.Figuretheestimatedvarianceofthepopulationofindividualscores.-calculateSBetwee-CalculateFRatioStep5:Rejecthull?No?Yes?-identifyFratioandcutoff(withlevelofsig)·-Statereasoningbehindwhywedidordidnotreject-Ifwedid,westate:-F(?,?)=Fratio,p<.OS levelofsig).
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PartBofProblem:1.PlannedComparisonsblu+and2ndgroupsstatewithingroupspopulvarianceestimatefromStep4.Figurethebetween-groupspopulationvarianceestimateestimatevarianceofdisofmeansGroupsSampleGMDerfromSG.Dev.fromMeansM)GM/m-GM)GM(M-GM)?1stGroupandGroup2:totalOtotal-calculateGMandSir2.Figuretheestimatedvarianceofthepopulationoftheindividualscores.-SetweenfigureFratioandcomparetocutoffF=SBetweenStwithinThe.05(1)intoffforaFdistributionsw?and?degreesoffreedomis(?)↑Istheplannedcomparisonsignif?Rejectnull?Repeatfor1stand3RPgraps.
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