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ECU PSYC 2101 - Final Exam Study Guide
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ARCH 350 1st EditionFinal Exam Study Guide• Chi-square• Χ2• Overview• Question from last time?• Analyses with a nominal DV• Analyses with a single nominal variable• Analyses with two nominal variables• A new test!• What makes chi square different?Non-parametric test (measure when it’s nominal or ordinal DV)• What do correlations, regression, z tests, t tests and ANOVA have in common?The DV is continuous; predicting a continuous outcome variable (measured on an interval or ratio scale)• Non-parametric tests• What if your DV is not continuous?• Non-parametric tests allow us to analyze data when the DV is nominal or ordinal.• Limitations of Non-parametric tests• With nominal or ordinal data, we cannot easily use confidence intervals• Non-parametric tests have less statistical power than parametric tests• Gives us a range of possible values that the means can be• The test has “less power” power=probability of correctly rejecting the null• More likely to make a type II error (false negative) = false to reject eh null but there is a difference• The chi square test• There are two different chi square tests:The chi square “goodness-of-fit” test1) Single normal variable to a know population value2) The chi square “test of independence”is there a relationship btw two nominal variables• The test of goodness-of-fit• The chi square test of goodness-of-fit is used with only 1 nominal variableNo other variables are considered.Compare sample results to some know relationship.Example: Are there equal numbers of men and women in class today?• How do we use chi square?• To use the chi square goodness-of-fit test we use the 5 steps of hypothesis testing!• Example• Step #1Population: 1) ECU students2) Students in PSYCH 2101Test: Chi-squared goodness of fit test(uses single, nominal variable = gender)Assumptions: (only 2)1) The DV is nominal (man or woman)2) At least 5 observations per cell (assumption not met)• Step #2 (words only)Null Ho: “The gender breakdown is the same in PSYCH 2101 as it is at ECU”Research H1: “The gender breakdown is not the same in PSYCH 2101 as it is at ECU”• Step #3 (chi squared is always positive & so is the critical value)df= “k-1” à 2 - 1 = 1 (k=categories)E.1 (alpha .05) Χ2=3.84• Step #4EM= 13(.47) = 6.11EM = 13(.53) = 6.89Χ2 = (3-6.11)2 / 6.11 + (10-6.89)2/6.89 à 1.58+1.40=2.98 à Χ2=2.98• Step #5“Fail to reject the null” Χ2(1)=2.98, p>.05.“There is no difference in the gender breakdown between Psych 2101 and ECU ”• Step 1• Populations: 2 populations1 population matching the frequencies in cells we observed1 populations matching the frequencies specified by the null hypothesis• Assumptions:Variable is nominalAt least 5 observations in each cell (10 is better)• Step 2• Null hypothesis – In wordsSpecify the relationship between cells• Alternative hypothesis – In wordsSpecify the alternative:• Step 3• The chi square distribution• Step 3• The only characteristic of the chi square distribution we need is degrees of freedomdf = k -1 K is the number of categoriesUse the df &chi square table (Table E.1)• Step 4• Formula:O = observed frequencyE = expected frequency• Step 4• How do we find E?Determine proportion of responses for each cell under the null hypothesisMultiply each proportion by N to find E for each cell• Step 5• Compare to critical value and make a decision.• Example: Is someone using “loaded” dice?Number Frequency• 1 7• 2 6• 3 6• 4 18• 5 7• 6 6• The test of Independence• The chi square test of independence is used when we have two nominal variables(relationship btw the 2 nominal variables)Example: Is there a relationship between gender and voting in the presidential election?Gender: male or femaleVoting: yes or no**WE use the 5 steps!• Step 1• Populations (4 populations)One population for each cell in our design• Assumptions: same we goodness of fit1) Both variables are nominal (if not nominal than do a different test)2) At least 5 observations per cell• Step 2• Null hypothesis – In wordsSpecify the relationship between cells• Alternative hypothesis – In wordsSpecify the alternative:• Step 3• The chi square distribution• The only characteristic of the chi square distribution we need is degrees of freedomdf = (krow -1)(kcolumn -1) K is the number of categoriesUse the df and chi square table (Table E.1)• Step 4• Formula:O = observed frequencyE = expected frequency• Step 4• How do we find the expected value?• Step 5• Compare to critical value & make a decision• Example: Students and children• Is there a relationship between being a part time student and having children?Asked 229 students.• Example: Gender and votingMen WomenVoted 2792 3591Didn't vote 1486 2131 • Power (effect size & choosing a test)• Overview• Question from last time?• What else can we know from a hypothesis test?Effect sizeConfidence intervalsPower• Choosing a statistical test• Hypothesis Testing• When we do a hypothesis test, there are only two outcomes.If the two means are different• Is there any more information we can get from the data?• Hypothesis testing• Statistically significant does not always mean “very important”Our observed stat is further from zero than our critical valueWith a large enough sample, any difference between means will be significant• Knowing two means differ is only part of the story• Other measures• If hypothesis testing does not tell us enough what does?Effect sizehow differentConfidence intervalsWhat range of values that we might see for the difference between meansPowerAbility to reject the null hypothesis• Effect size• How big is the difference between means?• Significant means differentIt gives no info about how big a difference between mean isReject null means the means are different but doesn’t say how different• Effect size• Effect size – the standardized value that indicates the size of a difference with respect to spread but is not influenced by sample sizeTells us how much two populations don’t overlap• Effect size• Effect size for z or t – Cohen’s d• For zd = ( - µ) / σ• For td = ( - µ) / sd = (difference - µ*) / sdifferenced = (X- Y)/ sPooled*=always 0• Effect size• Cohen’s dSmall 0.2 85% overlapMedium 0.5 67% overlapLarge 0.8 53% overlapDifference between the means which is


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ECU PSYC 2101 - Final Exam Study Guide

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