The mean effect of three treatments on fasting blood sugar levels for three samples of 10 patients are shown below. Treatment Mean Fasting Blood Glucose Levels (mg/dL) A 82.1 B 80.0 C 88.7 The ANOVA output for this experiment is as follows. df Sum of Squares Mean Square F-value Pr(>F) Treatment 2 412.2 206.1 4.631 0.0186 Residuals 27 1202.5 44.5 Assuming the level of significance is α=0.05, compare the pairwise differences in the mean blood glucose level for the three treatments using Fisher's Least Significant Difference method. Step 1 of 2 : Compute Fisher's Least Significant Difference for comparing the mean blood glucose level for the three treatments. Round your answer to four decimal places.
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 + ...
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