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The value of the estimated standard error for the following set of D scores 2, 2, 10, 2 is 4 .
The standard error of a statistic is the standard deviation of the sample distribution, or a close approximation of that standard deviation. A statistic that is the sample mean is referred to as having a "standard error of the mean."
The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation. In statistics, a sample mean deviates from the actual mean of a population; this deviation is the standard error of the mean.
Consider the following set of D scores,
2, 2, 10, 2
We will calculate ∑D and ∑D² to find the SS for the D scores.
Therefore,
∑D = 2 + 2 + 10 + 2
We can sum or difference of the coefficients,
∑D = 4 + 10 + 2
∑D = 14 + 2
∑D = 16
Then,
∑D² = 2² + 2² + 10² + 2²
∑D² = 4 + 4 + 100 + 4
∑D² = 8 + 100 + 4
∑D² = 100 + 12
∑D² = 112
So,
The formula for the standard score is given as:
SS = ∑[tex]D^{2}[/tex] - (∑D*∑D) / n
SS = 112 - [ (16)² /4 ]
SS = 112 - [ 256 /4 ]
SS = 112 - 64
SS = 48
Then,
[tex]S_{D}[/tex] = [tex]\sqrt{\frac{SS}{n-1} }[/tex]
[tex]S_{D}[/tex] = [tex]\sqrt{\frac{48}{4-1} }[/tex]
[tex]S_{D}[/tex] = [tex]\sqrt{\frac{48}{3} }[/tex]
[tex]S_{D}[/tex] = [tex]\sqrt{16}[/tex]
[tex]S_{D}[/tex] = 4
Therefore,
The value of the estimated standard error for the following set of D scores 2, 2, 10, 2 is 4 .
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