400 B.C. 131 138 125 129 132 135 132 134 138 1850 B.C. 129 134 136 137 137 129 1136 138 134 150B A.C. 128 138 136 139 141 142 137 145 137 Listed on the top are skull breadths obtained from skulls of Egyptian makes from three different epochs( based on the data from Ancient Races of the Thebaid by Thomson and Randall-Maciver). Assume that we plan to use analysis of variance with a 0.05 significance level to test the claim that the different epochs have mean skull breadths that are not all the same. The results from XI.STAT are shown down below.  Source DF Sum of squares Means squares F Pr>F Model 2 138.7407 69.3704 4.0497 0.0305 Error 24 411.1111 17.1296     Corrected Total 26 549.8519         5-Type of test Is the hypothesis test described in Exercise 1 left-tailed, right-tailed or two-tailed? Are all one-way analysis of variance tests left-tailed, right-tailed, or two-tailed? 6- Which Mean is different? For the three samples described in Exercise 1, if we use analysis of variance and reach a conclusion to reject equality of the three population means, can we then conclude that any of the specific population has a mean that is different from the others?  7-One vs Two  What is the fundamental difference between one-way analysis of variance and two-way analysis of variance?

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 + ...