Give detail introduction about the Standard Error of the Difference between Means?
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 + ...
Expert Solution
Step 1
Standard error of the mean:
The standard error of the mean is defined as the value of the standard deviation of all possible sample means for the given sample size. In other words, it explains the variability between the sample means if the different samples are considered from the given population. That is, there is a deviation between the sample mean and the population mean which is explained by the standard error.
Step 2
The standard error decreases by the value of the square root of the sample size (n) when the sample size increases,. Hence, it is clear that the standard error of mean and the standard deviation are inversely related to the square root of n.
The relationship between the standard error of meanand the standard deviationis given by,
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and the standard deviation
is given by,
