Google is testing 3 different search algorithms, A, B, and C. Ideally, a good algorithm would show the user a link they want to click on right away. An algorithm where the user needs to try many searches before they find something they want is not as good. One way Google judges a search algorithm is to see how many searches a user does until the user clicks on a link. The fewer the searches, the better the algorithm. After collecting sample data from random users running the three algorithms, Google conducts an ANOVA (analysis of variance) test for the mean number of searches before clicking on a link. Suppose the p-value is 0.024.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...