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UA PSY 230 - Psychological Measurement

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Psych 230 Psychological Measurement and StatisticsSlide 2This Time….Statistical Testing1. Decide which test to useAssumptionsChi-SquareSlide 8One-Way Chi-SquareProblem2. State the Hypotheses3. Calculate the obtained value (2obt)Slide 13Slide 14Slide 15Slide 164. Calculate the critical value2 crit and 2 obt5. Make our ConclusionSlide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Problem - Your turnSlide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Two-Way Chi-SquareSlide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Slide 61Slide 62Slide 63Slide 64Slide 65Populations and SamplesDescriptive and Inferential StatisticsStatistics and ParametersExperimental StudiesCorrelational StudiesWhich Scale?Things you need to knowThings you need to know (continued)Slide 74Know how to Know how to (continued)Slide 77Slide 78Psych 230Psychological Measurement and StatisticsPedro WolfDecember 9, 2009This Time….•Non-Parametric statistics•Chi-Square test–One-way–Two-wayStatistical Testing1. Decide which test to use2. State the hypotheses (H0 and H1)3. Calculate the obtained value - calculate r4. Calculate the critical value (size of α)5. Make our conclusion1. Decide which test to use•Are we comparing a sample to a population?–Yes: Z-test if we know the population standard deviation–Yes: One-sample T-test if we do not know the population std dev–No: Keep looking•Are we looking for the difference between samples?–Yes: How many samples are we comparing?•Two: Use the Two-sample T-test–Are the samples independent or related?»Independent: Use Independent Samples T-test»Related: Use Related Samples T-test–More than Two Groups: Keep looking•How many independent variables–One: Use a One-way ANOVA–Two: Use a Two-factor ANOVA–No: Keep looking•Are we looking for the relationship between variables?–Yes: Use the Correlation test•Are we examining the frequencies of categorical, mutually exclusive classes?–Yes: How many variables are we examining?•One: Use one-way Χ2•Two: Use two-way Χ2Assumptions•Mutually exclusive categories–One category per subject•Independence of observations–equivalent criteria for entrance into each category•Sufficient Sample Size–General rule: none of the expected frequencies be less than fiveChi-Square•Chi-Square is used when subjects are measured using a nominal variable–gender; political preference; handedness; nationality….•With these variables, we do not measure an amount, but instead we count the frequency of observations in each of the categories–are psychology majors more likely to vote Republican or Democrat?•We are interested in proportionsChi-Square•In a Chi-Square test, we compare the actual frequencies of occurrence with what we would expect to happen by chance•Two types of Chi-Square test•One-way: we have one variable•Two-way: we have two variablesOne-Way Chi-Square•We use this test when data consist of frequencies spread amongst different categories of a single variable–Are men or women more likely to smoke?–Is Coke or Pepsi more preferred by U.S. soda drinkers?–Are different ethnic groups well represented at the UofA?Problem•In a Psyc 230 class, are there equal numbers of people from rural, suburban and urban backgrounds?–Rural: 23–Suburban: 119–Urban: 50•3 levels, but still just one variable–One-way Chi-Square2. State the Hypotheses•H0 : all frequencies are equal–Rural, suburban and urban backgrounds are equally represented in the class•HA : not all frequencies are equal–Rural, suburban and urban backgrounds are not equally represented in the class3. Calculate the obtained value (χ2o b t)Rural Suburban Urban TotalObserved (fo) 23 119 50 192Expected (fe)3. Calculate the obtained value (χ2o b t)Rural Suburban Urban TotalObserved (fo) 23 119 50 192Expected (fe) 192/3 192/3 192/3fein eachcateg ory =Nk3. Calculate the obtained value (χ2o b t)Rural Suburban Urban TotalObserved (fo) 23 119 50 192Expected (fe) 64 64 64 1923. Calculate the obtained value (χ2o b t)Rural Suburban Urban TotalObserved (fo) 23 119 50 192Expected (fe) 64 64 64 192χ2= Σ fo− fe2fe3. Calculate the obtained value (χ2o b t)Rural Suburban Urban TotalObserved (fo) 23 119 50 192Expected (fe) 64 64 64 192χ2= Σ fo− fe2feχ2o b t = Σ[(fo-fe)2 / fe ][(23-64)2 / 64] + [(119-64)2 / 64] + [(50-64)2 / 64] = [(-41)2 / 64] + [(55)2 / 64] + [(-14)2 / 64] =[ 1681 / 64] + [ 3025 / 64] + [ 196 / 64] =26.266 + 47.266 + 3.062 = 76.5944. Calculate the critical value•Assume α=0.05•Always a two-tail test with Chi-square•Look up Table Q on page 572–“Critical values of Chi-square: The χ2 tables”•df = k - 1 = 3 - 1 = 2•χ2c r i t for 2 degrees of freedom and α = 0.05 is 5.99χ2 c r it and χ2 o b tχ2 c r it = 5.99χ2 o b t = 76.5945. Make our Conclusion•χ2c r it = 5.99•χ2o b t = 76.594•χ2o b t is inside the rejection region, so we reject H0 and accept HA•We conclude that there is a significant difference in frequencies between our groups–Rural, suburban and urban backgrounds are not equally represented in our classProblem•In a Psyc 230 class, does the proportion of males and females in the class match the proportion of males and females who are psychology majors?–Psych majors: 75% female, 25% male–Females in the class: 142–Males in the class: 562. State the Hypotheses•The exact hypothesis will depend on the specific question we are asking•H0 : frequencies in the class are equal to the psych population–75% of our class are female, 25% are male•HA : frequencies in the class are not equal to the psych population–75% of our class are not female and 25% are not male3. Calculate the obtained value (χ2o b t)Females Males TotalObserved (fo) 142 56 198Expected (fe)3. Calculate the obtained value (χ2o b t)Females Males TotalObserved (fo) 142 56 198Expected (fe) (198*0.75) (198*0.25)3. Calculate the obtained value (χ2o b t)Females Males TotalObserved (fo) 142 56 198Expected (fe) 148.5 49.5 1983. Calculate the obtained value (χ2o b t)Females Males TotalObserved (fo) 142 56 198Expected (fe) 148.5 49.5 198χ2= Σ fo− fe2feχ2o b t = Σ[(fo-fe)2 / fe ][(142-148.5)2 / 148.5] + [(56-49.5)2 / 49.5] = [(-6.5)2 / 148.5] + [(6.5)2 / 49.5] =[ 42.25 / 148.5] + [ 42.25 /


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UA PSY 230 - Psychological Measurement

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