Study Guide for Midterm Study Guide for Exam #2 Psy 52 1 Logistic Regression When would you use logistic regression ( i.e. how would your DV and IVs be distributed)? Outcome variable is dichotomous Predictor variable(s) are continuous or categorical NOT appropriate for categorical DV’s Like Multiple Regression , logistic regression: Examines the strength and direction of relationships, Makes predictions – GROUP MEMBERSHIP Can add interactions or nonlinear trends to the model When would you use an ordinal logistic regression ? This is a variation of the basic logistic regression. It differs only in that the outcome variable is ordinal rather than dichotomous Instead of comparing category A to B it creates a cut-off and compares Categories: A and B to C or A to B and C It is not limited by the number of categories More categories create more complex analyses What type of statistic is used to compute statistical relationships in logistic regression? Chi Square measures discrepancy between expected frequencies and observed frequencies ( Properly classified vs. misclassified ) Wald Chi Square Is variable a significant predictor? Is number of years smoking a significant predictor of whether or not one would stop smoking Report: b, Wald ( x 2 ), df, p-value What effect size measurements are used in logistic regression ? Effect size = % you are correct in classifying them in group McFadden’s Rho Square r 2 between .2 and .4 is good Cox and Snell R 2 conside rs sample size, but may underest imate Nagelkerke’s R 2 adjusts C ox &S nells ’s R 2 , suitable for better models. Percent of correct classification is also used to assess the fit of a model (prediction vs Observed) 55% of the predictions are correct Cancer No Cancer Cancer 25 % 25 % No Cancer 20 % 30 % Odds ratio is often used to estimate an effect size for a variable ( AD / BC ) Smoker Non Smoker Cancer 40 10 No Cancer 50 100 What are the assumptions of a logistic regression ? Does Assume Linear relationships between continuous predictors and the logit transformation of the outcome variable The outcome variable is categorical, either dichotomous or ordinal Does NOT assume Homogeneity of variance Many of the other concerns that we have with Multiple Regression, apply to Logistic Regression ANOVA, ANCOVA, MANOVA, MANCOVA When would you use the following tests: Between-subjects ANOVA Single outcome variable is continuous Single predictor (independent) variable is categorical Units in categories are independent (different) No limit on the number of categories, commonly known as conditions, group , s or factor levels For K < 3, t-test may be simpler Use a t-test when DV is dichotomous, use ANOVA when there are more than 2 levels to the DV [i.e. Average, Elevated, Extremely Elevated] With a t-test you can say: There was a significant difference between clinical child students on depression levels (High vs. Low) With a ANOVA you can say: There was significant difference between clinical child students and level of depression (post-hoc), such that there was a significant difference between average and extremely elevated Adding conditions decreases degrees of freedom Within-subjects ANOVA Units in categories are dependent Same participants, different conditions Same participants, different times of observation Different participants who are matched Example: Is there a change in graduate students’ optimism over time? Advantages Reduces individual differences = less error Increases power Disadvantages Carry-oven effect are problematic Time related threats to validity are possible Mixed D esign Fac torial ANOVA (IV1 + IV2 + DV) Have more than one independent variable Test effects for each independent variable (factor) Main Effect for Factor A Compare marginal means of the levels of Factor A Main Effect for Factor B Compare marginal means of the levels of Factor B Test effects of the unique combination of each level of each factor Interaction between Factor A and Factor B Compare group means to marginal means One factor depends on the level of the other factor Each factor can have 2+ groups/levels (no limit on # of factors) The number of levels (groups) for one factor does not have to be the same as the number of levels (groups) for the other factors Factors can be: All between-subjects All within-subjects Mixed design, both between and within More factors, more complex analyses ANCOVA (IV + Covariate + DV) Adds a covariate to a model to extract extra variation from the treatment effects. The covariate is simply treated as “noise” The purpose is to give a clearer relationship between the outcome and predictors of interest. The within group variance is reduced by accounting for the relationship between the covariate and outcome variable. Types of Covariates: Categorical (blocking) Continuous (combines regression with ANOVA) Covariate in ANCOVA Suppressor Variable When the covariate is continuous, an ANOVA is computed by comparing regression equations that measure the relationship between the covariate and the outcome variables. MANOVA (IV + DV + DV) Advantages Replacement for Repeated Measures Design No assumption of Sphericity Reduction of experiment-wise Type 1 error compared to ANOVA for multiple DVs ; Control of family-wise type I error across multiple indicators of a behavior Can be a more powerful design ; Allows for the examination of multiple indicators of a construct ; If DVs are negatively correlated Disadvantages Need larger N than ANOVA ( Rule of Thumb X K DVs ) Additional assumptions over ANOVA Multicolinearity Multivariate Normality Multivariate Outliers Homogeneity of Variance-Covariance Complexity of design Two stages of Nature of Effect tests needed Can be LESS powerful than ANOVA If DVs are positively correlated or uncorrelated Factorial MANOVA we have More than one categorical predictor variable More than one continuous outcome variable Any significant interactions require simple main effects tests for each outcome variable MANCOVA The decision to use a MANCOVA instead of a MANOVA is based on the same logic and hypotheses reasoning as ANOVA vs ANCOVA Covariate can be continuous or categorical Covariate is used to account for variation it contributes to the dependent variables Including a covariate in the model can reduce or increase the F ratio Only accounts for linear relationships Must check assumption What are post hoc tests used for ? Post hoc tests determine which groups are different from each other. Paired comparisons that do not inflate Type I error. Types of Post Hoc tests: Shefee: ANOVA comparing only 2 groups Tukey’s HSD: based on mean diff’s, limited to equal sized groups Newmann-Keuls LSD: no control for Type 1 ; only use when you can’t find the difference in other post hoc tests Wh at is the difference between a main effect and a simple main effect ? Main Effect: Comparing marginal means of levels of Factor A and levels of Factor B Means for each level of one factor across levels of the other factors If marginal means differ = chance for a main effect Main effects look at significant trends in the data Simple Main Effect: ANOVA test for a significant interaction Examines each level of the IV’s Tests to see how each level of Factor A was effected by Factor B and how each level of Factor B was effected by Factor A ON the DV When would you include a variable as a covariate instead of as an independent variable? Not all extra variance should be removed -a n alternative is to examine differences between “extra” factors Include as a covariate when you want to extract variation from the treatment effects so that there is a clearer relationship between the outcome and predictors of interest; all extra variance should be removed Include as an independent variable when you want that variable to account for an alternative explanation of the difference between factors What is sphericity? The variance of the difference between the levels of the IV are equal Homogeneity of variance for within subjects Repeated Measures and when k>2 IV Sphericity is an important assumption of a repeated-measures ANOVA. It refers to the condition where the variances of the differences between all possible pairs of groups (i.e., levels of the independent variable ) are equal. The violation of sphericity occurs when it is not the case that the variances of the differences between all combinations of the groups are equal. If sphericity is violated, then the variance calculations may be distorted, which would result in an F-ratio that would be inflated. Sphericity can be evaluated when there are three or more levels of a repeated measure factor and, with each additional repeated measures factor, the risk for violating sphericity increases. If sphericity is violated, a decision must be made as to whether a univariate or multivariate analysis is selected. If a univariate method is selected, the repeated-measures ANOVA must be appropriately corrected depending on the degree to whi ch sphericity has been violated - taken right off Wikipedia What statistics are available to correct for a violation of the sphericity assumption? Mauchley’s Test - test the assumption of sphericity; we want p > .05, we have confirmed sphericity Bartlett’s Test Which of those adjustments are optimal ? Greenhouse-Geisser Huynt-Feldt Lower Bound When spericity is violated, run a Mauchly’ s Test (want it to be in significant, greater than .05) If Mauchy’ s Test is greater than .05 , run a MANOVA If Mauchly’ s Test is less than .05 : examine homogeneity of variance, run Huynh-Feldt/Greehouse-Geisser What are the four different types of statistics used in SPSS when testing MANOVAs? When would you use each of them? MANOVA Omnibus Run a MANOVA to look for effects across all DV’s at once ANOVA Omnibus If MANOVA is significant , examine ANOVA’s for each DV Post Hoc or Planned Comparison tests If ANOVA is significant, run post hoc tests or planned comparisons to examine the nature of the effect for each DV Simple Main Effects If the ANOVA is significant and you have an interaction , run simple main effects tests to examine the nature of effect for each DV Why might I get significant univariate tests, but not a significant multivariate test? Univariate tests may not control for alpha inflation p = .02 is really p = .06 Multivariate tests examine the correlations between the dependent variables Once these relationships are considered the power of the tests may be affected Instead of examining mean differences for a single outcome, multivariate tests examine multi- dimensional mean differences Centroid is a multidimensional (mutivariate) mean Aggregated by weighted means What are the assumptions for a MANCOVA? Assumptions for a MANOVA: Multivariate Normality Assumes that all of the dependent variables are normally distributed Homogeneity of Variance (and Covariance) Assumes similar variances between DVs and across other factor levels (when using multiple predictors) Box’s M is used to test this Homogeneity of Regression (MANCOVA) There are linear relationships between each dependent variable and the covariate Absence of Multicolinearity Highly correlated DVs are redundant Conditions which must be met to use any (M)AN(C)OVA 1. Dependant variable(s) must be continuous and normally distributed 2. Observations between subjects are independent 3. Group variances are homogeneous 4. Independent variables must be categorical (ordinal or nominal) What is profile analysis? Profile Analysis can only be used when the same scale is used for each dependent variable Grade (percent) on a statistics, psychpathology, and vocational psych exams Verbal and Quantitative GRE scores (not writing) Be able to (Logistic Regression) compare models in terms of their fit using -2LL A Logistic Regression was conducted to examine whether high school GPA, ACT score, mother’s and father’s years of education, and student’ fall semester GPA predicts membership into the Saluki Advantage Program . High school GPA did not significantly predict membership in the Saluki Advantage Program, B = -0.28, χ 2 (1) = 0.76, p = 0.38. ACT score did not significantly predict membership in the Saluki Advantage Program, B = 0.09, χ 2 (1) = 2.91, p = 0.09. Mother’s years of education did not significantly predict membership in the Saluki Advantage Program, B = 0.08, χ 2 (1) = 0.65, p = 0.42. Father’s years of education significantly predicted membership in the Saluki Advantage Program, B = 0.26, χ 2 (1) = 8.25, p = 0.004, such that those students whose father’s had more years of education were more likely to become members of the Saluki Advantage Program. Student’ s GPA for the f all semester significantly predicted membership in the Saluki Advantage Program, B = 0.78, χ 2 (1) = 7.90, p = 0.005, such that those st udents with higher GPA for the f all semester were more likely to become members of the Sal uki Advantage Program. Father’s years of education and and fall s emester GPA were the only significant predictors in the first model. Model Summary Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square 1 170.778 a .187 .253 a. Estimation terminated at iteration number 5 because parameter estimates changed by less than .001. Classification Table a Observed Predicted SalukiAdv Percentage Correct no yes Step 1 SalukiAdv no 74 16 82.2 yes 30 30 50.0 Overall Percentage 69.3 a. The cut value is .500 Variables in the Equation B S.E. Wald df Sig. Exp(B) Step 1 a HSGPA -.284 .325 .764 1 .382 .753 ACT .091 .053 2.906 1 .088 1.095 MomDegree .080 .100 .645 1 .422 1.083 DadDegree .255 .089 8.251 1 .004 1.291 Fl_04_GPA .777 .276 7.903 1 .005 2.174 Constant -8.571 1.905 20.243 1 .000 .000 a. Variable(s) entered on step 1: HSGPA, ACT, MomDegree, DadDegree, Fl_04_GPA. compute the predicted probability of being in a condition from regression coefficients compute odds of being in a condition from regression coefficients Be able to interpret SPSS results (in APA format when appropriate) for : A one-way ANCOVA was conducted to examine the relationships between therapist and PTSD symptomology. Depression scores were used as a covariate. After controlling for depression scores, there was not a significant relationship between therapist and PTSD symptoms, F (2,96)=2.20, p = .12. The client’s therapist did not impact changes in PTSD symptoms when controlling for the client’s depression symptoms. Tests of Between-Subjects Effects Dependent Variable: PCL Post Traumatic Stress Disorder Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 4923.050 a 3 1641.017 14.925 .000 Intercept 165.022 1 165.022 1.501 .224 Depression 3607.757 1 3607.757 32.813 .000 therapist 484.733 2 242.366 2.204 .116 Error 10555.110 96 109.949 Total 113322.000 100 Corrected Total 15478.160 99 a. R Squared = .318 (Adjusted R Squared = .297) A one-way MANOVA was conducted to examine the relationship between client’s sex and PTSD, State Anxiety, and Trait Anxiety scores. There was a significant relationship between clients sex and clients symptomology, = 0.92, F (3,96) = 2.84, p = .04 . Univariate ANOVAs indicated there was a significant relationship between client’s sex and PTSD symptoms, F (1,98) = 4.84, p = .03 , partial eta squared = .05 . This was a small effect. There was not a significant relationships between client’s sex and State Anxiety symptoms, F (1,98) = .16, p = .69; and client’s sex and Trait Anxiety symptoms, F (1,98) = .90, p = .35. This suggest that females ( M =33.98, SD =12.69) reported significantly higher PTSD symptoms than males ( M =28.58, SD =11.84). There were no other significant differences in male and female scores for State or Train Anxiety. Descriptive Statistics sex Mean Std. Deviation N PCL Post Traumatic Stress Disorder female 33.9800 12.68534 50 male 28.5800 11.83576 50 Total 31.2800 12.50380 100 STAI-State Anxiety female 35.2200 12.50843 50 male 36.2000 11.70383 50 Total 35.7100 12.06154 100 STAI-Trait Anxiety female 36.8600 10.95447 50 male 38.8400 9.91466 50 Total 37.8500 10.44212 100 Multivariate Tests a Effect Value F Hypothesis df Error df Sig. Partial Eta Squared Intercept Pillai's Trace .939 492.234 b 3.000 96.000 .000 .939 Wilks' Lambda .061 492.234 b 3.000 96.000 .000 .939 Hotelling's Trace 15.382 492.234 b 3.000 96.000 .000 .939 Roy's Largest Root 15.382 492.234 b 3.000 96.000 .000 .939 sex Pillai's Trace .081 2.838 b 3.000 96.000 .042 .081 Wilks' Lambda .919 2.838 b 3.000 96.000 .042 .081 Hotelling's Trace .089 2.838 b 3.000 96.000 .042 .081 Roy's Largest Root .089 2.838 b 3.000 96.000 .042 .081 a. Design: Intercept + sex b. Exact statistic Tests of Between-Subjects Effects Source Dependent Variable Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared Corrected Model PCL Post Traumatic Stress Disorder 729.000 a 1 729.000 4.844 .030 .047 STAI-State Anxiety 24.010 b 1 24.010 .164 .687 .002 STAI-Trait Anxiety 98.010 c 1 98.010 .898 .346 .009 Intercept PCL Post Traumatic Stress Disorder 97843.840 1 97843.840 650.118 .000 .869 STAI-State Anxiety 127520.410 1 127520.410 869.140 .000 .899 STAI-Trait Anxiety 143262.250 1 143262.250 1312.521 .000 .931 sex PCL Post Traumatic Stress Disorder 729.000 1 729.000 4.844 .030 . 047 STAI-State Anxiety 24.010 1 24.010 .164 .687 .002 STAI-Trait Anxiety 98.010 1 98.010 .898 .346 .009 Error PCL Post Traumatic Stress Disorder 14749.160 98 150.502 STAI-State Anxiety 14378.580 98 146.720 STAI-Trait Anxiety 10696.740 98 109.150 Total PCL Post Traumatic Stress Disorder 113322.000 100 STAI-State Anxiety 141923.000 100 STAI-Trait Anxiety 154057.000 100 Corrected Total PCL Post Traumatic Stress Disorder 15478.160 99 STAI-State Anxiety 14402.590 99 STAI-Trait Anxiety 10794.750 99 a. R Squared = .047 (Adjusted R Squared = .037) b. R Squared = .002 (Adjusted R Squared = -.009) c. R Squared = .009 (Adjusted R Squared = -.001) Factorial MANOVA (Interaction): A 2 (male vs. female) X 3 (Cashel vs. Gilbert vs. Rodriguez) Factorial MANOVA was conducted to determine the relationship between client’s sex and therapist on PTSD, State Anxiety, and Trait Anxiety symptoms. There was a significant interaction between client’s sex and therapist on symptomology, = 0.7 2, F ( 6,184 ) = 5.36 , p > .0 01, partial eta squared = .15. The interaction was a moderate effect. Simple main effects were conducted to determine the nature of the interaction. Among those who had Cashel as at therapist, there was a significant difference between sex and State Anxiety scores, such that Cashel’s male clients ( M =42.00, SD =11.86) reported significantly higher State Anxiety symptoms than Cashel’s female clients ( M =30.00, SD =10.54). There were no other significant differences between sex and therapist on PTSD symptoms or State Anxiety. Multivariate Tests a Effect Value F Hypothesis df Error df Sig. Partial Eta Squared Intercept Pillai's Trace .941 493.032 b 3.000 92.000 .000 .941 Wilks' Lambda .059 493.032 b 3.000 92.000 .000 .941 Hotelling's Trace 16.077 493.032 b 3.000 92.000 .000 .941 Roy's Largest Root 16.077 493.032 b 3.000 92.000 .000 .941 sex Pillai's Trace .072 2.366 b 3.000 92.000 .076 .072 Wilks' Lambda .928 2.366 b 3.000 92.000 .076 .072 Hotelling's Trace .077 2.366 b 3.000 92.000 .076 .072 Roy's Largest Root .077 2.366 b 3.000 92.000 .076 .072 therapist Pillai's Trace .194 3.329 6.000 186.000 .004 .097 Wilks' Lambda .814 3.326 b 6.000 184.000 .004 .098 Hotelling's Trace .219 3.323 6.000 182.000 .004 .099 Roy's Largest Root .158 4.911 c 3.000 93.000 .003 .137 sex * therapist Pillai's Trace .279 5.031 6.000 186.000 .000 .140 Wilks' Lambda .724 5.362 b 6.000 184.000 .000 .149 Hotelling's Trace .375 5.689 6.000 182.000 .000 .158 Roy's Largest Root .361 11.182 c 3.000 93.000 .000 .265 a. Design: Intercept + sex + therapist + sex * therapist b. Exact statistic c. The statistic is an upper bound on F that yields a lower bound on the significance level. Tests of Between-Subjects Effects Dependent Variable: STAI-State Anxiety therapist Source Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared Cashel Corrected Model 1178.182 a 1 1178.182 9.472 .004 .234 Intercept 42414.545 1 42414.545 340.988 .000 .917 sex 1178.182 1 1178.182 9.472 .004 .234 Error 3856.000 31 124.387 Total 46516.000 33 Corrected Total 5034.182 32 Gilbert Corrected Model 129.889 b 1 129.889 .758 .390 .023 Intercept 46535.536 1 46535.536 271.531 .000 .895 sex 129.889 1 129.889 .758 .390 .023 Error 5484.229 32 171.382 Total 52754.000 34 Corrected Total 5614.118 33 Rodriguez Corrected Model 280.534 c 1 280.534 2.607 .117 .078 Intercept 38117.625 1 38117.625 354.280 .000 .920 sex 280.534 1 280.534 2.607 .117 .078 Error 3335.344 31 107.592 Total 42653.000 33 Corrected Total 3615.879 32 a. R Squared = .234 (Adjusted R Squared = .209) b. R Squared = .023 (Adjusted R Squared = -.007) c. R Squared = .078 (Adjusted R Squared = .048) Descriptive Statistics sex therapist Mean Std. Deviation N PCL Post Traumatic Stress Disorder female Cashel 38.7778 11.37880 18 Gilbert 28.1429 10.70483 14 Rodriguez 33.7222 13.93601 18 Total 33.9800 12.68534 50 male Cashel 31.1333 11.21776 15 Gilbert 25.4500 11.27865 20 Rodriguez 30.2000 12.96258 15 Total 28.5800 11.83576 50 Total Cashel 35.3030 11.78051 33 Gilbert 26.5588 10.96328 34 Rodriguez 32.1212 13.41118 33 Total 31.2800 12.50380 100 STAI-State Anxiety female Cashel 30.0000 10.53845 18 Gilbert 39.5714 13.99293 14 Rodriguez 37.0556 11.92364 18 Total 35.2200 12.50843 50 male Cashel 42.0000 11.85628 15 Gilbert 35.6000 12.43679 20 Rodriguez 31.2000 8.09938 15 Total 36.2000 11.70383 50 Total Cashel 35.4545 12.54265 33 Gilbert 37.2353 13.04319 34 Rodriguez 34.3939 10.62997 33 Total 35.7100 12.06154 100 STAI-Trait Anxiety female Cashel 40.1667 9.91879 18 Gilbert 37.8571 11.71362 14 Rodriguez 32.7778 10.60830 18 Total 36.8600 10.95447 50 male Cashel 41.9333 12.46404 15 Gilbert 37.6500 8.83936 20 Rodriguez 37.3333 8.24332 15 Total 38.8400 9.91466 50 Total Cashel 40.9697 11.00138 33 Gilbert 37.7353 9.95234 34 Rodriguez 34.8485 9.73756 33 Total 37.8500 10.44212 100 Factorial ANOVA (main effect): A 2 (male vs. female) X 3 (Cashel vs. Gilbert vs. Rodriguez) Factorial MANOVA was conducted to determine the relationship between client’s sex and therapist on PTSD, State Anxiety, and Trait Anxiety symptoms. There was a significant main effect for therapist on symptomology, = 0.81 , F ( 6,184) = 3.32 , p = .0 04, partial eta squared = .10. This was a moderate main effect. There was not a significant main effect for sex on symptomology, = 0.93 , F ( 6,184 ) = 2.37 , p = .0 8. A Tukey’s HSD post hoc test was conducted to determine the nature of the main effect. There was a significant difference between Cashel’s clients and Gilbert’s clients reports of PTSD symptoms, such that Cashel’s clients ( M =35.30, SD =11.78) reported significantly higher PTSD symptoms than Gilbert’s clients ( M =26.56, SD =10.96). Additionally, there was a significant difference between Cashel’s clients and Rodriguez’s clients reports of Trait Anxiety, such that Cashel’s clients ( M =40.97, SD =11.00) reported significantly higher Trait Anxiety symptoms than Rodriguez’s clients ( M =34.85, SD =9.74). There were no other significant differences between therapist and client’s symptomology. Multivariate Tests a Effect Value F Hypothesis df Error df Sig. Partial Eta Squared Intercept Pillai's Trace .941 493.032 b 3.000 92.000 .000 .941 Wilks' Lambda .059 493.032 b 3.000 92.000 .000 .941 Hotelling's Trace 16.077 493.032 b 3.000 92.000 .000 .941 Roy's Largest Root 16.077 493.032 b 3.000 92.000 .000 .941 sex Pillai's Trace .072 2.366 b 3.000 92.000 .076 .072 Wilks' Lambda .928 2.366 b 3.000 92.000 .076 .072 Hotelling's Trace .077 2.366 b 3.000 92.000 .076 .072 Roy's Largest Root .077 2.366 b 3.000 92.000 .076 .072 therapist Pillai's Trace .194 3.329 6.000 186.000 .004 .097 Wilks' Lambda .814 3.326 b 6.000 184.000 .004 .098 Hotelling's Trace .219 3.323 6.000 182.000 .004 .099 Roy's Largest Root .158 4.911 c 3.000 93.000 .003 .137 sex * therapist Pillai's Trace .279 5.031 6.000 186.000 .000 .140 Wilks' Lambda .724 5.362 b 6.000 184.000 .000 .149 Hotelling's Trace .375 5.689 6.000 182.000 .000 .158 Roy's Largest Root .361 11.182 c 3.000 93.000 .000 .265 a. Design: Intercept + sex + therapist + sex * therapist b. Exact statistic c. The statistic is an upper bound on F that yields a lower bound on the significance level. Main Effects Tukey’s HSD POST HOC – Significant for PTSD/Trait Multiple Comparisons Tukey HSD Dependent Variable (I) therapist (J) therapist Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval Lower Bound Upper Bound PCL Post Traumatic Stress Disorder Cashel Gilbert 8.7442 * 2.93104 .010 1.7642 15.7242 Rodriguez 3.1818 2.95283 .530 -3.8501 10.2137 Gilbert Cashel -8.7442 * 2.93104 .010 -15.7242 -1.7642 Rodriguez -5.5624 2.93104 .145 -12.5424 1.4176 Rodriguez Cashel -3.1818 2.95283 .530 -10.2137 3.8501 Gilbert 5.5624 2.93104 .145 -1.4176 12.5424 STAI-State Anxiety Cashel Gilbert -1.7807 2.83766 .805 -8.5384 4.9769 Rodriguez 1.0606 2.85876 .927 -5.7473 7.8685 Gilbert Cashel 1.7807 2.83766 .805 -4.9769 8.5384 Rodriguez 2.8414 2.83766 .578 -3.9163 9.5990 Rodriguez Cashel -1.0606 2.85876 .927 -7.8685 5.7473 Gilbert -2.8414 2.83766 .578 -9.5990 3.9163 STAI-Trait Anxiety Cashel Gilbert 3.2344 2.51794 .407 -2.7618 9.2306 Rodriguez 6.1212 * 2.53666 . 046 .0804 12.1620 Gilbert Cashel -3.2344 2.51794 .407 -9.2306 2.7618 Rodriguez 2.8868 2.51794 .488 -3.1094 8.8830 Rodriguez Cashel -6.1212 * 2.53666 .046 -12.1620 -.0804 Gilbert -2.8868 2.51794 .488 -8.8830 3.1094 Based on observed means. The error term is Mean Square(Error) = 106.172. *. The mean difference is significant at the .05 level. Descriptive Statistics sex therapist Mean Std. Deviation N PCL Post Traumatic Stress Disorder female Cashel 38.7778 11.37880 18 Gilbert 28.1429 10.70483 14 Rodriguez 33.7222 13.93601 18 Total 33.9800 12.68534 50 male Cashel 31.1333 11.21776 15 Gilbert 25.4500 11.27865 20 Rodriguez 30.2000 12.96258 15 Total 28.5800 11.83576 50 Total Cashel 35.3030 11.78051 33 Gilbert 26.5588 10.96328 34 Rodriguez 32.1212 13.41118 33 Total 31.2800 12.50380 100 STAI-State Anxiety female Cashel 30.0000 10.53845 18 Gilbert 39.5714 13.99293 14 Rodriguez 37.0556 11.92364 18 Total 35.2200 12.50843 50 male Cashel 42.0000 11.85628 15 Gilbert 35.6000 12.43679 20 Rodriguez 31.2000 8.09938 15 Total 36.2000 11.70383 50 Total Cashel 35.4545 12.54265 33 Gilbert 37.2353 13.04319 34 Rodriguez 34.3939 10.62997 33 Total 35.7100 12.06154 100 STAI-Trait Anxiety female Cashel 40.1667 9.91879 18 Gilbert 37.8571 11.71362 14 Rodriguez 32.7778 10.60830 18 Total 36.8600 10.95447 50 male Cashel 41.9333 12.46404 15 Gilbert 37.6500 8.83936 20 Rodriguez 37.3333 8.24332 15 Total 38.8400 9.91466 50 Total Cashel 40.9697 11.00138 33 Gilbert 37.7353 9.95234 34 Rodriguez 34.8485 9.73756 33 Total 37.8500 10.44212 100 A one-way MANCOVA was conducted to determine the relationship between client’s sex and PTSD, State Anxiety, and Trait Anxiety symptoms. Depression symptoms were used as a covariate. After controlling for depression, there was a significant relationship between client’s sex and symptomology, = 0.91 , F ( 3,95 ) = 3.12 , p = .0 3. Univariate ANCOVAs indicated that, after controlling for depression, there was a significant difference between client’s sex and State Anxiety, F (1,97) = 4.11 , p = . 045, partial eta squared = .04; and Trait Anxiety, F (1,97) = 7.98 , p = . 006, partial eta squared = .08. Both were small effects. There was not a significant difference between client’s sex and PTSD symptoms, F (1,97) = .58 , p = . 45. This suggest that males ( M = 36.20 , SD =11 . 70 ) re ported significantly higher State Anxiety symptoms than fe males ( M =35.22 , SD =12.51) when controlling for depression. Additionally, males ( M =38.84, SD =9.91) reported significantly higher Trait Anxiety symptoms than females ( M =36.86, SD =10.95) when controlling for depression. There were no significant differences in male and female scores for PTSD. Multivariate Tests a Effect Value F Hypothesis df Error df Sig. Partial Eta Squared Intercept Pillai's Trace .121 4.346 b 3.000 95.000 .006 .121 Wilks' Lambda .879 4.346 b 3.000 95.000 .006 .121 Hotelling's Trace .137 4.346 b 3.000 95.000 .006 .121 Roy's Largest Root .137 4.346 b 3.000 95.000 .006 .121 Depression Pillai's Trace .414 22.398 b 3.000 95.000 .000 .414 Wilks' Lambda .586 22.398 b 3.000 95.000 .000 .414 Hotelling's Trace .707 22.398 b 3.000 95.000 .000 .414 Roy's Largest Root .707 22.398 b 3.000 95.000 .000 .414 sex Pillai's Trace .090 3.122 b 3.000 95.000 .030 .090 Wilks' Lambda .910 3.122 b 3.000 95.000 .030 .090 Hotelling's Trace .099 3.122 b 3.000 95.000 .030 .090 Roy's Largest Root .099 3.122 b 3.000 95.000 .030 .090 a. Design: Intercept + Depression + sex b. Exact statistic Tests of Between-Subjects Effects Source Dependent Variable Type III Sum of Squares df Mean Square F Sig. Partial Eta Squared Corrected Model PCL Post Traumatic Stress Disorder 4503.733 a 2 2251.866 19.904 .000 .291 STAI-State Anxiety 3433.823 b 2 1716.911 15.183 .000 .238 STAI-Trait Anxiety 3063.838 c 2 1531.919 19.221 .000 .284 Intercept PCL Post Traumatic Stress Disorder 114.234 1 114.234 1.010 .317 .010 STAI-State Anxiety 559.112 1 559.112 4.944 .028 .049 STAI-Trait Anxiety 1043.587 1 1043.587 13.094 .000 .119 Depression PCL Post Traumatic Stress Disorder 3774.733 1 3774.733 33.364 .000 .256 STAI-State Anxiety 3409.813 1 3409.813 30.154 .000 .237 STAI-Trait Anxiety 2965.828 1 2965.828 37.212 .000 .277 sex PCL Post Traumatic Stress Disorder 65.415 1 65.415 .578 .449 .006 STAI-State Anxiety 465.265 1 465.265 4.114 .045 .041 STAI-Trait Anxiety 636.016 1 636.016 7.980 .006 .076 Error PCL Post Traumatic Stress Disorder 10974.427 97 113.138 STAI-State Anxiety 10968.767 97 113.080 STAI-Trait Anxiety 7730.912 97 79.700 Total PCL Post Traumatic Stress Disorder 113322.000 100 STAI-State Anxiety 141923.000 100 STAI-Trait Anxiety 154057.000 100 Corrected Total PCL Post Traumatic Stress Disorder 15478.160 99 STAI-State Anxiety 14402.590 99 STAI-Trait Anxiety 10794.750 99 a. R Squared = .291 (Adjusted R Squared = .276) b. R Squared = .238 (Adjusted R Squared = .223) c. R Squared = .284 (Adjusted R Squared = .269) Descriptive Statistics sex Mean Std. Deviation N PCL Post Traumatic Stress Disorder female 33.9800 12.68534 50 male 28.5800 11.83576 50 Total 31.2800 12.50380 100 STAI-State Anxiety female 35.2200 12.50843 50 male 36.2000 11.70383 50 Total 35.7100 12.06154 100 STAI-Trait Anxiety female 36.8600 10.95447 50 male 38.8400 9.91466 50 Total 37.8500 10.44212 100 � Formula Sheet Odds Ratio To compute the Probability from Regression Estimate To compute the odds of being in a condition: Regression Equation: Only use significant predictors, calculate equation, gives you overall probability Pre(event) = % of occurrence “There is a probability of approx.. #% that event will occur” Pre(non-event) = 1-Pre(event) Odds = “The odds of the event happening is #” “Membership into a PhD program is the event. For Devin, the Pre(event) = .8333 and the Pre(non-event) = .1667. The probability of Devin being accepted into a PhD program is about 83.33%. The odds of Devin being accepted into a PhD is 5.00, suggesting that Devin is 5 times more likely to be accepted into a PhD program than anyone else. ANOVA Effect Sizes Eta 2 ( η 2 ) = SS bet /SS total Partial η 2 = SS bet / (SS bet + SS win ) Chi-squared Critical Values (Big Model-Small Model) = # (Df1-Df2) = # (look at chart below and find Wald’s ) Bigger = Use the more complex model Smaller = Use the simpler model K = # of conditions � PAGE � � PAGE � 1 � _1425984173.unknown _1425984174.unknown _1425984172.unknown