# Sample of a compare and contrast essay

At least one file will be created in the output directory specified by -o. For most methods, a single output file containing the results of the test (. the effect size statistic and p-value) will be created. The format of the output files will vary between methods as some are generated by native QIIME code, while others are generated by R’s vegan or ape packages. Please refer to the script description for details on how to access additional information for these methods, including what information is included in the output files.

An orange grown in Florida usually has a thick and tightly fitting skin, and is also heavy with juice. Californians say that if you want to eat a Florida orange you have to get into a bathtub first. California oranges are light in weight and have thick skins that break easily and come off in hunks. The flesh inside is marvelously sweet, and the segments almost separate themselves. In Florida, it is said that you can run over a California orange with a ten-ton truck and not even wet the pavement. The differences from which these hyperboles arise will prevail in the two states even if the type of orange is the same. In arid climates, like California's, oranges develop a thick albedo, which is the white part of the skin. Florida is one of the two or three most rained-upon states in the United States. California uses the Colorado River and similarly impressive sources to irrigate its oranges, but of course irrigation can only do so much. The annual difference in rainfall between the Florida and California orange-growing areas is one million one hundred and forty thousand gallons per acre. For years, California was the leading orange-growing state, but Florida surpassed California in 1942, and grows three times as many oranges now. California oranges, for their part , can safely be called three times as beautiful.

This calculator uses the following formulas to compute sample size and power, respectively: $$n_A=\kappa n_B \;\text{ and }\; n_B=\left(\frac{p_A(1-p_A)}{\kappa}+p_B(1-p_B)\right) \left(\frac{z_{1-\alpha/2}+z_{1-\beta}}{p_A-p_B}\right)^2$$
$$1-\beta= \Phi\left(z-z_{1-\alpha/2}\right)+\Phi\left(-z-z_{1-\alpha/2}\right) \quad ,\quad z=\frac{p_A-p_B}{\sqrt{\frac{p_A(1-p_A)}{n_A}+\frac{p_B(1-p_B)}{n_B}}}$$ where

• $\kappa=n_A/n_B$ is the matching ratio
• $\Phi$ is the standard Normal distribution function
• $\Phi^{-1}$ is the standard Normal quantile function
• $\alpha$ is Type I error
• $\beta$ is Type II error, meaning $1-\beta$ is power