What is standard deviation and how to find standard deviation
When you’re summarizing large amounts of data as a researcher, you’re using summary statistics or descriptive statistics. And the most popular among these is the mean or average. But a mean by itself is “mean”ingless without the standard deviation. So, let’s understand this important statistic today.
What is standard deviation?
Standard deviation (SD) is a measure of dispersion. It tells you how widely the values are dispersed (i.e., vary) from the mean.
If SD is small, there’s less variation in the values, and they fall into a fairly narrow range around the mean. A very large SD implies that there’s a lot of variation in your data.
How to find standard deviation: Calculations and formula
This is pretty simple, if you follow the steps below:
Step 1: Collect data (e.g., systolic blood pressure readings)
Step 2: Calculate the mean. To do so, add up all the data values and divide by the total number of data points.
Step 3: Subtract the mean from each data point in order to get the Deviation.
Step 4: Square each deviation (so that you remove any negative values).
Step 5: Calculate the mean of the squared deviations. This is called Variance.
Step 6: Find the square root of the variance. This is your Standard Deviation.
How to report standard deviation: Symbol or abbreviation?
SD is sometimes denoted using the ± sign, but that’s not strictly necessary because SD by definition implies “plus or minus” (variation on both sides of the mean). It can also cause confusion about whether the number is a standard deviation or standard error of the mean (more on that below).
So, the ideal format to report standard deviation is
Mean = 13.5 (SD = 1.3)
Of course, you must adhere to the style guide set by your own journal (“SD” vs “s.d.” vs “sd”, etc.). And remember, if you’re reporting more than one mean, each mean must have its corresponding SD.
Standard deviation versus standard error of the mean
Researchers sometimes confuse standard deviation with standard error of the mean (SEM). The latter is actually a measure of precision. It tells you how close your sample mean is to the population mean. SEM doesn’t tell you about the variation in the data. Check out Lee et al. (2015)’s helpful article on the differences between SD and SEM.
SEM is often misused as a substitute for SD, because its values are typically smaller than those of SD.
For this reason, many biostatisticians (e.g., Barde & Barde, 2012; Garg & Mohanty, 2012; Ko et al., 2014) and journals discourage authors from reporting SEM along with means when describing their data. Journals like Nature Communications and Obstetrics & Gynecology Science ask authors to clearly identify whether a measure is SD or SEM.
Standard deviation vs variance
As you saw earlier, one of the steps in calculating SD is to calculate Variance (Step 5). Variance and SD are not the same. SD is the square root of variance for a dataset.
SD and variance also serve different purposes:
SD: quantifies how far data points are from the mean
Variance: measures the spread between numbers in a dataset
We hope this guide helped you in understanding standard deviation and its importance in research. Here, we have summarized the definition, calculation methods and reporting of standard deviation.
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