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Stats Exam 4 Study Guide

by: Julia_K

Stats Exam 4 Study Guide PSYCH-UA 10 - 001

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One and Two way ANOVA, Error terms, MSw and MSbet, F ratio, HSD, LSD, Bonferonni, Scheffe, following up, pairwise and complex comparisons, comparing means and grand means, interactions, experiment...
Statistics for the Behavioral Sciences
Elizabeth A. Bauer
Study Guide
Math, Statistics, Psychology, Science
50 ?




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This 7 page Study Guide was uploaded by Julia_K on Monday April 25, 2016. The Study Guide belongs to PSYCH-UA 10 - 001 at New York University taught by Elizabeth A. Bauer in Spring 2016. Since its upload, it has received 116 views. For similar materials see Statistics for the Behavioral Sciences in Psychlogy at New York University.


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Date Created: 04/25/16
            EXAM 4             Study Guide Chapters 12-14 Chapter 12 – Three or More Groups (One-Way Independent ANOVA) If you run multiple tests within a study  you increase Type 1 error probability. Instead, use ANOVA (analysis of variance). “One way” = one independent variable (factor). So the question becomes: are group means separated or close together?  MSbetween shows how far means are spread out from each other. The variability of group means. MSwithin – the average of these variances. Shows how far scores are generically spread out from means. Known as the error term. The variability of scores around their group means. F = ( MS Between / MS Within )  they both independently estimate population variance but in different ways (not related to each other). 1. Degrees of Freedom:  Df bet = k -1 (where k=number of groups)  Df w = NT – k  Df total = NT – 1 (NT = total number of participants) Xbar G = grand mean (everybody put together  the mean of the means) Example 1: a researcher wants to compare 3 diff. types of therapy to alleviate phobias: general counseling, systematic desensitization, and counter conditioning. (Factor = therapy) 1. The null: mu1 = mu2 = mu3 . When the null is true, F ratio = 1 (b/c there is no difference between the groups). A larger F ratio means there’s a bigger difference between the groups. F cannot be negative. The alternative: the null is not true. 2. Find MSw and MSBet using formulas 3. Find F ratio using Ms w and Ms bet values Then test for significance: 1. Get dfbet = k – 1 = 2 [on the chart, this is the numerator] 2. Get dfw = NT – k = 42 [this is the denominator] 3. Use these values to find the F critical value on table A.7 4. In this case, F calc > F cv  we reject the null. ANOVA Summary Table MS* DF = SS Source SS Df MS - Mean The F ratio Square Between 210.0 2 105 16.3 Within 270.06 42 6.43 (ERROR TERM) Total 480.06 44 In SPSS: Do we have homogeneity of variance? Look at Levene’s box. If sig > 0.05, we have HOV. Varieties of a One-Way ANOVA: -levels can be created or preexisting -fixed vs random effects  Fixed effects ANOVA: choosing factors levels to study  Random Effects ANOVA: many possibilities to be tested, you select a few CHAPTER 13 – Multiple Comparisons (W/O Inflating Type 1 Error Rate) Experiment wise alpha (alpha )EW the total alpha  the probability that an experiment will produce a Type 1 Error. (this increases as # of groups goes up). 1. Figuring out number of t-tests needed (j): k(k-1) / 2 (where k = # of groups) j 2. The probability of making a Type 1 error for that # of tests: 1 – (1 – [alpha] ) You shouldn’t allow multiple t-tests unless you get a significant ANOVA (F)  though a significant F does not tell us which pairs or groups of means are significantly different from each other. POST HOC TESTS: Pairwise comparisons If you have a significant F and 3 groups, then follow up (the same problem from before) with (Fischer’s LSD) 2MS LSDt W cv n   note: use dfw to find tcv on chart LSD = 1.87 Checking for significance: if the difference between a mean pair is bigger than LSD, then it is significant Counseling – Systematic Desensitization = 10 – 6 = 4 (Sig) Counseling – Counter Conditioning = 10 – 5 = 15 (Sig) Systematic Desensitization – Counter Conditioning = 6 – 5 = 1 (Not Sig) But…if you don’t have significant F and have more than 3 groups, then follow up with pairwise Tukey’s HSD. MS HSD  q cv W n  note: look up qcv in table A.11 (“k” across top, and “dfw” down the side) Checking for significance: First, compare ONLY the smallest and largest means. -If the difference between them is greater than HSD, then keep going and compare other pairs of means. -If no, then stop. With HSD, it is possible to find pairs of means sig. different even when the overall ANOVA is not sig. A priori test: Bonferroni t (Dunn’s test): Alpha per comparison (alpha ) PCthe alpha used for each test following an ANOVA Alpha PC= .05 / 4 = 0.0125  this is your adjusted alpha. You compare this to the sig values from the regular t tests for SPSS. Problem: Bonferroni is very conservative – it can make alpha really small. Use the Bonferroni when you know you can eliminate tests from consideration (this must be done before you see the data). Complex comparisons: still comparing two things, but unlike Pairwise, it doesn’t have to be between 2 groups. It’s a difference score involving group means, and we “weight” these means with coefficients. 1. Coefficients: 3, 3, -2, -2  if the coefficients add up to 0, this combination is called a linear contrast. You use it to contrast one group mean from others. This is symbolized by “psi” 2. Use this to find L: 3. To test this for significance: must convert your “L” into an SScontrast. Note: MScontrast will always equal SScontrast !! 4. Calculate the F ratio to test this contrast: F = (MScont) / (MSwithin) 5. Find Fcv (1, dfwithin) 6. If F > Fcv, and the comparison was planned, then this is significant. 7. BUT if the comparison was not planned (you looked at data after), then we need to use Scheffe’s test (instead of Fcv) : Scheffe’s F test: K = # of groups NT= total number of subjects -Compare initial F to Fs. If F > FS, then there is significance and you reject the null. Problems: very conservative. lose a lot of power with Sheffe’s test  only use them when comparisons haven’t been planned. Chapter 14 – Two Way ANOVA (2 independent factors) *Refer to the Arousal and Task problem* A Two Way ANOVA works with not just the Main Effects (Arousal and Task), but the Interaction between them Not working with “groups”, but cells. Balanced design = equal sample sizes in each of the cells. 2X3 table = 2 task difficulties and 3 arousal levels Questions to ask about summary table: 1. How many levels do I have of the row factor? 2 levels 2. How many levels are there of the column factor? 3 levels 3. How many cells does this yield? 6 4. What is the “n” for each cell? 5 5. What is NT? 5*6 = 30 2 Way ANOVA summary table (steps for completing this are down below): SS df MS F Between # # -- -- cells Task # # # # Arousal # # # # Interaction # # # # Within Cells# # # Total # # STEPS: 1. dfBetween: r (c) – 1 dfrow: r-1 dfcolumn: c - 1 dfinteraction: (r - 1) (c - 1) dfwithin: NT – r (c) dftotal: NT -1 1. MSw (same formula, but k = # of cells) 2. SSw = MSw (dfw) 2 3. SSBet = (NT) ( sigma for cell means)  list cell means in calculator and calculate sigma 4. SSrow = NT (sigma for row means) 5. MSrow = SSrow / dfrow 6. SScolumn = (NT) (sigma for column means) 7. MScolumn = SScolumn / dfcolumn 8. SSinteraction = SSBetween – (SSrow + SScolumn) 9. MSinteraciton = SSint / dfint 10.Now we ask: how much is due to task, how much is due to arousal, and how much is due to interaction (or the combination of those 2 factors) So we create F ratios for low, medium, and high arousal: F = MSBet (low) / Msw F = MsBet(med) / MSw F = MSBet (high) / Msw 11.Fcv (dfbetween, dfwithin)  dfbetween corresponds to its specific category. 12.Compare F ratios to Fcv to find significance 13.Is my interaction significant? If yes  other tests (simple effects) 14.If interaction is not significant and significant main effect involves more than two levels,  then use post­hoc tests (either HSD or LSD  denominators are different compared to  other previous tests in One­Way ANOVA) Interactions: F ratio tests the main effects of arousal and difficulty. Interaction – when the effects of one independent variable change with different levels of the other IV. Parallel lines = no interaction. If the lines are not parallel, you have an interaction (yet we don’t know if it’s significant) … When lines are not parallel but go in the same direction, it’s called an ordinal interaction. When the lines are crisscrossed, this is called a disordinal interaction (the effects shift) **As a rule, a significant interaction tells you not to take the main effects as face value, meaning there’s some underlying relationship to consider. Comparing Arousal conditions and task conditions to the grand mean Low Med High Easy 3 6 9 6 Diff 1 4 7 4 2 5 8 5 (Grand mean) Effect of being in:  An easy condition: +1  A difficult condition: -1  A low condition: -3  A medium condition: no effect  A high effect: +3 Sum up (of caffeine example): What we did: Was there an effect in gender? No. Was there a significant interaction? No. Was there a significant effect of one of the factors? Yes – dosage. Following that up with an HSD  we saw that the only significant difference in dosage was between ZERO and SMALL amounts of caffeine.


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