# Usage of Plus-minus sign

I have a question concerning statistical conventions. I want to report the classification rate of a 3-fold cross validated machine learning experiment. Of course I report the mean and some measure of the diversity in the different folds. I want to use a shorthand notation like $95.5\% \pm 0.9\%$.

My question is: What is most commonly used as "measure of the diversity"? On Wikipedia we find that standard deviation or standard error is used. On the same page under In statistics we find that usually it is corresponding to either 1 or 2 standard deviation.

So is there a best practice what to report? Standard deviation, standard error or even variance? And 1 or 2 times?

• There's differences of conventions in different application areas, and many areas don't even have a convention. – Glen_b -Reinstate Monica Jul 8 '15 at 14:38

## 1 Answer

All the three statistics are connected. If you take a square root of variance you get standard deviation: $\sigma = \sqrt \sigma^2$, if you divide standard deviation by square root of number of observations you get standard error: $\text{SE} = \sigma / \sqrt n$. To read more on the differences and similarities between those measures check this thread. You often see statistical results described as $X \pm \text{some number} \times \sigma$, those are confidence intervals and in most cases the "1 or 2" number is chosen so that you get 95% confidence intervals. The magic number 1.96 corresponds to 95% confidence interval for a variable with Normal distribution.

• Thanks for your answer! I am aware that the three statistics are connected. I would like to know which of them is most commonly used for a report, especially in the case of reporting about the classification rate of a machine learning experiment. – Frank Zalkow Jul 8 '15 at 14:36
• @FrankZalkow it depends on what information you want to focus on. Check the links I posted to learn more on the differences, that would give you better ideas on when to use which of these. – Tim Jul 8 '15 at 14:38