VetZone vet zone dog cat veterinary medicine veterinarian technician tech health CE continuing education preventive diplomate ACVPM DACVPM health Christopher Anthony Lee Kayla Wells MPH DVM biostats epidemiology blue line dot meaning positive predictive value negative sensitivity specificity standard error standard deviation confidence intervals p-values p value determine September October November December names of month second king Rome Numa Pompilius

The Ancient Roman Calendar Consisted of Ten Months

If the words September, October, November, and December have ever triggered the numbers 7, 8, 9, and 10 in your head, they do so with good reason. The ancient Romans divided the year into ten months with a month-less winter period at the end where the astronomers could adjust for the Earth’s orbit. As error in Earth’s apogee estimation lessened, the legendary second king of Rome, Numa Pompilius added January and February to the calendar around 700 BCE. Science consistently uses estimations and compensates for statistical errors to better understand our world.

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Podcast: Do These Definitions Ring a Bell Curve?
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VetZone vet zone dog cat veterinary medicine veterinarian technician tech health CE continuing education preventive diplomate ACVPM DACVPM health Christopher Anthony Lee Kayla Wells MPH DVM biostats epidemiology blue line dot meaning positive predictive value negative sensitivity specificity standard error standard deviation confidence intervals p-values p value determine September October November December names of month second king Rome Numa Pompilius James Joyce

“A man's errors are his portals of discovery.”

James Joyce wrote, “A man's errors are his portals of discovery.” Statistical Standard Errors are portals into p-values, Confidence Intervals, and the tinted scientific lenses we must use to focus upon our world. By understanding the definitions and relationships of standard error, standard deviation, confidence intervals and p-values, clinicians can better plot their trajectory through studies and towards the truth.

VetZone vet zone dog cat veterinary medicine veterinarian technician tech health CE continuing education preventive diplomate ACVPM DACVPM health Christopher Anthony Lee Kayla Wells MPH DVM biostats epidemiology blue line dot meaning positive predictive value negative sensitivity specificity standard error standard deviation confidence intervals p-values p value determine September October November December names of month second king Rome Numa Pompilius James Joyce

Let's Consider the Perfect Bell Curve

While these values work with many types of curves, let’s keep the discussion easy and just talk about a normal distribution, your basic bell curve. Imagine your perfect bell curve, at its apex, is the mean or average. The Standard Deviation (SD) measures variability around the mean, independent of sample size. Two Standard Deviations from the mean encompass 95% of all the values that made up that result. The Standard Error (SE), a type of Standard Deviation, estimates the uncertainty of the result by incorporating sample size. Basically, we just divide the Standard Deviation by the square root of the sample size. We inject the square root because, after a while, greater sample sizes have less potential to bring new, previously unseen data. Makes sense, right? A sample size shifting from 100 to 1000 could shed new light, but would a shift from 1 million to 10 million be as dramatic? 
VetZone vet zone dog cat veterinary medicine veterinarian technician tech health CE continuing education preventive diplomate ACVPM DACVPM health Christopher Anthony Lee Kayla Wells MPH DVM biostats epidemiology blue line dot meaning positive predictive value negative sensitivity specificity standard error standard deviation confidence intervals p-values p value determine September October November December names of month second king Rome Numa Pompilius James Joyce

Standard Error is a type of Standard Deviation

While Standard Deviation gives you variation within the study, SE provides potential variation that might exist in a wider, shall we say global, environment. For this reason, we often chose Standard Error to calculate p-values and Confidence Intervals, two values that assist us in evaluating data. For example, let’s say that a study showed that kissing an aardvark reduces your chances of catching the flu by 70%. Was this result accurate or just a product of random chance within the study? The p-value provides the percentage that the data resulted from random chance. A p-value of 0.05 indicates that the potential of the data being as extreme from pure random chance is only 5 %, a common threshold for scientific studies. With Confidence Intervals, we can state with 95% confidence that a value lies between A and B. For example, we might have a confidence that true value for aardvark flu-reducing kissing lies between 65 and 75 %.

VetZone vet zone dog cat veterinary medicine veterinarian technician tech health CE continuing education preventive diplomate ACVPM DACVPM health Christopher Anthony Lee Kayla Wells MPH DVM biostats epidemiology blue line dot meaning positive predictive value negative sensitivity specificity standard error standard deviation confidence intervals p-values p value determine September October November December names of month second king Rome Numa Pompilius James Joyce

We must look beyond simple p-values and take in all the data

When reading a study, aardvark or otherwise, the p-value tells how likely you should believe the particular study finding and the confidence interval tell you how far to believe it. With a p-value threshold of 5%, we can easily utilize this value. If above 5%, then we decide that the result is inconclusive. If below, we can accept that kissing aardvarks may be beneficial to our health. For confidence intervals, we must employ common sense. A confidence interval of 25 to 100% is vastly different than 69-71% when it comes to deciding to kiss an aardvark. In the first scenario, even if beneficial, is a possible 25% reduction in risk worth kissing an ant eater? If one degree from 70%, we might be more amenable to the situation. So, whether evaluating data on celestial orbits, aardvark kissing, or vaccine efficacy, we must look beyond simple p-values and take in all the data.

References and Further Reading

  1. Altman, D. G., & Bland, J. M. (2005). Standard deviations and standard errors. BMJ : British Medical Journal, 331(7521), 903.

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