A researcher is interested in hamster wheel-running activity during the summer versus the winter. He suspects that either the hamsters will run less during the winter to conserve energy or they will run more to keep warm. He records the activity of n = 16 hamsters during June, July, and August and compares their running-wheel revolutions per hour to the activity of the same hamsters during December, January, and February. The data are collected, and the results show an average difference score of MDD = 3.8 and a sum of squares of SS = 522.15. What is the value for degrees of freedom for this repeated-measures t test? 47   15   50   16     What is the sample standard deviation (s) for the D scores? 1.48   5.9   522.15   34.81     What is the estimated standard error of the mean difference (sMDMD) for this study? 0.37   2.18   1.48   1.22

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 + ...