The "standard deviation of the sample score" divided by the "square root of the sample size" is the formula for computing the ...?
A. Coefficiant of Determination
B. Absolute Deviation
C. Variance
D. Standard Error
The formula you mentioned, where the standard deviation of the sample score is divided by the square root of the sample size, is used to compute the standard error.
To understand why this formula is used for calculating the standard error, it's essential to know what the standard deviation and standard error represent.
The standard deviation measures the spread of data points from the average or mean. It tells us how much variation or dispersion exists in a set of values. On the other hand, the standard error is a measure of the statistical accuracy of an estimate.
When we have a sample from a population and want to make inferences about the population based on the sample, we often calculate a statistic like the sample mean or sample proportion. However, we're aware that these sample statistics might be different from the population parameters due to sampling variability.
The standard error quantifies this sampling variability. It measures the average distance between the sample statistic and the population parameter if we were to take many different samples from the same population and compute the sample statistic each time. It provides an estimate of how much our sample statistic is likely to deviate from the true population parameter.
Since the standard deviation represents the variability within a sample, we divide it by the square root of the sample size to account for the fact that larger sample sizes tend to provide more precise estimates. This correction accounts for the fact that as sample size increases, the variability of the sample mean decreases, making it a more accurate estimate of the population mean.
Therefore, the correct answer to your question is D. Standard Error.