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 df Shapiro-Wilk Sig. Statistic df Sig. TL 10 .200* .883 10 .140 AL .224 9 .200* .921 9 .399 SL Score .179 .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 df Shapiro-Wilk Sig. Statistic df Sig. TL 10 .200* .883 10 .140 AL .224 9 .200* .921 9 .399 SL Score .179 .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 \fPage 1 of 3 Name: Jane Bragg SPSS Worksheet 2: (ANOVA) Instructions: Lesson 25 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 is no significant difference in the amount of extrovertednesss among blondes, brunettes, and redheads. Assumptions Outliers: Create a Box and Whisker plot for each group. Hint: Graph > Legacy > Boxplot > Simple. Insert the Box and Whisker plot below: Note: Look for extreme outliers. Insert Graph or Table Here Fill in the blanks: Groups Outliers (Item #) Are there any outliers? Blonde Brunet Redhead < Note: Remove any outliers from the dataset before continuing.> Assumption of Normality: Run a normality test for each group. Insert Tests of Normality table below: Page 2 of 3 Insert Graph or Table Here Fill in the blanks: Should you use a Shapiro-Wilks or Kolmogorov-Smirnov test? Why? Answer: Groups Significance Is the assumption of normality met? Blonde Brunet Redhead Assumption of Equal Variance: Insert Levene's Test of Equality of Error Variancesa table(s) below: Insert Graph or Table Here Fill in the blanks: Significance Is the assumption of equal variance met? Results Insert Tests of Between-Subjects Effects table(s) below: Insert Graph or Table Here Page 3 of 3 Fill in the blanks: Value d.f. between Groups d.f. within Groups F-statistic F-critical (Hint: See Appendix C in Warner) p- value Partial Eta Squared Is the F- statistic greater than F-critical? Answer: Is the p- value less than .05? Answer: Should you reject or fail to reject the null? Answer: Is the effect size small, medium, or large? Hint: See Table 5.2 in Warner, p. 208. Answer: Should you run post hoc analysis? Answer: Descriptive Statistics Groups Blonde Brunet Redhead Mean S.D. GROUP 1 WRITE-UP: ASSIGNMENT 2 (ANOVA) by Kate Astor Liberty University Partial Fulfillment Of the Requirements for EDUC 812 Liberty University 2015 FINDINGS Research Question The research question for this study was: RQ1: Whether there is a difference between the amount of extrovertednesss among blondes, brunettes, and redheads. Null Hypothesis The null hypothesis for this study is: H01: There is no significant difference in the amount of extrovertednesss among blondes, brunettes, and redheads. Descriptive Statistics Th descriptive statistics table for the dependent variable Social Extroversion for three Hair Colors is given in Table 1. Table 1 Descriptives Social Extroversion 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum Blond 6 5.17 2.787 1.138 2.24 8.09 2 10 Brunet 6 3.67 1.211 .494 2.40 4.94 2 5 Redhead 6 2.33 1.033 .422 1.25 3.42 1 4 18 3.72 2.109 .497 2.67 4.77 1 10 Total Results Data screening Data screening/filtering the best start up for any analysis to identify if the data contains some errors or outliers. The presence of outliers seriously affects the validy of any test thus it should be checked at the 1st step itself and should be corrected if needed. Using the Box and whiskers plots for dependent variables (Social Extroversion score) any presence of data inconsistencies and outliers are checked. No data errors or inconsistencies as well as outliers are identified from the graphs. See Figure 1 for box and whisker plot. Figure 1. Box and Whisker Plot for Hair colors Assumptions The subjects with three types of hair color are independent samples thus an one way ANOVA was used to test the null hypothesis to find significant difference between the groups' mean. An ANOVA requires several assumptions to be fulfilled to be valid. First, the dependent variable is measured on a continuous scale (interval scaled data atleast). As the Social Extroversion score is scores so the 1st assumption is validated. Second, the independent variable must include more than two categorical groups. Three hair colors are used in this study hence the 2nd condition is also satisfied. Third, the observations in each sample must be independently selected from the population. Here no single participant was included in more than one of the categorical groups and the data is not repeated measure data, moreover the hair color of one individual cant affect the hair color of another individual so this condition is also fulfilled. Fourth, there are no significant outliers. The Box and Wisker Plot indicated that there were no significant outliers. Fifth, the dependent variable should be approximately normally distributed for each independent group. The Shapiro-Wilk test was used to check for Normality (because the sample size was less than 50 so Shapiro-Wilk test was used). No violations of normality were found. See Table 2 for Shapiro-Wilk test. Table 2 Tests of Normality Kolmogorov-Smirnova Hair Color Social Extroversion Statistic Blond df Shapiro-Wilk Sig. Statistic df Sig. 6 .216 .200* .923 6 .525 * .907 6 .415 .915 6 .473 Brunet .209 6 .200 Redhead .293 6 .117 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction The sixth assumption is that of homogeneity of variance i.e. the variance in all the groups are not significantly different. This was examined using the Levene's test. The result indicated no significance found thus the assumption of homogeneity of variance assumption is met. See Table 3 for Levene's Test. Table 3 Test of Homogeneity of Variances Social Extroversion Levene Statistic 1.520 df1 df2 2 Sig. 15 .250 Levene's Test of Equality of Error Variance Results for Null Hypothesis One An ANOVA test was used to test the null hypothesis. The null hypothesis was not rejected at a 95% confidence level as the test statistic F(2,15) = 3.511, is smaller than the F-critical value of 3.682 for 95% CI and when df= (2,15); p = .056, with no significant difference at 0.05 significnance level. See Table 4 the ANOVA Test. Table 4 ANOVA Social Extroversion Sum of Squares df Mean Square Between Groups 24.111 2 12.056 Within Groups 51.500 15 3.433 Total 75.611 17 F 3.511 Sig. .056 GROUP 1 WRITE-UP: ASSIGNMENT 2 (ANOVA) by Kate Astor Liberty University Partial Fulfillment Of the Requirements for EDUC 812 Liberty University 2015 FINDINGS Research Question The research question for this study was: RQ1: Whether there is a difference between the amount of extrovertednesss among blondes, brunettes, and redheads. Null Hypothesis The null hypothesis for this study is: H01: There is no significant difference in the amount of extrovertednesss among blondes, brunettes, and redheads. Descriptive Statistics Th descriptive statistics table for the dependent variable Social Extroversion for three Hair Colors is given in Table 1. Table 1 Descriptives Social Extroversion 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum Blond 6 5.17 2.787 1.138 2.24 8.09 2 10 Brunet 6 3.67 1.211 .494 2.40 4.94 2 5 Redhead 6 2.33 1.033 .422 1.25 3.42 1 4 18 3.72 2.109 .497 2.67 4.77 1 10 Total Results Data screening Data screening/filtering the best start up for any analysis to identify if the data contains some errors or outliers. The presence of outliers seriously affects the validy of any test thus it should be checked at the 1st step itself and should be corrected if needed. Using the Box and whiskers plots for dependent variables (Social Extroversion score) any presence of data inconsistencies and outliers are checked. No data errors or inconsistencies as well as outliers are identified from the graphs. See Figure 1 for box and whisker plot. Figure 1. Box and Whisker Plot for Hair colors Assumptions The subjects with three types of hair color are independent samples thus an one way ANOVA was used to test the null hypothesis to find significant difference between the groups' mean. An ANOVA requires several assumptions to be fulfilled to be valid. First, the dependent variable is measured on a continuous scale (interval scaled data atleast). As the Social Extroversion score is scores so the 1st assumption is validated. Second, the independent variable must include more than two categorical groups. Three hair colors are used in this study hence the 2nd condition is also satisfied. Third, the observations in each sample must be independently selected from the population. Here no single participant was included in more than one of the categorical groups and the data is not repeated measure data, moreover the hair color of one individual cant affect the hair color of another individual so this condition is also fulfilled. Fourth, there are no significant outliers. The Box and Wisker Plot indicated that there were no significant outliers. Fifth, the dependent variable should be approximately normally distributed for each independent group. The Shapiro-Wilk test was used to check for Normality (because the sample size was less than 50 so Shapiro-Wilk test was used). No violations of normality were found. See Table 2 for Shapiro-Wilk test. Table 2 Tests of Normality a Kolmogorov-Smirnov Hair Color Statistic df Shapiro-Wilk Sig. Statistic df Sig. Blond .216 6 .200 Brunet .209 6 .200 * .907 6 .415 Redhead Social Extroversion * .293 6 .117 .915 6 .473 .923 6 .525 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction The sixth assumption is that of homogeneity of variance i.e. the variance in all the groups are not significantly different. This was examined using the Levene's test. The result indicated no significance found thus the assumption of homogeneity of variance assumption is met. See Table 3 for Levene's Test. Table 3 Test of Homogeneity of Variances Social Extroversion Levene Statistic 1.520 df1 df2 2 Sig. 15 .250 Levene's Test of Equality of Error Variance Results for Null Hypothesis One An ANOVA test was used to test the null hypothesis. The null hypothesis was not rejected at a 95% confidence level as the test statistic F(2,15) = 3.511, is smaller than the F- critical value of 3.682 for 95% CI and when df= (2,15); p = .056, with no significant difference at 0.05 significnance level. See Table 4 the ANOVA Test. Table 4 ANOVA Social Extroversion Sum of Squares df Mean Square Between Groups 24.111 2 12.056 Within Groups 51.500 15 3.433 Total 75.611 17 F 3.511 Sig. .056 GROUP 1 WRITE-UP: ASSIGNMENT 2 (ANOVA) by Kate Astor Liberty University Partial Fulfillment Of the Requirements for EDUC 812 Liberty University 2015 FINDINGS Research Question The research question for this study was: RQ1: Whether there is a difference between the amount of extrovertednesss among blondes, brunettes, and redheads. Null Hypothesis The null hypothesis for this study is: H01: There is no significant difference in the amount of extrovertednesss among blondes, brunettes, and redheads. Descriptive Statistics Th descriptive statistics table for the dependent variable Social Extroversion for three Hair Colors is given in Table 1. Table 1 Descriptives Social Extroversion 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum Blond 6 5.17 2.787 1.138 2.24 8.09 2 10 Brunet 6 3.67 1.211 .494 2.40 4.94 2 5 Redhead 6 2.33 1.033 .422 1.25 3.42 1 4 18 3.72 2.109 .497 2.67 4.77 1 10 Total Results Data screening Data screening/filtering the best start up for any analysis to identify if the data contains some errors or outliers. The presence of outliers seriously affects the validy of any test thus it should be checked at the 1st step itself and should be corrected if needed. Using the Box and whiskers plots for dependent variables (Social Extroversion score) any presence of data inconsistencies and outliers are checked. No data errors or inconsistencies as well as outliers are identified from the graphs. See Figure 1 for box and whisker plot. Figure 1. Box and Whisker Plot for Hair colors Assumptions The subjects with three types of hair color are independent samples thus an one way ANOVA was used to test the null hypothesis to find significant difference between the groups' mean. An ANOVA requires several assumptions to be fulfilled to be valid. First, the dependent variable is measured on a continuous scale (interval scaled data atleast). As the Social Extroversion score is scores so the 1st assumption is validated. Second, the independent variable must include more than two categorical groups. Three hair colors are used in this study hence the 2nd condition is also satisfied. Third, the observations in each sample must be independently selected from the population. Here no single participant was included in more than one of the categorical groups and the data is not repeated measure data, moreover the hair color of one individual cant affect the hair color of another individual so this condition is also fulfilled. Fourth, there are no significant outliers. The Box and Wisker Plot indicated that there were no significant outliers. Fifth, the dependent variable should be approximately normally distributed for each independent group. The Shapiro-Wilk test was used to check for Normality (because the sample size was less than 50 so Shapiro-Wilk test was used). No violations of normality were found. See Table 2 for Shapiro-Wilk test. Table 2 Tests of Normality Kolmogorov-Smirnova Hair Color Social Extroversion Statistic Blond df Shapiro-Wilk Sig. Statistic df Sig. 6 .216 .200* .923 6 .525 * .907 6 .415 .915 6 .473 Brunet .209 6 .200 Redhead .293 6 .117 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction The sixth assumption is that of homogeneity of variance i.e. the variance in all the groups are not significantly different. This was examined using the Levene's test. The result indicated no significance found thus the assumption of homogeneity of variance assumption is met. See Table 3 for Levene's Test. Table 3 Test of Homogeneity of Variances Social Extroversion Levene Statistic 1.520 df1 df2 2 Sig. 15 .250 Levene's Test of Equality of Error Variance Results for Null Hypothesis One An ANOVA test was used to test the null hypothesis. The null hypothesis was not rejected at a 95% confidence level as the test statistic F(2,15) = 3.511, is smaller than the F-critical value of 3.682 for 95% CI and when df= (2,15); p = .056, with no significant difference at 0.05 significnance level. See Table 4 the ANOVA Test. Table 4 ANOVA Social Extroversion Sum of Squares df Mean Square Between Groups 24.111 2 12.056 Within Groups 51.500 15 3.433 Total 75.611 17 F 3.511 Sig. .056 GROUP 1 WRITE-UP: ASSIGNMENT 2 (ANOVA) by Kate Astor Liberty University Partial Fulfillment Of the Requirements for EDUC 812 Liberty University 2015 FINDINGS Research Question The research question for this study was: RQ1: Whether there is a difference between the amount of extrovertednesss among blondes, brunettes, and redheads. Null Hypothesis The null hypothesis for this study is: H01: There is no significant difference in the amount of extrovertednesss among blondes, brunettes, and redheads. Descriptive Statistics Th descriptive statistics table for the dependent variable Social Extroversion for three Hair Colors is given in Table 1. Table 1 Descriptives Social Extroversion 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum Blond 6 5.17 2.787 1.138 2.24 8.09 2 10 Brunet 6 3.67 1.211 .494 2.40 4.94 2 5 Redhead 6 2.33 1.033 .422 1.25 3.42 1 4 18 3.72 2.109 .497 2.67 4.77 1 10 Total Results Data screening Data screening/filtering the best start up for any analysis to identify if the data contains some errors or outliers. The presence of outliers seriously affects the validy of any test thus it should be checked at the 1st step itself and should be corrected if needed. Using the Box and whiskers plots for dependent variables (Social Extroversion score) any presence of data inconsistencies and outliers are checked. No data errors or inconsistencies as well as outliers are identified from the graphs. See Figure 1 for box and whisker plot. Figure 1. Box and Whisker Plot for Hair colors Assumptions The subjects with three types of hair color are independent samples thus an one way ANOVA was used to test the null hypothesis to find significant difference between the groups' mean. An ANOVA requires several assumptions to be fulfilled to be valid. First, the dependent variable is measured on a continuous scale (interval scaled data atleast). As the Social Extroversion score is scores so the 1st assumption is validated. Second, the independent variable must include more than two categorical groups. Three hair colors are used in this study hence the 2nd condition is also satisfied. Third, the observations in each sample must be independently selected from the population. Here no single participant was included in more than one of the categorical groups and the data is not repeated measure data, moreover the hair color of one individual cant affect the hair color of another individual so this condition is also fulfilled. Fourth, there are no significant outliers. The Box and Wisker Plot indicated that there were no significant outliers. Fifth, the dependent variable should be approximately normally distributed for each independent group. The Shapiro-Wilk test was used to check for Normality (because the sample size was less than 50 so Shapiro-Wilk test was used). No violations of normality were found. See Table 2 for Shapiro-Wilk test. Table 2 Tests of Normality a Kolmogorov-Smirnov Hair Color Statistic df Shapiro-Wilk Sig. Statistic df Sig. Blond .216 6 .200 Brunet .209 6 .200 * .907 6 .415 Redhead Social Extroversion * .293 6 .117 .915 6 .473 .923 6 .525 *. This is a lower bound of the true significance. a. Lilliefors Significance Correction The sixth assumption is that of homogeneity of variance i.e. the variance in all the groups are not significantly different. This was examined using the Levene's test. The result indicated no significance found thus the assumption of homogeneity of variance assumption is met. See Table 3 for Levene's Test. Table 3 Test of Homogeneity of Variances Social Extroversion Levene Statistic 1.520 df1 df2 2 Sig. 15 .250 Levene's Test of Equality of Error Variance Results for Null Hypothesis One An ANOVA test was used to test the null hypothesis. The null hypothesis was not rejected at a 95% confidence level as the test statistic F(2,15) = 3.511, is smaller than the F- critical value of 3.682 for 95% CI and when df= (2,15); p = .056, with no significant difference at 0.05 significnance level. See Table 4 the ANOVA Test. Table 4 ANOVA Social Extroversion Sum of Squares df Mean Square Between Groups 24.111 2 12.056 Within Groups 51.500 15 3.433 Total 75.611 17 F 3.511 Sig. .056