How to determine what's hot and what's not using standard deviation

Let's suppose you are analyzing the Average Annual Growth Rates for all the counties in a nation, and you want to determine which counties have above average growth and which are below average. Or you might want to know in which counties the church is growing at a significantly faster rate. How do you determine this? But how do you determine to where to draw the line between average growth and extraordinary growth, or on the other side, decline and significant decline? Or suppose you are evaluating results from a survey that evaluated a conference or a program in a local church. How do you determine which categories received significantly high scores and which areas were low?

The statistical tool you need to use is standard deviation. Standard deviation expresses the amount that a value varies from the mean. Values that are more than one standard deviation from the mean are considered statistically significant. The distribution of these values forms what is commonly referred to as a bell curve. For a more detailed discussion of Standard Deviation, consult http://en.wikipedia.org/wiki/Standard_deviation or a statistics manual. But let's not get bogged down in technicalities here, Rather let's look at an example to see how this works.

Example 1: Evaluating Average Annual Growth Rates
I have worked with data from a report published in 2013 by the Center for the Study of Global Christianity that gives projected Average Annual Growth Rates for the number of Christians in the fifty year period, 1970-2020 fro all the countries in the world. These AAGRs range from a high of 10.93% to a low of -6.87%; 208 values are positive, 29 are equal to zero or are negative. This is interesting data. But I want to know in which countries the number of Christians is increasing at a significant rate. Using standard deviation will help me figure out which of these countries are hot and which are not. Since I already have this data in a spreadsheet, it is rather easy to perform the calculations. There are four steps.

Step One: Determine the average or mean of the data series. In a spread sheet use the "average" formula for the data series. In this example, the average AAGR or mean is 1.47%.

Step Two: Determine the standard deviation of the data series. Use the standard deviation formula, STDEV.P in Excel for the same data series. In this example the standard deviation is 2.05%

Step Three: Determine the limits for one, two and three standard deviations above and below the the mean. Since the mean in this example is 1.47%, the first standard deviation above the mean runs to 3.52%, the second standard deviation runs to 5.57%, the third to 7.62%, the fourth to 9.67%.For the values below the mean, the the standard deviation scores are -0.58%, -2.63%, -4.68% and -7.33%.

Step Four: Categorize data by standard deviation. Values that are greater than or less than one standard deviation are statistically significant. Sort your data series in descending order, from high to low. In the example under discussion, 36 countries have an AAGR greater than 3.52%. These countries have statistically significant growth rates, or that is to say, they are hot. On the other hand, eleven countries have an AAGR more than one standard deviation from the mean (<-0.58) These countries are in significant decline, or we might say they are not hot. Also take note of the data in the "average" category. In this example, 77 countries that have average growth (AAGR > 1,47 to 3.52) and 45 countries fall into the category one standard deviation below the mean (AAGR in the range from -0.58 to 1.47)

By calculating the mean and using standard deviation, I was able to determine which countries are hot, that is to say, those with statistically significant AAGRs. and which countries are not. This analysis let to a deeper inquiry concerning the factors that contributed to significant growth or decline.

Example 2: Evaluating a Local Church Mission's Program
I once assisted a church in the evaluation of its mission's program. A survey developed by the Association of Church Mission Committees (ACMC) was used to gather people's opinions about the mission program. There were twelve questions with ranking options from 1 to 6. 39 persons completed the survey. Scores ranged from a high of 4.28 to a low of 3.05.The average or mean was 3.73. I wanted to determine which areas of the missions program were ranked as significantly strong and which were perceived as weak. But where to draw the line? Standard Deviation again gives the tool to determine what is statistically significant. Using a spread sheet, the standard deviation was determined for the data series (0.34). Thus two areas of the missions program were ranked above 4.07 (indicating areas of strength) and three areas were ranked at 3.39 or lower, e.g. areas of perceived weakness. Identifying the areas of perceived weakness and strength was useful in developing a strategy and establishing priorities to develop the missions program of this particular church.