(X

X)

2

s

n

1

When the distribution of the observations is Normal, then 95% of all observations are located in the interval 

mean   1.96 SD to mean + 1.96 SD  (for other values see table p. 172). 

This interval should not be confused with the smaller 95% confidence interval for the mean.  The interval 

mean   1.96 SD to mean + 1.96 SD represents a descriptive 95% confidence range for the individual 

observations, whereas the 95% CI for the mean represents a statistical uncertainty of the arithmetic mean. 

Relative standard deviation (RSD): this is the standard deviation divided by the mean.  If appropriate, 

this number can be expressed as a percentage by multiplying it by 100 to obtain the coefficient of variation. 

Standard error of the mean (SEM): is calculated by dividing the standard deviation by the square root of 

the sample size.  

s

=

S.E.M.

n

The SEM is used to calculate confidence intervals for the mean.  When the distribution of the observations 

is Normal, or approximately Normal, and the sample size is large, then there is 95% confidence that the 

population mean is located in the interval 

X

    1.96 SEM.  If the sample size is less than 30 then the 

multiplier is not 1.96, but is taken from the t distribution with n 1 degrees of freedom and a confidence of 

95% (table on p. 173).  The 95% confidence interval is calculated by 

X

   t SEM. 

Skewness 

The coefficient of Skewness is a measure for the degree of symmetry in the variable distribution.  If the 

corresponding P value is low (P<0.05) then the variable symmetry is significantly different from that of a 

Normal distribution, which has a coefficient of Skewness equal to 0 (Sheskin, 2004). 

Negatively skewed distribution 

Normal distribution 

Positively skewed distribution 

or Skewed to the left 

Symmetrical 

or Skewed to the right 

Skewness < 0 

Skewness = 0 

Skewness > 0 

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