What is
Standard Deviation
?
The spread around the center of a normal distribution
The amount of variation in a population
The point where the normal curve changes from concave down to concave up
What is the Sample Standard Deviation?
The variance around the mean of a sample from the population
Calculation:
\[\begin{aligned}
s &= \sqrt{\frac{(x-\bar{x})^2}{n-1}}
\end{aligned} \]
What is the Empirical Rule?
68% of the data falls within 1 Standard Deviation of the center
95% of the data falls within 2 Standard Deviations of the center
99.7% of the data falls within 3 Standard Deviations of the center
If the percentages don't match the data, the distribution isn't normal
What is the Standard Error?
The amount of variance the measure of central tendency (e.g. the mean) has:
\[ \begin{aligned}
SE &= \frac{\sigma}{\sqrt{n}}
\end{aligned}\]
Sample Standard Deviation is the variance within a sample, Standard Error is how close the Sample mean is to the Population Mean
What is a Margin Of Error?
A multiple of the Standard Error
The multiple is based on the Confidence Interval you want
For example: 68% Confidence uses a multiple of 1 (see the Empirical Rule)
\[\begin{aligned}
MOE &= multiple \times StandardError
\end{aligned}\]
What is a Confidence Interval?
Level of Confidence based on the percent of the distribution your Margin of Error covers
If you have a small data set or you don't know that the distribution is normal use the t-distribution:
\[\begin{aligned}
ConfidenceInterval &= \bar{x} \pm t_{n-1} \frac{s}{\sqrt{n-1}}
\end{aligned}\]
n
is the size of the sample
s
is the Sample Standard Deviation
If you know that the distribution is normal and/or your sample is large, use the z-score instead.
Source
: Statistic For Dummies