\fPage 1 of 6 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 Name: Jane Bragg SPSS Worksheet 4: (ANCOVA) Instructions: Lesson 27 Exercise File 2 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 among the depression scores of students who receive Journal and Counseling therapy, Journal therapy only, or Counseling therapy only, while controlling for pre-test depression scores. Assumptions Outliers: Create a Box and Whisker plot for each group. Insert Graph or Table Here Fill in the blanks: Group (Pre-Test): Journal and Counseling Outliers (Item #) Are there any outliers? Outliers (Item #) Are there any outliers? Journal only Counseling only Group (Post-Test): Journal and Counseling Journal only Counseling only < Note: Remove any outliers from the dataset before continuing.> Page 2 of 6 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 Assumption of Normality: Run a normality test for each group. Insert Tests of Normality table below: Insert Graph or Table Here Fill in the blanks: Should you use a Shapiro-Wilks or Kolmogorov-Smirnov test? Why? Answer: Groups (Pre-Test) Significance Is the assumption of normality met? Significance Is the assumption of normality met? Journal and Counseling Journal only Counseling only Groups (Post-Test) Journal and Counseling Journal only Counseling only Assumption of Linearity: Hint: Run a series of scatter plots between the pre-test variable and post-test variable for each group. Begin by going to Data > Split File (see lesson 15, p. 64), and then make the plots. Add line of fit. See Warner p. 168- 172. After making the scatterplots, go to Data > Split File > RESET before continuing with the analysis. Insert Graph or Table Here Page 3 of 6 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 Fill in the blanks: Variables Is the assumption of linearity met? Journal & Counseling (Pre) Journal only (Pre) Journal & Counseling (Post) Journal only (Post) Counseling only (Pre) Counseling only (Post) Assumption of Bivariate Normal Distribution: Hint: Run a series of scatter plots between the pre-test variable and post-test variable for each group (Same as above). Look for the classic \"cigar shape.\" See Warner p. 168- 172. Insert Graph or Table Here Fill in the blanks: Variables Is the assumption of Bivariate Normal Distribution met? Journal & Counseling (Pre) Journal only (Pre) Journal & Counseling (Post) Journal only (Post) Counseling only (Pre) Counseling only (Post) Assumption of Homogeneity of Slopes: Hint: Remember to go to Univariate > Model > Custom and look for an interaction. Insert Graph or Table Here Fill in the blanks: F-stat Significance Is the assumption of Homogeneity-of- Slopes met? Page 4 of 6 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 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 Fill in the blanks: Value d.f. between Groups d.f. within Groups F-statistic F-critical (See Appendix C in Warner) p- value Partial Eta Squared Page 5 of 6 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 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: What is the effect size small, medium, or large (See Table 5.2 in Warner, p. 208)? Answer: Should you run post hoc analysis? Answer: Descriptive Statistics Groups (Pre-Test) Journal and Counseling Mean S.D. Mean S.D. Adjusted Mean S.E. Journal only Counseling only Groups (Post-Test) Journal and Counseling Journal only Counseling only Groups (Estimates) Journal and Counseling Journal only Page 6 of 6 This worksheet was developed by Dr. Kurt Michael of Liberty University 2015 Counseling only GROUP # WRITE-UP: ANCOVA 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 the depression scores among students who receive Journal and Counseling therapy, Journal therapy only, or Counseling therapy only, while controlling for pre-test depression scores? Null Hypothesis The null hypothesis for this study is: H01: There is no significant difference among the depression scores of students who receive Journal and Counseling therapy, Journal therapy only, or Counseling therapy only, while controlling for pre-test depression scores. Descriptive Statistics Data obtained for the dependent variable the depression scores for the students receiving Journal and Counseling therapy, Journal therapy only, or Counseling therapy only can be found in Table 1. Table 1 Descriptive Statistics Dependent Variable: Depression scores after treatnent Therapy type Counseling and journal Mean Std. Deviation N 70.30 7.981 20 Journal therapy only 65.85 8.381 20 Counseling only 71.10 7.210 20 Total 69.08 8.081 60 therapy Results Data screening Data screening was conducted on each group's dependent variables 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 and the covariate. No outliers were identified. See Figure 1 and Figure 2 for box and whisker plots. 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 Depression scores prior to treatment Figure 2. Box and Whisker Plot for Depression scores after treatment Assumptions An Analysis of Covariance (ANCOVA) was used to test the null hypothesis that looked at the differences among method of treatment while controlling for pre-test depression scores. The ANCOVA 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 Therapy type Kolmogorov-Smirnova Shapiro-Wilk Statistic Depression scores prior to treatment Depression scores after treatnent df Sig. Statistic df Sig. Counseling and journal therapy .124 20 .200* .960 20 .545 Journal therapy only .087 20 .200* .974 20 .828 Counseling only .096 20 .200* .969 20 .735 Counseling and journal therapy .115 20 .200* .972 20 .807 Journal therapy only .103 20 .200* .970 20 .747 Counseling only .138 20 .200* .955 20 .452 *. 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 = .004) so the assumption of homogeneity was not met. However, the ANCOVA is considered a robust test against the homogeneity assumption. 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 Variancesa Dependent Variable: Depression scores after treatnent F df1 6.037 df2 2 Sig. 57 .004 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept + group + depprior + group * depprior An ANCOVA also needs the Assumption of Linearity to be satisfied. This assumption tells us that the convariate term is linear with the dependent variable for each level of the factor. The obtained graphs are used to test for this assumption. The above graphs indicate linear relationships between the covariate term and the dependent variable indicating that the assumption of linearity has been met. The next assumption we need to check is the Assumption of Bivariate Normal Distribution. This assumption can directly be checked from the above scatter plots. The plots above indicates that this assumption might not be met for few groups. Assumption of Homogeneity of Slopes is the next assumption we need to verify. The following Table 4 is used for that purpose. Table 4 Tests of Between-Subjects Effects Dependent Variable: Depression scores after treatnent Type III Sum of Source Corrected Model Intercept group depprior Squares Partial Eta df Mean Square F Sig. Squared 2213.027a 5 442.605 14.578 .000 .574 1377.155 1 1377.155 45.358 .000 .457 31.713 2 15.857 .522 .596 .019 1885.246 1 1885.246 62.092 .000 .535 group * depprior 25.689 2 12.844 Error 1639.557 54 30.362 Total 290203.000 60 3852.583 59 Corrected Total .423 .657 .015 a. R Squared = .574 (Adjusted R Squared = .535) The table indicates the assumption is met at a 95% confidence level, F(2, 54) = .423, p = . 657, 2 = .015. Results for Null Hypothesis One An ANCOVA was used to test the null hypothesis; differences among method of treatment while controlling for pre-test depression scores. The null hypothesis was not rejected at a 95% confidence level were F(2, 54) = .522, p = .596, 2 = .019. See Table 5 Tests of BetweenSubjects Effects. Table 5 Tests of Between-Subjects Effects Dependent Variable: Depression scores after treatnent Type III Sum of Source Squares Partial Eta df Mean Square F Sig. Squared 2213.027a 5 442.605 14.578 .000 .574 1377.155 1 1377.155 45.358 .000 .457 31.713 2 15.857 .522 .596 .019 1885.246 1 1885.246 62.092 .000 .535 25.689 2 12.844 .423 .657 .015 Error 1639.557 54 30.362 Total 290203.000 60 3852.583 59 Corrected Model Intercept group depprior group * depprior Corrected Total a. R Squared = .574 (Adjusted R Squared = .535) Because the null was not rejected, post hoc analysis was not conducted. GROUP # WRITE-UP: ANCOVA 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 the depression scores among students who receive Journal and Counseling therapy, Journal therapy only, or Counseling therapy only, while controlling for pre-test depression scores? Null Hypothesis The null hypothesis for this study is: H01: There is no significant difference among the depression scores of students who receive Journal and Counseling therapy, Journal therapy only, or Counseling therapy only, while controlling for pre-test depression scores. Descriptive Statistics Data obtained for the dependent variable the depression scores for the students receiving Journal and Counseling therapy, Journal therapy only, or Counseling therapy only can be found in Table 1. Table 1 Descriptive Statistics Dependent Variable: Depression scores after treatnent Therapy type Counseling and journal Mean Std. Deviation N 70.30 7.981 20 Journal therapy only 65.85 8.381 20 Counseling only 71.10 7.210 20 Total 69.08 8.081 60 therapy Results Data screening Data screening was conducted on each group's dependent variables 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 and the covariate. No outliers were identified. See Figure 1 and Figure 2 for box and whisker plots. Tests of Normality Group a Kolmogorov-Smirnov Statistic TL Score .179 df Shapiro-Wilk Sig. 10 Statistic df Sig. .200 * .883 10 .140 .921 9 .399 .958 11 .751 AL .224 9 .200 * SL .105 11 .200 * *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Figure 1. Box and Whisker Plot for Depression scores prior to treatment Figure 2. Box and Whisker Plot for Depression scores after treatment Assumptions An Analysis of Covariance (ANCOVA) was used to test the null hypothesis that looked at the differences among method of treatment while controlling for pre-test depression scores. The ANCOVA 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 Therapy type a Kolmogorov-Smirnov Shapiro-Wilk Statistic df Sig. .124 20 .200 * .960 20 .545 Journal therapy only .087 20 .200 * .974 20 .828 Counseling only .096 20 .200 * .969 20 .735 Counseling and journal therapy .115 20 .200 * .972 20 .807 Journal therapy only .103 20 .200 * .970 20 .747 Counseling only .138 20 .200 * .955 20 .452 Depression scores prior to treatment Counseling and journal therapy Depression scores after treatnent Statistic df Sig. *. 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 = .004) so the assumption of homogeneity was not met. However, the ANCOVA is considered a robust test against the homogeneity assumption. 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 Variances a Dependent Variable: Depression scores after treatnent F df1 6.037 df2 2 Sig. 57 .004 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept + group + depprior + group * depprior An ANCOVA also needs the Assumption of Linearity to be satisfied. This assumption tells us that the convariate term is linear with the dependent variable for each level of the factor. The obtained graphs are used to test for this assumption. The above graphs indicate linear relationships between the covariate term and the dependent variable indicating that the assumption of linearity has been met. The next assumption we need to check is the Assumption of Bivariate Normal Distribution. This assumption can directly be checked from the above scatter plots. The plots above indicates that this assumption might not be met for few groups. Assumption of Homogeneity of Slopes is the next assumption we need to verify. The following Table 4 is used for that purpose. Table 4 Tests of Between-Subjects Effects Dependent Variable: Depression scores after treatnent Type III Sum of Source Corrected Model Intercept group depprior Squares Partial Eta df Mean Square F Sig. Squared a 5 442.605 14.578 .000 .574 1377.155 1 1377.155 45.358 .000 .457 31.713 2 15.857 .522 .596 .019 1885.246 1 1885.246 62.092 .000 .535 2213.027 group * depprior 25.689 2 12.844 Error 1639.557 54 30.362 Total 290203.000 60 3852.583 59 Corrected Total .423 .657 .015 a. R Squared = .574 (Adjusted R Squared = .535) The table indicates the assumption is met at a 95% confidence level, F(2, 54) = .423, p = .657, 2 = .015. Results for Null Hypothesis One An ANCOVA was used to test the null hypothesis; differences among method of treatment while controlling for pre-test depression scores. The null hypothesis was not rejected at a 95% confidence level were F(2, 54) = .522, p = .596, 2 = .019. See Table 5 Tests of BetweenSubjects Effects. Table 5 Tests of Between-Subjects Effects Dependent Variable: Depression scores after treatnent Type III Sum of Source Squares Partial Eta df Mean Square F Sig. Squared a 5 442.605 14.578 .000 .574 1377.155 1 1377.155 45.358 .000 .457 31.713 2 15.857 .522 .596 .019 1885.246 1 1885.246 62.092 .000 .535 25.689 2 12.844 .423 .657 .015 Error 1639.557 54 30.362 Total 290203.000 60 3852.583 59 Corrected Model Intercept group depprior group * depprior Corrected Total 2213.027 a. R Squared = .574 (Adjusted R Squared = .535) Because the null was not rejected, post hoc analysis was not conducted. GROUP # WRITE-UP: ANCOVA 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 the depression scores among students who receive Journal and Counseling therapy, Journal therapy only, or Counseling therapy only, while controlling for pre-test depression scores? Null Hypothesis The null hypothesis for this study is: H01: There is no significant difference among the depression scores of students who receive Journal and Counseling therapy, Journal therapy only, or Counseling therapy only, while controlling for pre-test depression scores. Descriptive Statistics Data obtained for the dependent variable the depression scores for the students receiving Journal and Counseling therapy, Journal therapy only, or Counseling therapy only can be found in Table 1. Table 1 Descriptive Statistics Dependent Variable: Depression scores after treatnent Therapy type Counseling and journal Mean Std. Deviation N 70.30 7.981 20 Journal therapy only 65.85 8.381 20 Counseling only 71.10 7.210 20 Total 69.08 8.081 60 therapy Results Data screening Data screening was conducted on each group's dependent variables 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 and the covariate. No outliers were identified. See Figure 1 and Figure 2 for box and whisker plots. 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 Depression scores prior to treatment Figure 2. Box and Whisker Plot for Depression scores after treatment Assumptions An Analysis of Covariance (ANCOVA) was used to test the null hypothesis that looked at the differences among method of treatment while controlling for pre-test depression scores. The ANCOVA 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 Therapy type Kolmogorov-Smirnova Shapiro-Wilk Statistic Depression scores prior to treatment Depression scores after treatnent df Sig. Statistic df Sig. Counseling and journal therapy .124 20 .200* .960 20 .545 Journal therapy only .087 20 .200* .974 20 .828 Counseling only .096 20 .200* .969 20 .735 Counseling and journal therapy .115 20 .200* .972 20 .807 Journal therapy only .103 20 .200* .970 20 .747 Counseling only .138 20 .200* .955 20 .452 *. 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 = .004) so the assumption of homogeneity was not met. However, the ANCOVA is considered a robust test against the homogeneity assumption. 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 Variancesa Dependent Variable: Depression scores after treatnent F df1 6.037 df2 2 Sig. 57 .004 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept + group + depprior + group * depprior An ANCOVA also needs the Assumption of Linearity to be satisfied. This assumption tells us that the convariate term is linear with the dependent variable for each level of the factor. The obtained graphs are used to test for this assumption. The above graphs indicate linear relationships between the covariate term and the dependent variable indicating that the assumption of linearity has been met. The next assumption we need to check is the Assumption of Bivariate Normal Distribution. This assumption can directly be checked from the above scatter plots. The plots above indicates that this assumption might not be met for few groups. Assumption of Homogeneity of Slopes is the next assumption we need to verify. The following Table 4 is used for that purpose. Table 4 Tests of Between-Subjects Effects Dependent Variable: Depression scores after treatnent Type III Sum of Source Corrected Model Intercept group depprior Squares Partial Eta df Mean Square F Sig. Squared 2213.027a 5 442.605 14.578 .000 .574 1377.155 1 1377.155 45.358 .000 .457 31.713 2 15.857 .522 .596 .019 1885.246 1 1885.246 62.092 .000 .535 group * depprior 25.689 2 12.844 Error 1639.557 54 30.362 Total 290203.000 60 3852.583 59 Corrected Total .423 .657 .015 a. R Squared = .574 (Adjusted R Squared = .535) The table indicates the assumption is met at a 95% confidence level, F(2, 54) = .423, p = . 657, 2 = .015. Results for Null Hypothesis One An ANCOVA was used to test the null hypothesis; differences among method of treatment while controlling for pre-test depression scores. The null hypothesis was not rejected at a 95% confidence level were F(2, 54) = .522, p = .596, 2 = .019. See Table 5 Tests of BetweenSubjects Effects. Table 5 Tests of Between-Subjects Effects Dependent Variable: Depression scores after treatnent Type III Sum of Source Squares Partial Eta df Mean Square F Sig. Squared 2213.027a 5 442.605 14.578 .000 .574 1377.155 1 1377.155 45.358 .000 .457 31.713 2 15.857 .522 .596 .019 1885.246 1 1885.246 62.092 .000 .535 25.689 2 12.844 .423 .657 .015 Error 1639.557 54 30.362 Total 290203.000 60 3852.583 59 Corrected Model Intercept group depprior group * depprior Corrected Total a. R Squared = .574 (Adjusted R Squared = .535) Because the null was not rejected, post hoc analysis was not conducted. GROUP # WRITE-UP: ANCOVA 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 the depression scores among students who receive Journal and Counseling therapy, Journal therapy only, or Counseling therapy only, while controlling for pre-test depression scores? Null Hypothesis The null hypothesis for this study is: H01: There is no significant difference among the depression scores of students who receive Journal and Counseling therapy, Journal therapy only, or Counseling therapy only, while controlling for pre-test depression scores. Descriptive Statistics Data obtained for the dependent variable the depression scores for the students receiving Journal and Counseling therapy, Journal therapy only, or Counseling therapy only can be found in Table 1. Table 1 Descriptive Statistics Dependent Variable: Depression scores after treatnent Therapy type Counseling and journal Mean Std. Deviation N 70.30 7.981 20 Journal therapy only 65.85 8.381 20 Counseling only 71.10 7.210 20 Total 69.08 8.081 60 therapy Results Data screening Data screening was conducted on each group's dependent variables 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 and the covariate. No outliers were identified. See Figure 1 and Figure 2 for box and whisker plots. Tests of Normality Group a Kolmogorov-Smirnov Statistic TL Score .179 df Shapiro-Wilk Sig. 10 Statistic df Sig. .200 * .883 10 .140 .921 9 .399 .958 11 .751 AL .224 9 .200 * SL .105 11 .200 * *. This is a lower bound of the true significance. a. Lilliefors Significance Correction Figure 1. Box and Whisker Plot for Depression scores prior to treatment Figure 2. Box and Whisker Plot for Depression scores after treatment Assumptions An Analysis of Covariance (ANCOVA) was used to test the null hypothesis that looked at the differences among method of treatment while controlling for pre-test depression scores. The ANCOVA 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 Therapy type a Kolmogorov-Smirnov Shapiro-Wilk Statistic df Sig. .124 20 .200 * .960 20 .545 Journal therapy only .087 20 .200 * .974 20 .828 Counseling only .096 20 .200 * .969 20 .735 Counseling and journal therapy .115 20 .200 * .972 20 .807 Journal therapy only .103 20 .200 * .970 20 .747 Counseling only .138 20 .200 * .955 20 .452 Depression scores prior to treatment Counseling and journal therapy Depression scores after treatnent Statistic df Sig. *. 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 = .004) so the assumption of homogeneity was not met. However, the ANCOVA is considered a robust test against the homogeneity assumption. 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 Variances a Dependent Variable: Depression scores after treatnent F df1 6.037 df2 2 Sig. 57 .004 Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept + group + depprior + group * depprior An ANCOVA also needs the Assumption of Linearity to be satisfied. This assumption tells us that the convariate term is linear with the dependent variable for each level of the factor. The obtained graphs are used to test for this assumption. The above graphs indicate linear relationships between the covariate term and the dependent variable indicating that the assumption of linearity has been met. The next assumption we need to check is the Assumption of Bivariate Normal Distribution. This assumption can directly be checked from the above scatter plots. The plots above indicates that this assumption might not be met for few groups. Assumption of Homogeneity of Slopes is the next assumption we need to verify. The following Table 4 is used for that purpose. Table 4 Tests of Between-Subjects Effects Dependent Variable: Depression scores after treatnent Type III Sum of Source Corrected Model Intercept group depprior Squares Partial Eta df Mean Square F Sig. Squared a 5 442.605 14.578 .000 .574 1377.155 1 1377.155 45.358 .000 .457 31.713 2 15.857 .522 .596 .019 1885.246 1 1885.246 62.092 .000 .535 2213.027 group * depprior 25.689 2 12.844 Error 1639.557 54 30.362 Total 290203.000 60 3852.583 59 Corrected Total .423 .657 .015 a. R Squared = .574 (Adjusted R Squared = .535) The table indicates the assumption is met at a 95% confidence level, F(2, 54) = .423, p = .657, 2 = .015. Results for Null Hypothesis One An ANCOVA was used to test the null hypothesis; differences among method of treatment while controlling for pre-test depression scores. The null hypothesis was not rejected at a 95% confidence level were F(2, 54) = .522, p = .596, 2 = .019. See Table 5 Tests of BetweenSubjects Effects. Table 5 Tests of Between-Subjects Effects Dependent Variable: Depression scores after treatnent Type III Sum of Source Squares Partial Eta df Mean Square F Sig. Squared a 5 442.605 14.578 .000 .574 1377.155 1 1377.155 45.358 .000 .457 31.713 2 15.857 .522 .596 .019 1885.246 1 1885.246 62.092 .000 .535 25.689 2 12.844 .423 .657 .015 Error 1639.557 54 30.362 Total 290203.000 60 3852.583 59 Corrected Model Intercept group depprior group * depprior Corrected Total 2213.027 a. R Squared = .574 (Adjusted R Squared = .535) Because the null was not rejected, post hoc analysis was not conducted