Stats: Variance, Standard Deviation and the Coefficient of Variance

11 Nov

Thought I’d try to recap bits of the statistics module I learnt last year in an effort to retain it in my brain cells that much longer. I thought I’d start by comparing variance, standard deviation (SD) and the coefficient of variance (CV). They are nicely interlinked and come up frequently in quantitative analyses used in public health, making them useful to remember. Of the three, SD is definitely used the most, followed by variance. I’ve not seen the CV being used in a paper but that’s probably due to its function, which will be described later.

Variance

In a nutshell: Describes the extent of variety in a sample

Variance looks at the spread around the mean within the sample. It is calculated as the sum of squares divided by the degrees of freedom:

Variance is described as the sum of squares divided by the degrees of freedom

Variance is described as the sum of squares divided by the degrees of freedom

Standard Deviation (SD)

In a nutshell: A version of variance which is easier to work with

SD represents variance but it is in the same unit as the observations, which is useful. However the SD depends on the magnitude of the data which makes it a little less reliable when based on skewed data.

SD: Square root of the variance

Square root of the variance

Coefficient of Variation (CV)

In a nutshell: A measure of variance used to compare different samples

CV represents the SD as a % of the mean. It is used to compare relative variability between data sets but it can only be used for positive variables.

 

 

 

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