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I have conducted an analysis in which I have modeled different variance components. When reporting the results in a table, it is much more concise to report standard deviations instead of variances.

So, this brings me to the question - is there ever a reason to report variance instead of standard deviation? Is it ever more appropriate to report one over the other?

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If you report the mean, then it is more appropriate to report the standard deviation as it is expressed in the same unity. Think about dimensional homogeneity in physics.

Moreover, it is easier for the reader to consider confidence intervals (for large n, in order to use the Central Limit Theorem and consider a normal distribution) if the standard deviation is provided rather than the variance.

However, you may consider reporting the variance if you are interested in comparing variance and bias, or giving "different variance components", since the total variance is the sum of the intra and inter variances, while the standard deviations do not sum up.

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This is equivalent. Nonetheless, standard deviation is expressed in the same units as the variable whereas the units of the variance are those of the variable to the power two. This makes standard deviation easier to interpret.

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Variance weights outliers more heavily than data very near the mean due to the square. A higher variance helps you spot that more easily.

Also, mathematically/theoretically speaking, dealing with variance is easier. And if you are dealing with more than one dataset you can add two independent variances (or more) to get the total variance due to those factors. But, adding one standard deviation to another gives you a meaningless number (if measure units are different).

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  • $\begingroup$ I don't think this answers the question. The question really doesn't make much sense since variance and standard deviation are directly related. So one gives you the other. It seems to me that they are equally appropriate. Some people might prefer to report the standard deviation because it is in the same units as the data. $\endgroup$ – Michael Chernick Feb 27 at 2:14
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Adding a number (x) to the standard deviation (the average deviation from the mean) and then dividing it by (******* dang, I had a whole response but apparently the site deleted 90% of it. Variance doesn't consider the direction of deviation from the mean, which is plotted on charts to show the nature of the sample, it just considers the total amount a deviation (that is the sum of squared deviations). Also, Variance's number allows you to add numbers to it to find an new variance. Can't do that do standard deviation... you have to add a new squared deviation and then add it to the total variance and divide by the new sample size -1. So, you might as well keep the variance saved in case you're planning on adding new integers to the chart. Apparently variance is used for other things besides pin pointing the finer number standard deviation. Idk, maybe you can multiply it by something, invert it, double it, idk...

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  • $\begingroup$ I don't understand this answer. $\endgroup$ – Michael Chernick yesterday

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