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).
