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 ttest
Hypothesis: H_{0}:
µ = 107; H_{1}: 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)?
OneSample Statistics



N

Mean

Std. Deviation

Std. Error Mean

2011 Average Worship Attd

16

114.6250

99.16375

24.79094

OneSample Test



Test Value = 107


t

Df

Sig. (2tailed)

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
ttest
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 ttest
Variables: LANGUAGE
(primary worship language) AVGWOR (Average
Weekly Worship)
Hypothesis: Ho: µ_{nonenglish}
= µ_{english}; H_{1}: µ_{nonenglish} ≠ µ_{english}
Question: Averaging
from 19922012 is there a difference in attendance between congregations in the
NTNL whose primary worship language is notEnglish versus those in English?
Group Statistics



LANGUAGE

N

Mean

Std. Deviation

Std. Error Mean

AVGWOR

NonEnglish

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

ttest for Equality of
Means


F

Sig.

t

df

Sig. (2tailed)

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 ttest
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 √((N_{1}+N_{2})/(N_{1}*N_{2}))
= .742√((9+98)/(9*98)) = .26 The effect
size is irrelevant as the results are not significant.
Conclusion: The
worship attendance in 19922012 of the 9 nonenglish 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 nonEnglish 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 ttest
Variables: PRIWORATT(20072009) POSWORATT (after 2009)
Hypothesis:
Ho: µ_{priworatt}  µ_{posworatt} = 0; H_{1}: µ_{priworatt}  µ_{postworatt
}≠ 0
Question:
Did average Sunday attendance in the Northern TexasNorthern Louisiana Mission
Territory fall in the three years after 2009 in comparison to the average for
20072009?
Paired Samples
Statistics



Mean

N

Std. Deviation

Std. Error Mean


Pair 1

Worship Att 20072009

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 20072009 &
Worship Att Post 2009

104

.678

.000


Paired Samples Test



Paired Differences

t

Df

Sig. (2tailed)


Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval
of the Difference


Lower

Upper


Pair 1

Worship Att 20072009  Worship Att Post 2009

8.28846

185.24079

18.16435

44.31317

27.73625

.456

103

.649


Figure 3 Output for a Dependent Samples ttest
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 (20072009) (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
StatisticsOutlier Removed



Mean

N

Std. Deviation

Std. Error Mean


Pair 1

Worship Att 20072009

104.4757

103

108.35977

10.67701


Worship Att Post 2009

94.9903

103

98.81122

9.73616


Paired Samples
CorrelationsOutlier Removed



N

Correlation

Sig.


Pair 1

Worship Att 20072009 & Worship Att Post 2009

103

.935

.000


Paired Samples TestOutlier
Removed



Paired Differences

t

df

Sig. (2tailed)


Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval
of the Difference


Lower

Upper


Pair 1

Worship Att 20072009  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 ttest 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 TexasNorthern 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 (20072009) (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: OneWay 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 20082012?
Hypothesis:
Ho: µ_{050} = µ_{50100 }= µ_{101150} = µ_{150200
}= µ_{200+}; H_{1}: 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


150

42

.1726

.43498

.06712

.0371

.3082

.00

1.90

51100

31

.0652

.21489

.03860

.0137

.1440

.00

1.06

101150

14

.1221

.37524

.10029

.0945

.3388

.00

1.40

151200

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 oneway 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.
Eta^{2}:
η^{2}= 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 20082012 is not statistically
significant different based on the size category of the congregation, F(4,102)
= .766, p > .05, η^{2}= .030. There was not a significant difference
in growth or decline rates based on the size category of a congregation between
20082012. Posthoc 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: ChiSquare test of
Independence
Variables:
LOCATION(Urban, Suburban, Rural or Small City)
GROWTH (growing, stagnant
or declining 20082012)
Assumptions: The
ChiSquare 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).
H_{1}:
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%


ChiSquare Tests



Value

df

Asymp. Sig. (2sided)


Pearson ChiSquare

3.728^{a}

3

.292


Likelihood Ratio

3.518

3

.318


LinearbyLinear 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 chisquare 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 =
√(χ^{2}/(N(k1))) = √(3.728/(107(21))) = .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, χ^{2}(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 20082012) GROWTH (% inc/dec worship attd 20082012)
Figure 6.1 Scatterplot with regression line for SIZE and GROWTH
Hypothesis:
H_{0} : β_{size} = 0; H_{1 }: β_{size} ≠ 0
Question:
Does the size of a congregation predict their growth or decline?
Descriptive Statistics



Mean

Std. Deviation

N


Growth Rate 20082012

.0222

.48394

107


Church Worship Attd

111.1963

178.64931

107







Correlations



Growth Rate 20082012

Church Worship Attd


Pearson Correlation

Growth Rate 20082012

1.000

.386


Church Worship Attd

.386

1.000


Sig. (1tailed)

Growth Rate 20082012

.

.000


Church Worship Attd

.000

.


N

Growth Rate 20082012

107

107


Church Worship Attd

107

107


Variables Entered/Removed^{a}


Model

Variables Entered

Variables Removed

Method


1

Church Worship Attd^{b}

.

Enter


a. Dependent Variable: Growth Rate
20082012


b. All requested variables entered.


Model Summary


Model

R

R Square

Adjusted R Square

Std. Error of the Estimate


1

.386^{a}

.149

.141

.44849


a. Predictors: (Constant), Church
Worship Attd


ANOVA^{a}


Model

Sum of Squares

df

Mean Square

F

Sig.


1

Regression

3.705

1

3.705

18.420

.000^{b}


Residual

21.120

105

.201




Total

24.825

106





a. Dependent Variable: Growth Rate
20082012


b. Predictors: (Constant), Church
Worship Attd


Coefficients^{a}


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
20082012


Figure 6.2 Output for the linear regression procedure
R/ R^{2}:
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. R^{2} 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 Ŷ_{GROWTH} = .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 (20082012) as
the criterion variable and average worship attendance (20082012) 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% (R^{2} = .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 20082012. 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 20082012)
Independent
Variables: SIZE (avg worship attd 20082012), LOCATION (Urban, Suburban,
Rural, Small City), 1990GD (19922002 Growth/Decline), 2000GD (20022012 Growth/Decline)
Individual
Hypotheses:
H_{0}: β_{size}=
0 (H.1) H_{1}:
β_{size} ≠ 0
H_{0}: β_{location}
= 0
(H.2) H_{1}: β_{location}
≠ 0
H_{0}: β_{GD1990}
= 0
(H.3) H_{1}: β_{GD1990}
≠ 0
H_{0}: β_{GD2000}
= 0
(H.4) H_{1}: β_{GD2000}
≠ 0
Overall
Regression Model Hypothesis:
H_{0}: R^{2} = 0 (H.5) H_{1}: R^{2} > 0
Research
Questions For Individual Predictors:
H.1: Does average size predict inc/dec in average worship attendance
from 20082012?
H.2: Does location predict inc/dec in average worship attendance from
20082012?
H.3: Does growth or decline (19922002) predict inc/dec in average
worship attendance from 20082012?
H.4: Does growth or decline (20022012) predict inc/dec in average
worship attendance from 20082012?
Research
Question For Overall Regression Model…
H.5: When taken
together, do size, location, growth or decline from 19922002 and growth or decline 20022012 predict % inc/dec
in average worship attendance from 20082012?
Descriptive Statistics



Mean

Std. Deviation

N

Growth/Decline 20082012

.0524

1.26847

94

Congregation Size 20082012

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
20082012

Congregation Size
20082012

Urban,Suburban, Rural,
Small City

Growth/Decline 1990's

Growth/Decline 2000s


Pearson Correlation

Growth/Decline 20082012

1.000

.030

.075

.103

.939

Congregation Size 20082012

.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. (1tailed)

Growth/Decline 20082012

.

.386

.237

.162

.000

Congregation Size 20082012

.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 20082012

94

94

94

94

94

Congregation Size 20082012

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/Removed^{a}


Model

Variables Entered

Variables Removed

Method

1

Growth/Decline 2000s, Urban,Suburban, Rural, Small City,
Growth/Decline 1990's, Congregation Size 20082012^{b}

.

Enter

a. Dependent Variable: Growth/Decline 20082012


b. All requested variables entered.

Model Summary


Model

R

R Square

Adjusted R Square

Std. Error of the
Estimate

1

.943^{a}

.889

.884

.43129

a. Predictors: (Constant), Growth/Decline 2000s, Urban,Suburban,
Rural, Small City, Growth/Decline 1990's, Congregation Size 20082012

ANOVA^{a}


Model

Sum of Squares

df

Mean Square

F

Sig.


1

Regression

133.084

4

33.271

178.864

.000^{b}

Residual

16.555

89

.186




Total

149.640

93





a. Dependent Variable: Growth/Decline 20082012


b. Predictors: (Constant), Growth/Decline 2000s, Urban,Suburban,
Rural, Small City, Growth/Decline 1990's, Congregation Size 20082012

Coefficients^{a}


Model

Unstandardized
Coefficients

Standardized
Coefficients

t

Sig.


B

Std. Error

Beta


1

(Constant)

.523

.131


3.979

.000

Congregation Size 20082012

.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 20082012

Figure 7 Output
for the multiple regression procedure
R/ R^{2}:
R is .943 which indicate these
measures of growth and location are positively correlated with the overall
regression model based on the four predictors. R^{2}=.889 which indicates that 89% of the variance in growth/decline
from 20082012 can be attributed to the predictor variables.
Significant
Predictors: p(.044)<.05 for SIZE (CONG SIZE 20082012) 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 20082012.
NonSignificant
Predictors: p (.270) > .05 for LOCATION (Urban, Suburban, Rural, Small
City) and p(.106) > .05 for GD1990 (Growth/Decline 19922002). Apparently
the location and the level of growth from 19922002 in worship attendance is
not a significant predictor of worship
attendance growth 20082012.
Reject/Fail to
Reject:
Individual Hypotheses:
H_{0}: β_{SIZE}= 0 (H.1)
H_{1}: β_{SIZE} ≠ 0
REJECT THE NULL p<.05
H_{0}: β_{LOCATION} =
0 (H.2) H_{1}: β_{LOCATION} ≠
0 FAIL TO REJECT p>.05
H_{0}: β_{GD1990} = 0
(H.3) H_{1}: β_{GD1990}
≠ 0 FAIL TO REJECT p > .05
H_{0}: β_{GD2000} = 0
(H.4) H_{1}: β_{GD2000}
≠ 0 REJECT THE NULL p<.05
Overall Regression Model Hypothesis:
H_{0}: R^{2} = 0 (H.5) H_{1}: R^{2} > 0 REJECT THE NULL p<.05
Regression Equation:
Ŷ = a + b_{1}X_{1} + b_{2}X_{2
}+ b_{3}X_{3} + b_{4}X_{4}
Ŷ_{GROWTH} = .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 20082012. This equation shows the increasing importance
and impact on the correlation from overall size from 20082012 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 19922002 mattered.
Conclusion:
A multiple regression was conducting predicting growth in worship attendance
from 20082012 based on growth of the congregations worship attendance from
19922002 and 20022012 as well as the location of the congregation and its
overall average size from 20082012. 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, R^{2}:= .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 20082012 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 20082012 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: H_{0}:
ρ = 0; H_{1}: ρ ≠ 0
Question:
Is there a relationship between Attendance growth/decline from 19922002
and attendance growth/decline from 20022012?
Figure 8.1 Scatterplot with regression line for Att1990s and
Att2000s
Correlations



Att. Growth/Decline
19922002

Att. Growth/Decline
20022012


Att. Growth/Decline 19922002

Pearson Correlation

1

.146

Sig. (2tailed)


.157


N

95

95


Att. Growth/Decline 20022012

Pearson Correlation

.146

1

Sig. (2tailed)

.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 19922002 and
20022012 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: NonParametric (Wilcoxon
Signed Rank Test)
Variables:
PRIWORATT(20072009) POSWORATT (after
2009)
Hypothesis:
Ho: µ_{priworatt}  µ_{posworatt} = 0; H_{1}: µ_{priworatt}  µ_{postworatt
}≠ 0
Question:
Did average Sunday attendance in the Northern TexasNorthern Louisiana Mission
Territory fall in the three years after 2009 in comparison to the average for
20072009?
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 20072009

104

108.5096

115.33385

8.00

626.00

38.2500

71.8333

137.9167

Ranks



N

Mean Rank

Sum of Ranks


Worship Att 20072009  Worship Att Post 2009

Negative Ranks

22^{a}

40.75

896.50

Positive Ranks

79^{b}

53.85

4254.50


Ties

3^{c}




Total

104




a. Worship Att 20072009 < Worship Att Post 2009


b. Worship Att 20072009 > Worship Att Post 2009


c. Worship Att 20072009 = Worship Att Post 2009

Test Statistics^{a}



Worship Att 20072009 
Worship Att Post 2009

Z

5.688^{b}

Asymp. Sig. (2tailed)

.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 ttest 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 (nonparametric) was performed
which helps control for such outliers through the use of medians and ranking.
This study shows that worship attendance prior (20072009) (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 20072009 (Md = 72) to post 2009 (Md = 63).