The data analysis output below is a repeated measures ANOVA that was conducted to answer the following research question Does the use of an on line safety planning app decrease depression among survivors of intimate partner violence (IPV) Women were introduced to the app after completing a baseline survey They were surveyed again at 3 months, 6 months, and 12 months after using the safety planning app Depression was measured using the Patient Health Questionnaire 9 (PHQ9) PHQ9 Baseline, BPHQ9 3 months, CPHQ9 6 months, DPHQ9 12 months Please answer the questions that appear after the SPSS output (7 points) For pairwise comparisons the variables are coded 1 PHQ9 at Baseline 2 BPHQ9 at 3 months 3 CPHQ9 at 6 months 4 DPHQ9 at 12 months Descriptive Statistics Mean Std Deviation N 1 PHQ9 Baseline Patient Health Questionaire (PHQ) 13 8717 5 27303 207 2 BPHQ9 3 month Patient Health Questionaire (PHQ) 13 3895 4 81622 207 3 CPHQ9 6 months Patient Health Questionaire (PHQ) 13 0151 5 62743 207 4 DPHQ9 12 months Patient Health Questionaire (PHQ) 13 2965 5 19957 207 Mauchly's Test of Sphericity a Measure Depression Within Subjects Effect Mauchly's W Approx Chi Square df Sig Epsilon b Greenhouse Geisser Huynh Feldt Lower bound Time 800 45 753 5 000 859 871 333 Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix a Design Intercept Within Subjects Design Time b May be used to adjust the degrees of freedom for the averaged tests of significance Corrected tests are displayed in the Tests of Within Subjects Effects table Tests of Within Subjects Effects Measure Depression Source Type III Sum of Squares df Mean Square F Sig Time Sphericity Assumed 78 931 3 26 310 3 096 026 Greenhouse Geisser 78 931 2 577 30 635 3 096 033 Huynh Feldt 78 931 2 612 30 219 3 096 033 Lower bound 78 931 1 000 78 931 3 096 080 Error(Time) Sphericity Assumed 5251 615 618 8 498 Greenhouse Geisser 5251 615 530 762 9 894 Huynh Feldt 5251 615 538 068 9 760 Lower bound 5251 615 206 000 25 493 Pairwise Comparisons Measure Depression (I) Time (J) Time Mean Difference (I J) Std Error Sig b 95 Confidence Interval for Difference b Lower Bound Upper Bound 1 2 482 287 567 282 1 247 3 857 319 047 006 1 707 4 575 347 591 348 1 498 2 1 482 287 567 1 247 282 3 374 242 744 271 1 020 4 093 260 1 000 600 786 3 1 857 319 047 1 707 006 2 374 242 744 1 020 271 4 281 249 1 000 944 381 4 1 575 347 591 1 498 348 2 093 260 1 000 786 600 3 281 249 1 000 381 944 Based on estimated marginal means The mean difference is significant at the 05 level b Adjustment for multiple comparisons Bonferroni Based on the output tables provided Descriptively, at which time period did IPV survivors score highest on depression (1 point) Descriptively, at which time period did IPV survivors score lowest on depression (1 point) How would you interpret the results of the Mauchly's test for sphericity in the output (1 point) Based on the Mauchly's test result, which method would you select to test group differences (2 points) Please interpret the pairwise comparisons for these variables In the interpretation, indicate mean scores and standard deviations (or mean differences and standard errors) where significant differences exist (2 points)

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The data analysis output below is a repeated measures ANOVA that was conducted to answer the following research question: Does the use of an on-line safety planning app decrease depression among survivors of intimate partner violence (IPV). Women were introduced to the app after completing a baseline survey. They were surveyed again at 3-months, 6-months, and 12-months after using the safety planning app. Depression was measured using the Patient Health Questionnaire 9 (PHQ9): PHQ9=Baseline, BPHQ9=3-months, CPHQ9=6-months, DPHQ9=12-months. Please answer the questions that appear after the SPSS output. (7 points)

For pairwise comparisons the variables are coded 1 = PHQ9 at Baseline; 2=BPHQ9 at 3-months; 3 = CPHQ9 at 6-months; 4 =DPHQ9 at 12-months.

Descriptive Statistics
	Mean	Std. Deviation	N
1=PHQ9 Baseline Patient Health Questionaire (PHQ)	13.8717	5.27303	207
2=BPHQ9 3-month Patient Health Questionaire (PHQ)	13.3895	4.81622	207
3=CPHQ9 6-months Patient Health Questionaire (PHQ)	13.0151	5.62743	207
4=DPHQ9 12-months Patient Health Questionaire (PHQ)	13.2965	5.19957	207

Mauchly's Test of Sphericity^a
Measure: Depression
Within Subjects Effect	Mauchly's W	Approx. Chi-Square	df	Sig.	Epsilon^b
Greenhouse-Geisser	Huynh-Feldt	Lower-bound
Time	.800	45.753	5	.000	.859	.871	.333
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.
a. Design: Intercept Within Subjects Design: Time
b. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.

Tests of Within-Subjects Effects
Measure: Depression
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Time	Sphericity Assumed	78.931	3	26.310	3.096	.026
Greenhouse-Geisser	78.931	2.577	30.635	3.096	.033
Huynh-Feldt	78.931	2.612	30.219	3.096	.033
Lower-bound	78.931	1.000	78.931	3.096	.080
Error(Time)	Sphericity Assumed	5251.615	618	8.498
Greenhouse-Geisser	5251.615	530.762	9.894
Huynh-Feldt	5251.615	538.068	9.760
Lower-bound	5251.615	206.000	25.493

Pairwise Comparisons
Measure: Depression
(I) Time	(J) Time	Mean Difference (I-J)	Std. Error	Sig.^b	95% Confidence Interval for Difference^b
Lower Bound	Upper Bound
1	2	.482	.287	.567	-.282	1.247
3	.857^*	.319	.047	.006	1.707
4	.575	.347	.591	-.348	1.498
2	1	-.482	.287	.567	-1.247	.282
3	.374	.242	.744	-.271	1.020
4	.093	.260	1.000	-.600	.786
3	1	-.857^*	.319	.047	-1.707	-.006
2	-.374	.242	.744	-1.020	.271
4	-.281	.249	1.000	-.944	.381
4	1	-.575	.347	.591	-1.498	.348
2	-.093	.260	1.000	-.786	.600
3	.281	.249	1.000	-.381	.944
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
b. Adjustment for multiple comparisons: Bonferroni.

Based on the output tables provided:

Descriptively, at which time period did IPV survivors score highest on depression? (1 point)

Descriptively, at which time period did IPV survivors score lowest on depression? (1 point)

How would you interpret the results of the Mauchly's test for sphericity in the output? (1 point)

Based on the Mauchly's test result, which method would you select to test group differences? (2 points)

Please interpret the pairwise comparisons for these variables. In the interpretation, indicate mean scores and standard deviations (or mean differences and standard errors) where significant differences exist. (2 points)