Actual property measured by individual observations
Single score or reading of a given variable
Normal distribution (ie Height):
If the data are Normally distributed, the distribution of data can be described by two parameters:
- Standard deviation (or variance)
Mean + / – 1 × SD = 68 %
Mean + / – 2 × SD = 95 % (more accurately 1.96 times SD)
Mean + / – 3 × SD = 99 %
A different mean shifts the curve along the x-axis, but does not alter its shape. When the standard deviation decreases, the curve becomes steeper; when the standard deviation increases, the curve becomes flatter.
Not Normal distribution:
Interval from lowest to highest value
Difference between upper and lower quartiles
Most common category
Equal number of measurements above and below
A skewed curve is skewed to the right if the ‘tail’ is on the right side and skewed to the left in the ‘tail’ is to the left.
The sample mean is an unbiased estimator of the population mean.
Central limit theorem: the distribution of mean (from different samples) will be a Normal distribution, even if the samples or population are not Normally distributed.
The distribution of the mean is Normal with the sample mean as mean and the standard error of the mean (SEM) as measure of dispersion (n is sample size):
Confidence intervals can be constructed by the mean plus or minus the standard error of the mean:
Mean + / – 1 × SEM = 68 %
Mean + / – 2 × SEM = 95 % (more accurately 1.96 times SEM)
Mean + / – 3 × SEM = 99 %