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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 meanĀ 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.

 

 

 

Bradford Hill Criteria: What every epidemiologist should know

1 Nov

Just because it needed to be done!

  1. Strength of association
  2. Consistency
  3. Specificity
  4. Temporal relationship
  5. Biological gradient (dose-response relationship)
  6. Plausibility (biological plausibility)
  7. Coherence
  8. Experiment (reversibility)
  9. Analogy (consideration of alternate explanations)

Causality: Necessary or Sufficient?

13 Oct

Third post today, it seems I’ve got a backlog! Last week was the introductory week where although we didn’t start any modules or “serious” studying, we were introduced to a few public health concepts and given the library inductions etc… Anyway something that was mentioned in the Putting Science into Context lecture has stayed in my memory until today, always a good sign!

The speaker was discussing causality and questioning whether it was always necessary or sufficient. Using this table with a few examples he explained the difference between “necessary” and “sufficient” factors quite neatly.

causality: necessary or sufficient?

causality: necessary or sufficient?

To explain the table in words:

Trisomy of chromosome 21 (where you have three copies instead of the usual two) leads to Down Syndrome. This is both necessary (you don’t get cases of Down Syndrome without trisomy chromosome 21) and sufficient (no other factors are needed for Down Syndrome to develop apart from trisomy chromosome 21). Such examples of where an exposure/event is both necessary AND sufficient for an outcome is rarely seen in medicine.

Mycobacterium is necessary for the development of pulmonary tuberculosis (TB), but it is not sufficient as there are many other variables that contribute to an individual’s susceptibility to the disease. There are many examples of such necessary but not sufficient factors in infectious disease, another one being human papilloma virus (HPV) infection which can lead to cervical cancer (variables such as length of cervix are considered to be critical in contributing to the risk of developing cancer), or H.pylori infection (most people are infected) which can lead to gastric cancer.

Smoking tobacco is neither necessary nor sufficient for the development of lung cancer. Other causes aside from smoking can lead to lung cancer, and not everyone who smokes will get cancer.

A guillotine is not necessary to cut someone’s neck; you can cut a neck in thousands of ways (this is not a confession don’t worry). It is pretty obvious that a guillotine is sufficient to cut a neck however as you don’t need any other factors to be present for the neck to be cut.

I thought this cross-tabulated contingency table was a really clear way of explaining causality, and the subtle difference between sufficient and necessary in the context of causality which I’ve always found difficult to visualise.