Growth in Membership as a Percentage of Population by State

In “Church Growth by State,” I suggested that membership as a percent of a state’s population (density) is a function of the previous year’s density, distance from Utah, and economic opportunities in other states.  The difference between this year’s membership and last year’s is a flow variable.  Members in states with high density are likely to move to states with lower density.  Likewise, non-members in states with low density are likely to move to states with higher density.  Two additional variables may be important.  To remain close to friends and family, people are more likely to move to relatively close states rather than distant states.  Economic opportunity is likely to drive moves. 

With these general ideas in mind, I have prepared a table showing the growth rate of density by state and a map that visualizes the data.  For the United States as a whole, density grew at a rate of .497% from 1.99% to 2.00%.  Although Delaware is hard to spot on the map, it experienced negative growth of -4.675% and North Dakota, the fastest growth in density of 12.432%.  To better detect the causes of growth or decline, I derived the following formula which breaks down growth in density between growth in church membership and growth in population.  The derivation of the formula is below the table.
G_D=((1+G_C)P_O/P_N)-1)100
G_D is the growth in density or more formally, membership as a percentage of a state’s population.  G_C is the rate of growth of membership in the state.  When multiplied by the membership from the previous year (M_O), the product is the number of new members.  When added to 1 and multiplied by the membership from the previous year, the product is the new membership.  P_O/P_N is the ratio of the previous population of a state to the new population.  If the ratio is greater than 1, population declined, if less than one, population increased.  Subtracting 1 yields the growth rate of density and multiplying by 100 yields growth as a percentage. 
I will use Kansas and Utah compared to the benchmark of the United States to illustrate the use of the formula.  Membership in Kansas grew at 1.8%, 50% higher than the average of the country as a whole.  Population growth was a little slower with the ratio of the population in 2010 to 2011*.985 at 99.6% compared to 99.3%.  Because a slower growing population implies a smaller downward adjustment to church growth, the growth in density was 1.344%, 2.7 times higher than the growth in density for the United States.
Utah experienced church growth of .9%, less than the country.  The state also experienced more rapid population growth than the country, with the population adjustment ratio at 98.5% compared to 99.3%.  The math in the interior of the equation implies that the growth in membership did not compensate for the increase in population (1.009*.985)-1=.994-1=.-.00614 or –.614% (differences with the table are due to rounding errors). 
The growth in density conforms to the model I present.  Kansas with low density, a small portion of its residents are LDS, experienced growing density and Utah, the state with the highest density, and rapidly growing population experienced a loss of density. 
The data hides more than it reveals.  Membership changes due to births, deaths, conversions and excommunications.  A state can benefit by a high birth rate and conversions but if more members move out than move in, it will suffer a decline in membership.  And I must add that a one year trend is not particularly telling.  I still have much to learn, but I enjoyed the process of comparing changes in church membership across states. 

State	GD =	((1+GC)	PO/PN	-1)*100
Alabama	.907%=	((1+.013)	.996	-1)*100
Alaska	-.283%=	((1+.009)	.988	-1)*100
Arizona	.804%=	((1+.019)	.989	-1)*100
Arkansas	1.365%=	((1+.019)	.994	-1)*100
California	-.293%=	((1+.007)	.991	-1)*100
Colorado	.333%=	((1+.017)	.986	-1)*100
Connecticut	1.620%=	((1+.018)	.999	-1)*100
Delaware	-4.675%=	((1-.039)	.992	-1)*100
Florida	.690%=	((1+.019)	.991	-1)*100
Georgia	.797%=	((1+.019)	.998	-1)*100
Hawaii	.826%=	((1++.017)	.992	-1)*100
Idaho	-.201%=	((1+.009)	.991	-1)*100
Illinois	-.024%=	((1+.002)	.998	-1)*100
Indiana	.395%=	((1+.008)	.996	-1)*100
Iowa	2.707%=	((1+.031)	.996	-1)*100
Kansas	1.344%=	((1+.018)	.996	-1)*100
Kentucky	.218%=	((1+.007)	.995	-1)*100
Louisiana	.628%=	((1+.013)	.994	-1)*100
Maine	.257%=	((1+.003)	.999	-1)*100
Maryland	2.610%=	((1+.034)	.993	-1)*100
Massachusetts	1.191%=	((1+.016)	.995	-1)*100
Michigan	.901%=	((1+.009)	1.00	-1)*100
Minnesota	.194%=	((1+.008)	.994	-1)*100
Mississippi	1.009%=	((1+.013)	.997	-1)*100
Missouri	.693%=	((1+.009)	.998	-1)*100
Montana	.597%=	((1+.013)	.993	-1)*100
Nebraska	-.206%=	((1+.005)	.993	-1)*100
Nevada	-.043%=	((1+.007)	.993	-1)*100
New Hampshire	.283%=	((1+.004)	.999	-1)*100
New Jersey	1.505%=	((1+.018)	.998	-1)*100
New Mexico	.717%=	((1+.015)	.992	-1)*100
New York	.659%=	((1+.012)	.996	-1)*100
North Carolina	1.006%=	((1+.020)	.990	-1)*100
North Dakota	12.432%=	((1+.140)	.986	-1)*100
Ohio	.489%=	((1+.006)	.999	-1)*100
Oklahoma	1.183%=	((1+.020)	.992	-1)*100
Oregon	-.113%=	((1+.008)	.991	-1)*100
Pennsylvania	1.504%=	((1+.017)	.998	-1)*100
Rhode Island	1.605%=	((1+.015)	1.001	-1)*100
South Carolina	1.085%=	((1+.020)	.991	-1)*100
South Dakota	1.889%=	((1+.028)	.991	-1)*100
Tennessee	1.856%=	((1+.026)	.993	-1)*100
Texas	1.471%=	((1+.032)	.984	-1)*100
Utah	-.623%=	((1+.009)	.985	-1)*100
Vermont	.008%=	((1+.001)	.999	-1)*100
Virginia	.702%=	((1+.016)	.991	-1)*100
Washington	.088%=	((1+.014)	.987	-1)*100
West Virginia	1.905%=	((1+.012)	.999	-1)*100
Wisconsin	2.524%=	((1+.029)	.996	-1)*100
Wyoming	1.521%=	((1+.022)	.994	-1)*100
USA	.497%=	((1+.012)	.993	-1)*100

Derivation of Formula