This is an example only. You will need to expand on each section. This example should only be used as a guide and for correct format. Refer to the end of each chapter in your textbooks and the Dissertation Handbook on how to write up the findings section. Remember to put the information in your own words in order to avoid plagiarism. GROUP # WRITE-UP: ASSIGNMENT NAME by Group Members Liberty University Partial Fulfillment Of the Requirements for EDUC 812 Liberty University Year FINDINGS Research Question The research question for this study was: RQ1: Is there a difference in learning attitude among traditional, adult, and senior vocational learners at a Northwestern public college? Null Hypothesis The null hypothesis for this study is: H01: There is no significant difference in learning attitude as measure by the Learning Attitude Learning Inventory among traditional, adult, and senior vocational learners at a Northwestern public college. Descriptive Statistics Data obtained for the dependent variable learning attitude for traditional, adult, and senior learners can be found in Table 1. Table 1 Descriptive Statistics Dependent Variable: Score Group Mean Std. Deviation N TL 18.7000 2.90784 10 AL 19.6667 1.73205 9 SL 22.8182 4.46807 11 Total 20.5000 3.70228 30 Results Data screening Data screening was conducted on each group's dependent variables (TL, AL, SL attitude) regarding data inconsistencies and outliers. The researcher sorted the data on each variable and scanned for inconsistencies. No data errors or inconsistencies were identified. Box and whiskers plots were used to detect outliers on each dependent variable. No outliers were identified. See Figure 1 for box and whisker plot. Tests of Normality Group Kolmogorov-Smirnova Statistic Score df Shapiro-Wilk Sig. Statistic df Sig. TL .179 10 .200* .883 10 .140 AL .224 9 .200* .921 9 .399 SL .105 11 .200* .958 11 .751 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Figure 1. Box and Whisker Plot for Traditional, Adult, and Senior Learners Assumptions An Analysis of Variance (ANOVA) was used to test the first null hypothesis that looked at the differences among type of learner and their learning attitudes. The ANOVA required that the assumptions of normality and homogeneity of variance are met. Normality was examined using a Shapiro-Wilk test. Shapiro-Wilk was used because the sample size was less than 50. No violations of normality were found. See Table 2 for Shapiro-Wilk test. Table 2 Tests of Normality Kolmogorov-Smirnova Group Statistic Score df Shapiro-Wilk Sig. Statistic df Sig. TL .179 10 .200* .883 10 .140 AL .224 9 .200* .921 9 .399 SL .216 11 .158 .893 11 .151 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction The assumption of homogeneity of variance was examined using the Levene's test. A violation was found (p = .009) so the assumption of homogeneity was not met. However, the ANOVA is considered a robust test against the homogeneity assumption (Warner, 2013, p. 474). For this reason, the researcher continued with the analysis. See Table 3 for Levene's Test. Table 3 Levene's Test of Equality of Error Variance Dependent Variable: Score F df1 5.647 df2 2 Sig. 27 .009 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept + Group Results for Null Hypothesis One An ANOVA was used to test the first null hypothesis; the differences in learning attitude among traditional, adult, and senior vocational learners. The first null hypothesis was rejected at a 95% confidence level were F(2, 27) = 4.40, p = .02, 2 = .25. See Table 4 Tests of BetweenSubjects Effects. Table 4 Tests of Between-Subjects Effects Dependent Variable: Score Source Type III Sum of df Mean Square F Sig. Partial Eta Squares Squared 97.764a 2 48.882 4.403 .022 .246 12395.150 1 12395.150 1116.545 .000 .976 Group 97.764 2 48.882 4.403 .022 .246 Error 299.736 27 11.101 Total 13005.000 30 397.500 29 Corrected Model Intercept Corrected Total a. R Squared = .246 (Adjusted R Squared = .190) Because the null was rejected, post hoc analysis was conducted using a Tukey Test HSD. There was a significant difference between the attitude scores of traditional (M = 18.7, S.D. = 2.9) and senior (M = 22.8, S.D. = 4.5) vocational learners (p = .02). See Table 5 for Multiple Comparisons Groups. Table 5 Multiple Comparisons Dependent Variable: Score Tukey HSD (I) Group (J) Group Mean Difference Std. Error Sig. (I-J) TL AL SL 95% Confidence Interval Lower Bound Upper Bound AL -.9667 1.53089 .804 -4.7624 2.8290 SL -4.1182* 1.45580 .023 -7.7277 -.5087 TL .9667 1.53089 .804 -2.8290 4.7624 SL -3.1515 1.49756 .108 -6.8646 .5616 TL * 4.1182 1.45580 .023 .5087 7.7277 AL 3.1515 1.49756 .108 -.5616 6.8646 Page 1 of 7 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 Name: SPSS Worksheet 6: (Multiple Regression) Instructions: Lesson 34 Exercise File 1 is located at the end of the chapter under the heading Exercises in your Green and Salkind textbook. Complete the exercise and then complete the worksheet below by filling in the blanks and answering the questions. H01: There will be no significant predictive relationship between the criterion variable (Stats Exam Scores) and the linear combination of predictor variables (Math test, English test, English GPA, Math GPA, and Other GPA) for college students. Assumptions Assumption of Bivariate Outliers: Hint: Run scatter plots between each pair of predictor variables (x, x) and also the predictor variables (x) and the criterion variable (y). You will need a total of 15 individual plots. Look for \"extreme\" bivariate outliers. See Warner pp. 165-166 and 169. Assumption of Multivariate Normal Distribution: Hint: Run scatter plots between each pair of predictor variables (x, x) and also the predictor variables (x) and the criterion variable (y). Look for the classic \"cigar shape.\" You will need a total of 15 individual plots. See Warner p. 269. Page 2 of 7 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 Fill in the blanks: Variables Math test (x) Stats Exam (y) English test (x) Stats Exam (y) English GPA (x) Stats Exam (y) Math GPA (x) Stats Exam (y) Other GPA (x) Stats Exam (y) English test (x) Math test (x) English GPA (x) Math test (x) Math GPA (x) Math test (x) Other GPA (x) Math test (x) English GPA (x) English test (x) Math GPA (x) English test (x) Other GPA (x) English test (x) Math GPA (x) English GPA Is the assumption of bivariate outliers tenable? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Is the assumption of multivariate normal distribution tenable? Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Page 3 of 7 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 Other GPA (x) Other GPA (x) English GPA Math GPA (x) Yes Yes Yes Yes Assumption of non-Multicollinearity among the Predictor Variables: If a predictor variable (x) is highly correlated with another predictor variable (x), they essentially provide the same information about the criterion variable. If the Variance Inflation Factor (VIF) is too high (greater than 10), you have multicollinearity and have violated the assumption. Acceptable values are between 1and 5. To run the VIF test, select Analyze > Regression > Linear > Statistics > then check the Collinearity diagnostics checkbox. ANOVAa Model 1 Sum of Squares df Mean Square F Regression 10432.432 5 2086.486 Residual 28333.358 94 301.419 Total 38765.790 99 Sig. 6.922 .000b a. Dependent Variable: Average percentage correct on statistics exams b. Predictors: (Constant), GPA in other high school classes, Math aptitude test score, High school English GPA, English aptitude test score, High school math GPA Coefficientsa Model 1 Unstandardized Standardized Collinearity Coefficients Coefficients Statistics B (Constant) Math aptitude test score English aptitude test score High school English GPA High school math GPA GPA in other high school classes Std. Error 6.745 27.691 .116 .025 .049 Beta t Sig. Tolerance VIF .244 .808 .453 4.726 .000 .847 1.181 .027 .179 1.816 .073 .801 1.249 -3.365 7.446 -.047 -.452 .652 .719 1.391 5.478 6.865 .084 .798 .427 .707 1.415 -9.702 8.500 -.109 -1.141 .257 .854 1.172 a. Dependent Variable: Average percentage correct on statistics exams Page 4 of 7 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 Collinearity Diagnosticsa Variance Proportions High Model Dimension Eigenvalue 1 GPA in Math English school High other high Condition aptitude aptitude English school school Index (Constant) test score test score GPA math GPA classes 1 5.948 1.000 .00 .00 .00 .00 .00 .00 2 .023 15.927 .00 .66 .18 .02 .00 .00 3 .014 20.479 .02 .21 .68 .02 .07 .02 4 .007 29.905 .11 .01 .02 .04 .64 .17 5 .005 33.501 .00 .10 .12 .85 .28 .08 6 .003 48.324 .86 .01 .01 .08 .01 .72 a. Dependent Variable: Average percentage correct on statistics exams Fill in the blanks: Variables VIF Math test English test English GPA Math GPA Other GPA Is the assumption of nonMulticollinearity met? Yes Yes Yes Yes Yes 1.181 1.249 1.391 1.415 1.172 Results Insert the ANOVA a table below: ANOVAa Model 1 Sum of Squares df Mean Square Regression 10432.432 5 2086.486 Residual 28333.358 94 301.419 Total 38765.790 99 a. Dependent Variable: Average percentage correct on statistics exams F 6.922 Sig. .000b Page 5 of 7 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 b. Predictors: (Constant), GPA in other high school classes, Math aptitude test score, High school English GPA, English aptitude test score, High school math GPA Fill in the blanks: Regression Model Regression Model (ANOVA a) Value d.f. between Groups 5 d.f. within Groups 94 F-statistic 6.922 F-critical (See Appendix C in Warner) 2.311 p- value .000 Is the F- statistic greater than F-critical? Answer: Yes Is the p- value less than .05? Answer: Yes Is the predictive model statistically significant? Answer: Yes Insert the Regression Model Coefficients a table below: Page 6 of 7 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 Coefficientsa Model 1 Unstandardized Standardized Collinearity Coefficients Coefficients Statistics B (Constant) GPA GPA in other high school classes .049 VIF .000 .847 1.181 .027 .179 1.816 .073 .801 1.249 -3.365 7.446 -.047 -.452 .652 .719 1.391 5.478 6.865 .084 .798 .427 .707 1.415 -9.702 8.500 -.109 -1.141 .257 .854 1.172 High school math GPA .025 Tolerance 4.726 score .116 Sig. .453 English aptitude test 27.691 t .808 score 6.745 Beta .244 Math aptitude test High school English Std. Error a. Dependent Variable: Average percentage correct on statistics exams Fill in the blanks: Regression Model Coefficients Regression Model Coefficients a Variables t- stat p- values Math test 4.72 .000 6 English test 1.81 .073 6 English GPA -.452 .652 Math GPA .798 .427 Other GPA 1.14 .257 1 What variable(s) best predicts stats exam scores? Hint: look at the p- value of each predictor variable under the t- stat coefficient and determine if it is less than .05. Answer: The Math Test best predicts the stats exam scores. Page 7 of 7 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 Descriptive Statistics Fill in the blanks: Variables Math test English test English GPA Math GPA Other GPA Stats Exam Mean S.D. 460.60 478.20 2.8183 2.7763 3.0236 460.60 77.366 71.653 .27633 .30234 .22220 77.366