Calvary Baptist School (Wisconsin) and Spurious correlation

Calvary Baptist School is a private Baptist school located in Menomonee Falls, Wisconsin, a suburb of Milwaukee. Calvary consists of preschool through twelfth grade and is one of the largest Christian schools in Wisconsin. It is a member of the American Association of Christian Schools.

Contents 1 History and mission 2 Doctrinal statement 3 Administration 4 Athletics 5 External links 6 References

History and mission

Calvary Baptist School was founded in the fall of 1975 as a ministry of Calvary Baptist Church, which desired to provide a quality Christian education to children in the Milwaukee area. Calvary's purpose is to educate students physically, emotionally, intellectually, socially and spiritually.

The school is one of the largest Christian schools in the Milwaukee area and the largest member of the Wisconsin Association of Christian Schools (WACS). In 2006, construction was completed on a new campus. Doctrinal statement

Calvary Baptist School adheres to the following: The divine verbal (word by word), plenary inspiration of Scriptures; the inerrancy of Scripture; the complete revelation in creation, the Bible (66 books) and Jesus Christ; God revealed in the Father, Son and Holy Spirit; that man is totally depraved and condemned apart from a personal recognition and turning from sin and trusting Jesus alone for salvation; that a believer is a new creature, therefore, should live a holy, clean and pure life by the power of God; that God’s work is fulfilled by believers as they unite in local, visible, Bible preaching churches; that the ordinances are believer’s baptism (by immersion) and the Lord’s table; that God expects believers to honor Him with their attendance in the local church on the first day of the week; that believers honor civil government; that the believer will go to be with Christ immediately at death and that unsaved go to damnation; and that Jesus Christ could come for the saved at any time. Administration

The School Board has seven to ten members, including at least one deacon appointed by the Deacon Board, at least five members elected at large, and a treasurer elected at large. The administrator and associate administrator are responsible for the leadership and activities of the school. Athletics

Sports offered by Calvary Baptist for middle and high school students include boys' soccer, girls' volleyball, and boys' and girls' basketball. The Eagles compete in the Indian Trails Conference and the Wisconsin Association of Christian Schools (WACS). Calvary's boys' high school basketball program has won numerous conference, tournament, and state championships. Recent victories include five consecutive WACS state championships. The high school soccer program, which began play in 1999, has won several conference titles and three state championships. Calvary's new campus facility completed in 2006 contains a full-size gym. External links Calvary Baptist School website

Spurious correlation and Calvary Baptist School (Wisconsin)

An illustration of spurious correlation, this figure shows 500 observations of x/z plotted against y/z. The sample correlation is 0.53, even though x, y, and z are statistically independent of each other (i.e., the pairwise correlations between each of them are zero). This figure shows the 500 observations of y/z plotted against x/z from above, this time with the z-values on a colour scale to highlight how dividing through by z induces spurious correlation.

Spurious correlation is a term coined by Karl Pearson to describe the correlation between ratios of absolute measurements that arises as a consequence of using ratios, rather than because of any actual correlations between the measurements.

The phenomenon of spurious correlation is one of the main motives for the field of compositional data analysis which deals with the analysis of variables that carry only relative information, such as proportions, percentages and parts-per-million.

Pearson's definition of spurious correlation is distinct from (and should not be confused with) misconceptions about correlation and causality, or the term spurious relationship.

Contents 1 Illustration of spurious correlation 2 Approximate amount of spurious correlation 3 Relevance to biology and other sciences 4 References

Illustration of spurious correlation

Pearson states a simple example of spurious correlation:

Select three numbers within certain ranges at random, say x, y, z, these will be pair and pair uncorrelated. Form the proper fractions x/y and z/y for each triplet, and correlation will be found between these indices.

The upper scatter plot on the right illustrates this example using 500 observations of x, y, and z. Variables x, y and z are drawn from normal distributions with means 10, 10 and 30, respectively, and standard deviation 10, i.e.,

Even though x, y, and z are statistically independent (i.e., pairwise uncorrelated), the ratios x/z and y/z have a sample correlation of 0.53. This is because of the common divisor (z) and can be better understood if we colour the points in the scatter plot by the z-value. Trios of (x, y, z) with relatively large z values tend to appear in the bottom left of the plot; trios with relatively small z values tend to appear in the top right. Approximate amount of spurious correlation

Pearson derived an approximation of the correlation that would be observed between two indices ( and ), i.e., ratios of the absolute measurements :

where is the coefficient of variation of , and the Pearson correlation between and .

This expression can be simplified for situations where there is a common divisor by setting , and are uncorrelated, giving the spurious correlation:

For the special case in which all coefficients of variation are equal (as is the case in the illustrations at right), Relevance to biology and other sciences

Pearson was joined by Sir Francis Galton and Walter Frank Raphael Weldon in cautioning scientists to be wary of spurious correlation, especially in biology where it is common to scale or normalize measurements by dividing them by a particular variable or total. The danger he saw was that conclusions would be drawn from correlations that are artifacts of the analysis method, rather than actual “organic” relationships.

However, it would appear that spurious correlation (and its potential to mislead) is not yet widely understood. In 1986 John Aitchison, who pioneered the log-ratio approach to compositional data analysis wrote:

It seems surprising that the warnings of three such eminent statistician-scientists as Pearson, Galton and Weldon should have largely gone unheeded for so long: even today uncritical applications of inappropriate statistical methods to compositional data with consequent dubious inferences are regularly reported.

More recent publications suggest that this lack of awareness prevails, at least in molecular bioscience.
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