# Standard deviation exceeds maximum value

I am trying to plot data that only has two possible values – 1 (present) or 0 (absent) – clearly not a normal distribution. The max value could be 1, but my standard deviation bars go to 1.3, which is impossible. I tried increasing the sample size, but the max column value + standard deviation are still 1.3. Is it OK to manipulate my graph and cap my column bars off at 1 since it is not possible to have a sample value larger than 1?

• What "standard deviation bars" are you talking about? What are you doing? What sort of graph? What are you trying to show? – Peter Flom May 29 '14 at 22:18
• See the wikipedia page and search here for binomial distribution. – John May 29 '14 at 22:35
• Define exactly what these "standard deviation bars" are giving, please. I suspect their definition (whatever it is) makes the value not "impossible", and you're simply plotting something other than your present needs. – Glen_b May 29 '14 at 23:17

What you have is a binomial distribution. The mean of your 0's and 1's is the proportion of 1's. The standard deviation is $\sqrt{p (1-p)}$, and the standard error is $\sqrt{\frac{p (1-p)}{n}}$ where $n$ is the number of samples. If you're trying to figure out a 95% confidence interval on the proportion (the mean), that would be $\pm 1.96 {\sqrt{\frac{p (1-p)}{n}}}$.
• @Andre The data have a Binomial$(1,p)$ distribution while a particular statistic--their sum--has a Binomial$(n,p)$ distribution. To that extent the language in this answer is correct. It also contains a lot of relevant information--thank you, Sofia! In its present form it falls a little short of addressing the question, though. It should be pointed out that because $\sqrt{p(1-p)}\le 1/2$ and $p+\sqrt{p(1-p)}$ never exceeds $1.20711$, the "standard deviation bars" of the question cannot possibly extend to $1.3$. Thus we need clarification from the OP in order to develop good answers. – whuber May 29 '14 at 23:16