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====Means====
====Means====
As described [[Data description|earlier]], means are the most appropriate measure of central tendency for normally distributed continuous variables, and the '''standard deviation''' is the most appropriate measure of 'spread' in these cases. An adjusted form of the '''sample standard deviation''' is used to approximate the standard deviation in the population, and is calculated by dividing the sum of the squared differences from the sample mean by the number of animals sampled minus 1, and taking the square root of the answer.
As described [[Data description|earlier]], means are the most appropriate measure of central tendency for normally distributed continuous variables, and the standard deviation is the most appropriate measure of 'spread' in these cases. An adjusted form of the sample standard deviation is used to approximate the standard deviation in the population, and is calculated by dividing the sum of the squared differences from the sample mean by the number of animals sampled minus 1, and taking the square root of the answer.
====Proportions====
====Proportions====
Proportions are the most appropriate method of description of [[Data description|categorical and binary]] variables. Although the concept of a 'variance' or 'standard deviation' for these samples is difficult to comprehend, the standard can be calculated by multiplying the proportion of positive animals by the proportion of negative animals, and by taking the square root of this.
Proportions are the most appropriate method of description of [[Data description|categorical and binary]] variables. Although the concept of a 'variance' or 'standard deviation' for a proportion is difficult to comprehend, it is based upon the 'binomial distribution'. The variance can be estimated by multiplying the proportion of positive animals by the proportion of negative animals; and the square root of this will give the standard deviation.
===Approach for rates and ratios===
===Approach for rates and ratios===
Although the general concept behind confidence intervals for rates and ratios is the same as that for means and proportions, the method of calculation is different. The number of 'outcomes' (i.e. the numerator of the rate) can be considered to follow a 'Poisson distribution'. This facilitates the estimation of the standard error for this count, as the standard error of a Poisson variable is the square root of the expected value (that is, the square root of the number of outcomes, in our case). From this, confidence intervals can be estimated as above (i.e. estimate the standard error, multiply this by 1.96 [for 95% confidence limits], and add and subtract this value to/from the number of outcomes). Finally, to convert these confidence limits into a rate (rather than a count), the confidence limits themselves should be divided by the total amount of animal-time under observation (i.e. the denominator of the rate).
[[Category:Veterinary Epidemiology - Statistical Methods|D]]
[[Category:Veterinary Epidemiology - Statistical Methods|D]]