Friday, May 3, 2013


 Not that anyone might be interested, but I thought this analysis might be of value to preserve, at least for me. Basically it is a series of statistical analyses on various aspects of worship attendance in the NTNL mission area. The jist of it is for me at least. 2009 did cost us worship attendance. Location of congregations (Urban, Suburban, Rural, Small City) does not predict growth or stagnation/decline. Size of a congregation also is only very slightly correlated with worship attendance growth. The language a congregation speaks is not a significant factor in differences in attendance. 

What is missing in all of this is analysis of the leadership of the congregations. Who were the pastors and lay leaders. I think if that was included, in a dissertation perhaps, that might get us somewhere.

EG






PHDL 7330 Final
Erik Gronberg
Dallas Baptist University


















1: One Sample t-test
Hypothesis: H0: µ = 107; H1: µ ≠ 107

Question: Did the average worship attendance of churches in the Greater Fort Worth conference of the ELCA in 2011 differ significantly from that of the entire Northern Texas Northern Louisiana mission territory (NTNL)?

One-Sample Statistics

N
Mean
Std. Deviation
Std. Error Mean
2011 Average Worship Attd
16
114.6250
99.16375
24.79094

One-Sample Test

Test Value = 107
t
Df
Sig. (2-tailed)
Mean Difference
95% Confidence Interval of the Difference
Lower
Upper
2011 Average Worship Attd
.308
15
.763
7.62500
-45.2156
60.4656

            Figure 1 Output for a one sample t-test

Reject/Fail to Reject: The null hypothesis is not rejected, p(0.763)> .05, there is not a significant difference between sample mean and test value.
Effect size: d= 7.63/99.16 =  .08 Effect size is very small (<.50).
Conclusion: This sample of sixteen ELCA churches in the Fort Worth area (M = 114.63, SD = 99.16) do not have a significantly different average worship attendance in 2011 than the average for the NTNL of 107, t(15) = .308, p > .05, d = 0.07. There is no significant difference in average worship attendance between the entire NTNL and the average in 2011 for the Greater Fort Worth Conference.


2: Independent Samples t-test
Variables: LANGUAGE (primary worship language)  AVGWOR (Average Weekly Worship)

Hypothesis: Ho: µnon-english = µenglish; H1: µnon-english ≠ µenglish

Question: Averaging from 1992-2012 is there a difference in attendance between congregations in the NTNL whose primary worship language is not-English versus those in English?

Group Statistics

LANGUAGE
N
Mean
Std. Deviation
Std. Error Mean
AVGWOR
Non-English
9
192.2222
304.64232
101.54744
English
98
116.4898
107.84164
10.89365

Independent Samples Test

Levene's Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
AVGWOR
Equal variances assumed
14.796
.000
1.629
105
.106
75.7324
46.48870
-16.44607
167.91093
Equal variances not assumed


.742
8.185
.479
75.7324
102.1300
-158.85612
310.32098
Figure 2 Output for an Independent sample t-test

Assumption of equality of variances: p(.000)<.05 so cannot assume equal variances.
Reject/Fail to Reject: Null hypothesis not rejected p(.479) > .05.  
Effect size: d = t √((N1+N2)/(N1*N2)) = .742√((9+98)/(9*98)) = .26  The effect size is irrelevant as the results are not significant.
Conclusion: The worship attendance in 1992-2012 of the 9 non-english speaking congregations (M = 192.22, SD = 101.55) in this sample was not significantly different than the worship attendance of the 98 English speaking congregations (M = 116.49, SD = 10.89), t(8.2) = .742, p > .05, d = .26. Equal variances could not be assumed (F(105) = 14.80, p < 0.05). Extrapolating from this sample it can be assumed that non-English speaking and English speaking congregations show no discernable difference in average weekly worship attendance. However, given that equal variances cannot be assumed, further testing should be done as a small set of outliers might be affecting the result.
























3: Dependent Samples t-test
Variables: PRIWORATT(2007-2009)  POSWORATT (after 2009)

Hypothesis: Ho: µpriworatt - µposworatt = 0;  H1: µpriworatt - µpostworatt ≠ 0
Question: Did average Sunday attendance in the Northern Texas-Northern Louisiana Mission Territory fall in the three years after 2009 in comparison to the average for 2007-2009?
Paired Samples Statistics


Mean
N
Std. Deviation
Std. Error Mean

Pair 1
Worship Att 2007-2009
108.4904
104
115.34322
11.31033

Worship Att Post 2009
116.7788
104
242.98547
23.82669

Paired Samples Correlations


N
Correlation
Sig.

Pair 1
Worship Att 2007-2009  & Worship Att Post 2009
104
.678
.000

Paired Samples Test

Paired Differences
t
Df
Sig. (2-tailed)
Mean
Std. Deviation
Std. Error Mean
95% Confidence Interval of the Difference
Lower
Upper
Pair 1
Worship Att 2007-2009 - Worship Att Post 2009
-8.28846
185.24079
18.16435
-44.31317
27.73625
-.456
103
.649
 Figure 3 Output for a Dependent Samples t-test
Reject/Fail to Reject: Fail to reject the null hypothesis p(.649)>.05. There is a not a significant difference in worship attendance prior to 2009 and after.
Effect size: d = -8.29/185.24 = -.045. Effect size is very small (<.20).
Conclusion: In 2009 the ELCA made a very controversial decision as a church body which has been widely assumed to decrease involvement and worship attendance. This study shows that worship attendance prior (2007-2009) (M = 108.49, SD = 115.34) is not significantly different than worship attendance after 2009 (M = 116.78, SD = 242.99), t(104) = -.46, p (.65) > .05, d = -.045.  However, a significant outlier congregation who has grown at a significant rate in those years may have skewed the results. Removing this outlier these results are displayed below…
Paired Samples Statistics-Outlier Removed


Mean
N
Std. Deviation
Std. Error Mean

Pair 1
Worship Att 2007-2009
104.4757
103
108.35977
10.67701

Worship Att Post 2009
94.9903
103
98.81122
9.73616

Paired Samples Correlations-Outlier Removed


N
Correlation
Sig.

Pair 1
Worship Att 2007-2009 & Worship Att Post 2009
103
.935
.000

Paired Samples Test-Outlier Removed

Paired Differences
t
df
Sig. (2-tailed)
Mean
Std. Deviation
Std. Error Mean
95% Confidence Interval of the Difference
Lower
Upper
Pair 1
Worship Att 2007-2009 - Worship Att Post 2009
9.48544
38.38833
3.78251
1.98284
16.98804
2.508
102
.014
Figure 4 Output for a Dependent Samples t-test less Outlier
Reject/Fail to Reject: Reject the null hypothesis p(.014)<.05. There is a significant difference in worship attendance prior to 2009 and after. It is lower.
Effect size: d = 9.49/38.39 = .25 Effect size is small (.20<E<.50).
Conclusion: In the Northern Texas-Northern Louisiana Mission Area one congregation has grown a great deal in the past three years. This congregation’s growth skewed previous analysis. This study shows that by removing this outlier average worship attendance prior (2007-2009) (M = 104.48, SD = 108.36) is significantly lower than worship attendance after 2009 (M = 94.99, SD = 98.81), t(103) = 2.51, p (.014) < .05, d = 0.25. The effect size of the difference is not large however, so further analysis is warranted to discern the significant causes of decline.
4: One-Way ANOVA

Variables: SIZE (Size categories) ATTGROW (percentage growth or decline in worship attd)

Question: Does the size of a congregations worship attendance in the NTNL predict their population growth or decline between 2008-2012?
Hypothesis: Ho: µ0-50 = µ50-100 = µ101-150 = µ150-200 = µ200+; H1: at least one pop. mean is different.

Test of Homogeneity of Variances
% Attendance Growth/Decline
Levene Statistic
df1
df2
Sig.
3.008
4
102
.022
Figure 5.1 Output for test of homogenous variances

Homogeneity of Variances: p(.022) < .05, null hypothesis rejected, equal variances not assumed.

Descriptives
% Attendance Growth/Decline

N
Mean
Std. Deviation
Std. Error
95% Confidence Interval for Mean
Minimum
Maximum
Lower Bound
Upper Bound
1-50
42
.1726
.43498
.06712
.0371
.3082
.00
1.90
51-100
31
.0652
.21489
.03860
-.0137
.1440
.00
1.06
101-150
14
.1221
.37524
.10029
-.0945
.3388
.00
1.40
151-200
10
.0380
.09295
.02939
-.0285
.1045
.00
.29
200+
10
.2740
.78577
.24848
-.2881
.8361
.00
2.50
Total
107
.1318
.40173
.03884
.0548
.2088
.00
2.50

ANOVA
% Attendance Growth/Decline

Sum of Squares
df
Mean Square
F
Sig.
Between Groups
.499
4
.125
.766
.550
Within Groups
16.608
102
.163


Total
17.107
106



Figure 5.2 Output for one-way ANOVA

Reject/Fail to Reject: p(.550) > .05, null hypothesis not rejected. No statistically significant difference between means (percentage growth of worship attendance). No post hoc tests required and as such are not shown here.
Eta2: η2= sum of squares between groups/sum of squares total = .499/16.608 = .030.
            -As the result is not significant, the effect size is irrelevant.
Conclusion: The percentage growth of a congregation from 2008-2012 is not statistically significant different based on the size category of the congregation, F(4,102) = .766, p > .05, η2= .030. There was not a significant difference in growth or decline rates based on the size category of a congregation between 2008-2012. Post-hoc tests are unnecessary and for the sake of space not presented here. This data would seem to support a conclusion congregational size is not significant in the growth or decline of a congregation. Additional testing should be done to determine if there are other statistical factors that significantly affect growth or decline of congregations.













5: Chi-Square test of Independence

Variables: LOCATION(Urban, Suburban, Rural or Small City)  GROWTH (growing, stagnant

or declining 2008-2012)

Assumptions: The Chi-Square test of Independence assumes a random sample with randomly collected observations in each cell of the data that are independent of each other. In other words, each randomly selected subject only contributes once to the sample. Additionally, there cannot be any empty cells and at least 80% of the cells must have a count or frequency greater than 5.
Question: Is there a relationship between internet use and marital status?
Hypotheses:     Ho: Worship growth/decline and location are independent (no relationship).
                        H1: Worship growth/decline and location are not independent (relationship).

Case Processing Summary


Cases

Valid
Missing
Total

N
Percent
N
Percent
N
Percent

Church Location * Growing or Decling
107
100.0%
0
0.0%
107
100.0%

Church Location * Growing or Decling Crosstabulation

Growing or Decling
Total
Growing
Stagnant or Declining
Church Location
Urban
Count
6
24
30
Expected Count
6.4
23.6
30.0
% within Church Location
20.0%
80.0%
100.0%
Suburban
Count
9
17
26
Expected Count
5.6
20.4
26.0
% within Church Location
34.6%
65.4%
100.0%
Rural
Count
5
28
33
Expected Count
7.1
25.9
33.0
% within Church Location
15.2%
84.8%
100.0%
Small City
Count
3
15
18
Expected Count
3.9
14.1
18.0
% within Church Location
16.7%
83.3%
100.0%
Total
Count
23
84
107
Expected Count
23.0
84.0
107.0
% within Church Location
21.5%
78.5%
100.0%
Chi-Square Tests


Value
df
Asymp. Sig. (2-sided)

Pearson Chi-Square
3.728a
3
.292

Likelihood Ratio
3.518
3
.318

Linear-by-Linear Association
.556
1
.456

N of Valid Cases
107



a. 1 cells (12.5%) have expected count less than 5. The minimum expected count is 3.87.


Symmetric Measures

Value
Approx. Sig.
Nominal by Nominal
Phi
.187
.292
Cramer's V
.187
.292
N of Valid Cases
107

a. Not assuming the null hypothesis.
b. Using the asymptotic standard error assuming the null hypothesis.
 Figure 5  Output for the chi-square test of independence

Reject/Fail to Reject: Since p(.292) > .05 the null hypothesis is not rejected. There is a not a significant relationship between the variables.
Effect Size: V = √(χ2/(N(k-1))) = √(3.728/(107(2-1))) = .187
The effect size (.19) is small. Additionally, since the null is not rejected, it is irrelevant.
Conclusion: There is not a significant relationship between location (urban, suburban, rural or small city) and whether a congregation is growing, stagnant or declining in worship attendance, χ2(4, N = 107) = 3.73, p > .05, Cramer’s V = .19. Congregations in Urban (20.0% growing, 80.0 % stagnant or declining), Suburban (34.6% growing, 65.4.1 % stagnant or declining), Rural (15.2% growing, 84.8 % stagnant or declining) or Small City (16.7% growing, 83.3% stagnant or declining) exhibit levels of growth and decline that are independent of location. Given the size of the sample (N=107) it is possible that a few outliers significant affect this procedure. Additionally, one cell has a count less than 5 which given that this is a larger table (greater than 4 cells) does not invalidate the results, but a larger sample might be helpful. Additional analysis should be done to discern what additional factors might be predictive of growth or decline. This will be done later through regression analysis.





















6: Simple Linear Regression

Variables: SIZE (avg worship attd 2008-2012) GROWTH (% inc/dec worship attd 2008-2012)

                        Figure 6.1 Scatterplot with regression line for SIZE and GROWTH

Hypothesis: H0 : βsize = 0; H1 : βsize ≠ 0
Question: Does the size of a congregation predict their growth or decline?
Descriptive Statistics


Mean
Std. Deviation
N

Growth Rate 2008-2012
-.0222
.48394
107

Church Worship Attd
111.1963
178.64931
107







Correlations


Growth Rate 2008-2012
Church Worship Attd

Pearson Correlation
Growth Rate 2008-2012
1.000
.386

Church Worship Attd
.386
1.000

Sig. (1-tailed)
Growth Rate 2008-2012
.
.000

Church Worship Attd
.000
.

N
Growth Rate 2008-2012
107
107

Church Worship Attd
107
107

Variables Entered/Removeda

Model
Variables Entered
Variables Removed
Method

1
Church Worship Attdb
.
Enter

a. Dependent Variable: Growth Rate 2008-2012

b. All requested variables entered.

Model Summary

Model
R
R Square
Adjusted R Square
Std. Error of the Estimate

1
.386a
.149
.141
.44849

a. Predictors: (Constant), Church Worship Attd

ANOVAa

Model
Sum of Squares
df
Mean Square
F
Sig.

1
Regression
3.705
1
3.705
18.420
.000b

Residual
21.120
105
.201



Total
24.825
106




a. Dependent Variable: Growth Rate 2008-2012

b. Predictors: (Constant), Church Worship Attd

Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
-.139
.051

-2.711
.008
Church Worship Attd
.001
.000
.386
4.292
.000
a. Dependent Variable: Growth Rate 2008-2012

Figure 6.2
Output for the linear regression procedure

R/ R2: R is the multiple correlation coefficient and is equal to the Pearson correlation. A value of .386 indicates that there is a positive correlation between SIZE and GROWTH. R2 indicates the percentage of the total variance in GROWTH that can be attributed to SIZE. In this case SIZE is responsible for 14.9% of the variance in GROWTH. These values show that the size of a congregation has some predictive impact on the growth/decline of a congregation.

Reject/Fail to Reject: As p (.000) < .05 we reject the null hypothesis that the beta weight of SIZE is equal to zero. There is a relationship between the variables.

Regression Equation: Ŷ = a + bx    ŶGROWTH = -.139 + .001(SIZE)
 The regression equation shows that there is a small positive correlation between the size of a congregation and their growth/decline.

Conclusion: A regression analysis was conducted with worship growth/decline (2008-2012) as the criterion variable and average worship attendance (2008-2012) completed as the predictor. Average worship attendance was a significant predictor of income level, β = .39, t(107) = 4.29, p < .05, and accounted for 15% (R2 = .15) of the variance in growth or decline. While not an overly large predictor of growth or decline this analysis demonstrates larger average worship attendance is correlated with a slightly higher percentage increase in worship attendance from 2008-2012. However the effect of this is small. For example, for every 100 average worshippers at a congregation the equation predicts an increase in growth rate of .1% over the four year period. There must be other significant factors that play into predicting a congregations growth rate.

7: Multiple Regression

Dependent Variable: GROWTH (% inc/dec worship attd 2008-2012)

Independent Variables: SIZE (avg worship attd 2008-2012), LOCATION (Urban, Suburban, Rural, Small City), 1990GD (1992-2002 Growth/Decline), 2000GD (2002-2012 Growth/Decline)
Individual Hypotheses:
H0: βsize= 0    (H.1)      H1: βsize ≠ 0
H0: βlocation  =  0   (H.2)      H1: βlocation ≠ 0  
H0: βGD1990   = 0    (H.3)      H1: βGD1990 ≠ 0
H0: βGD2000   = 0    (H.4)      H1: βGD2000 ≠ 0
Overall Regression Model Hypothesis:
H0:  R2 = 0           (H.5)      H1: R2 > 0

Research Questions For Individual Predictors:
     H.1: Does average size predict inc/dec in average worship attendance from 2008-2012?
     H.2: Does location predict inc/dec in average worship attendance from 2008-2012?    
     H.3: Does growth or decline (1992-2002) predict inc/dec in average worship attendance from              2008-2012?    
     H.4: Does growth or decline (2002-2012) predict inc/dec in average worship attendance from 2008-2012?
Research Question For Overall Regression Model…
     H.5: When taken together, do size, location, growth or decline from 1992-2002 and growth or             decline 2002-2012 predict % inc/dec in average worship attendance from 2008-2012?

Descriptive Statistics

Mean
Std. Deviation
N
Growth/Decline 2008-2012
.0524
1.26847
94
Congregation Size 2008-2012
97.8149
103.55718
94
Urban,Suburban, Rural, Small City
2.3723
1.07747
94
Growth/Decline 1990's
-.0490
.48417
94
Growth/Decline 2000s
-.1851
.89089
94

Correlations

Growth/Decline 2008-2012
Congregation Size 2008-2012
Urban,Suburban, Rural, Small City
Growth/Decline 1990's
Growth/Decline 2000s
Pearson Correlation
Growth/Decline 2008-2012
1.000
.030
-.075
-.103
.939
Congregation Size 2008-2012
.030
1.000
-.265
.386
.080
Urban,Suburban, Rural, Small City
-.075
-.265
1.000
-.127
-.050
Growth/Decline 1990's
-.103
.386
-.127
1.000
-.147
Growth/Decline 2000s
.939
.080
-.050
-.147
1.000
Sig. (1-tailed)
Growth/Decline 2008-2012
.
.386
.237
.162
.000
Congregation Size 2008-2012
.386
.
.005
.000
.222
Urban,Suburban, Rural, Small City
.237
.005
.
.110
.317
Growth/Decline 1990's
.162
.000
.110
.
.078
Growth/Decline 2000s
.000
.222
.317
.078
.
N
Growth/Decline 2008-2012
94
94
94
94
94
Congregation Size 2008-2012
94
94
94
94
94
Urban,Suburban, Rural, Small City
94
94
94
94
94
Growth/Decline 1990's
94
94
94
94
94
Growth/Decline 2000s
94
94
94
94
94


Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
Growth/Decline 2000s, Urban,Suburban, Rural, Small City, Growth/Decline 1990's, Congregation Size 2008-2012b
.
Enter
a. Dependent Variable: Growth/Decline 2008-2012
b. All requested variables entered.

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.943a
.889
.884
.43129
a. Predictors: (Constant), Growth/Decline 2000s, Urban,Suburban, Rural, Small City, Growth/Decline 1990's, Congregation Size 2008-2012

ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
133.084
4
33.271
178.864
.000b
Residual
16.555
89
.186


Total
149.640
93



a. Dependent Variable: Growth/Decline 2008-2012
b. Predictors: (Constant), Growth/Decline 2000s, Urban,Suburban, Rural, Small City, Growth/Decline 1990's, Congregation Size 2008-2012


Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
.523
.131

3.979
.000
Congregation Size 2008-2012
-.001
.000
-.081
-2.047
.044
Urban,Suburban, Rural, Small City
-.048
.043
-.041
-1.110
.270
Growth/Decline 1990's
.167
.102
.064
1.631
.106
Growth/Decline 2000s
1.357
.051
.953
26.420
.000
a. Dependent Variable: Growth/Decline 2008-2012

Figure 7 Output for the multiple regression procedure

R/ R2: R is .943 which indicate these measures of growth and location are positively correlated with the overall regression model based on the four predictors. R2=.889 which indicates that 89% of the variance in growth/decline from 2008-2012 can be attributed to the predictor variables.

Significant Predictors: p(.044)<.05 for SIZE (CONG SIZE 2008-2012) and  p(000) < .05 for GD2000s (Growth/Decline 2000s). These two predictor variables are significant as predictors of the rate of growth for worship attendance 2008-2012.
Non-Significant Predictors: p (.270) > .05 for LOCATION (Urban, Suburban, Rural, Small City) and p(.106) > .05 for GD1990 (Growth/Decline 1992-2002). Apparently the location and the level of growth from 1992-2002 in worship attendance is not a significant predictor of  worship attendance growth 2008-2012.
Reject/Fail to Reject:
            Individual Hypotheses:
      H0: βSIZE= 0    (H.1)      H1: βSIZE ≠ 0  REJECT THE NULL p<.05
      H0: βLOCATION  =  0   (H.2)      H1: βLOCATION ≠ 0    FAIL TO REJECT p>.05
      H0: βGD1990   = 0    (H.3)      H1: βGD1990 ≠ 0     FAIL TO REJECT p > .05
      H0: βGD2000   = 0    (H.4)      H1: βGD2000 ≠ 0     REJECT THE NULL p<.05

            Overall Regression Model Hypothesis:
      H0:  R2 = 0           (H.5)      H1: R2 > 0          REJECT THE NULL p<.05

Regression Equation: Ŷ = a + b1X1 + b2X2 + b3X3 + b4X4
ŶGROWTH =  .523 +  -.001(SIZE) +  -.048(LOCATION) +  .167(GD1990) +  1.357(GD2000)
The regression equation shows the negative correlation of two of the four of the predictor variables on the growth rate of congregational worship attendance from 2008-2012. This equation shows the increasing importance and impact on the correlation from overall size from 2008-2012 to growth from 2002 to 2012. The equation also shows how little in the overall equation the location and the growth/decline of worship attendance from 1992-2002 mattered.

Conclusion: A multiple regression was conducting predicting growth in worship attendance from 2008-2012 based on growth of the congregations worship attendance from 1992-2002 and 2002-2012 as well as the location of the congregation and its overall  average size from 2008-2012. The sample was limited to the 94 congregations with data that spanned this period. Overall, the regression was significant, F(4, 89) = 178.86, p< .05, R2:= .89. Of the predictors investigated, SIZE (β = -.00, t(89) = -2.05, p < .05) and GD2000 (β = 1.36, t(89) = 26.42, p < .05) were significant. GD1990 (β = .17, t(89) = 1.63, p > .05)  and LOCATION (β = -.05, t(89) = -1.11, p < .05) were not a predictor. These results indicate that the current size of a congregation is slightly negatively correlated with worship attendance growth while overall growth/decline over the decade of the 2000’s is much more positively associated with growth. From this analysis it can be stated that neither location (urban, suburban, rural or small city) nor growth/decline in the decade of the 1990s were significantly associated with growth during the 2008-2012 time span. The most significant predictor is the overall growth rate of the congregation during the decade of the 2000’s which is logical because that decade would include the 2008-2012 time frame in its statistics. As a result, this study is far from definitive on the predictors of growth and is more useful is demonstrating what are not significant predictors. More investigation should be done into why this study result occurred and the implications of these results.









8: Correlation
Hypothesis: H0: ρ = 0; H1: ρ ≠ 0

Question: Is there a relationship between Attendance growth/decline from 1992-2002 and attendance growth/decline from 2002-2012?
                        Figure 8.1 Scatterplot with regression line for Att1990s and Att2000s


Correlations

Att. Growth/Decline 1992-2002
Att. Growth/Decline 2002-2012
Att. Growth/Decline 1992-2002
Pearson Correlation
1
-.146
Sig. (2-tailed)

.157
N
95
95
Att. Growth/Decline 2002-2012
Pearson Correlation
-.146
1
Sig. (2-tailed)
.157

N
95
95
Figure 8.2 Output for the correlation procedure

Reject/Fail to Reject: As p (.157) > .05 we fail to reject the null hypothesis that the correlation coefficient is equal to zero. There is no significant relationship between the variables.

Effect size: ρ is commonly used as effect size in these cases. With ρ = -.15 this would be categorized as a small effect size.

Conclusion: There is not a significant positive or negative relationship r(93) = -.15, p > .05 between the growth/decline of attendance between 1992-2002 and 2002-2012 among the 95 churches in the Northern Texas/Northern Louisiana Synod that have statistics for these periods. There is no relationship between the growth or decline of congregations in these two decades. From this analysis it can be assumed that prior growth or decline are not correlated with later growth or decline. This is good news for congregations in decline as well as a challenge to those that are growing. Past results do not correlate to future results.







9: Non-Parametric (Wilcoxon Signed Rank Test)
Variables: PRIWORATT(2007-2009)  POSWORATT (after 2009)

Hypothesis: Ho: µpriworatt - µposworatt = 0;  H1: µpriworatt - µpostworatt ≠ 0
Question: Did average Sunday attendance in the Northern Texas-Northern Louisiana Mission Territory fall in the three years after 2009 in comparison to the average for 2007-2009?

Descriptive Statistics

N
Mean
Std. Deviation
Minimum
Maximum
Percentiles
25th
50th (Median)
75th
Worship Att Post 2009
104
116.7917
242.94776
10.00
2360.67
36.7500
63.0000
126.8333
Worship Att 2007-2009
104
108.5096
115.33385
8.00
626.00
38.2500
71.8333
137.9167


Ranks

N
Mean Rank
Sum of Ranks
Worship Att 2007-2009 - Worship Att Post 2009
Negative Ranks
22a
40.75
896.50
Positive Ranks
79b
53.85
4254.50
Ties
3c


Total
104


a. Worship Att 2007-2009 < Worship Att Post 2009
b. Worship Att 2007-2009 > Worship Att Post 2009
c. Worship Att 2007-2009 = Worship Att Post 2009

Test Statisticsa

Worship Att 2007-2009 - Worship Att Post 2009
Z
-5.688b
Asymp. Sig. (2-tailed)
.000
a. Wilcoxon Signed Ranks Test
b. Based on negative ranks.
Figure 9 Output for a Wilcoxon Signed Rank Test
Reject/Fail to Reject: Fail to reject the null hypothesis p(.649)>.05. There is a not a significant difference in worship attendance prior to 2009 and after.
Effect size: r  = z/√N = 5.69/√104 = .56  Effect size is large (>.50).
Conclusion: In 2009 the ELCA made a very controversial decision as a church body which has been widely assumed to decrease involvement and worship attendance. Previously a dependent samples t-test was performed that indicated there was no significant difference. However, an outlier was identified that might skew the results and when removed the result was significant. To contribute to the robustness of this analysis, a Wilcoxon Signed Rank Test (non-parametric) was performed which helps control for such outliers through the use of medians and ranking. This study shows that worship attendance prior (2007-2009) (M = 108.50, SD = 115.34) is significantly different than worship attendance after 2009 (M = 116.79, SD = 242.94), z = -5.69, p (.000) < .05, r = .56. The median average attendance decreased from 2007-2009 (Md = 72) to post 2009 (Md = 63).