New answers tagged standard-deviation
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As others have pointed out, whether it is correct to calculate the mean and the standard deviation of percentages depends on your intended use. For you use, at least as I understand it, it seems to be incorrect.
As I understand from your question and comment, you are trying to do anomaly detection. You are basically asking:
Is the number of missed ...
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Consider three set of data having same mean and MD but their ranges are changing. It is interesting to see how SD changes with change in the range of the data.
SET 1: 1, 3,5,7,9,11,13,15,17,19 Range:1-19 Mean=10, MD=5 SD= 6.05
SET 2: 2,3,5,7,7,9,13,15,14,23 Range: 1-23 Mean=10 MD=5 SD=6.28
SET 3: 3,5,5,7,7,8,10,12,13,30 Range: 1-30 Mean =10 MD=5 SD=7.70
...
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I would agree that your definition of standard deviation $\sigma= \dfrac{ \sqrt{ \sum\limits_{i=1}^n (x_i-\mu)^2} } {N} $ could be used to measure the spread of a population. However it is a harder concept to come up with. (And I think it is also harder to use to, for example, prove other theories.)
I don't know the exact history behind the invention of ...
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I found an excellent comment by the user Carl Why are we using a biased and misleading standard deviation formula for $\sigma$ of a normal distribution?
However no reference how the formula using excess kurtosis is derived
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If I want to use t-test for a hypothesis, then I have to assume normality of the population.
Not so. The population is irrelevant (well...not completely, we really only need to assume finite variance and make vague assumptions about the skew, mainly that the population is not "skewed too much". See the Berry-Esseen Theorem for more on how the ...
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The rule is very simple.
Regardless of the size $n$ of the normal sample:
If population standard deviation $\sigma$ is unknown and estimated by the sample standard deviation $S = \sqrt{\frac{1}{n-1}\sum_{i=1}^n (X_i-\bar X)^2},$ then use a t test. Critical value and P-value use Student's t distribution with $n-1$ degrees of freedom.
If population standard ...
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You propose a test to see it two binomial proportions are the same (null hypothesis) or whether one is larger than the other (one-sided alternative).
Minitab, does such a test, using a normal approximation, as follows:
Test and CI for Two Proportions
Sample X N Sample p
1 8 106 0.075472
2 8 9 0.888889
Difference = p (1) - p (2)
...
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Assuming $\mu, \sigma$ for mean and deviation respectively, you have two equations of the following form: $P(X\leq x)=p$. When standardised, it becomes
$$P(X\leq x)=P\left(\frac{X-\mu}{\sigma}\leq \frac{x-\mu}{\sigma}\right)=P\left(Z\leq \frac{x-\mu}{\sigma}\right)=\Phi\left(\frac{x-\mu}{\sigma}\right)$$
where $\Phi$ represents the CDF of the standard normal ...
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We know that for a Normal distribution Mean - 2SD TO Mean + 2SD accounts for 95% of the observations. This imply approximately
Mean + 1.96SD - (Mean - 1.96SD) = Range
Mean + 1.96SD - Mean + 1.96SD = Range
3.92*SD = Range
or SD = Range/3.92
Example: 4 6 7 9 12 15 18 19 20 21 23 25 27 ON CALCULATION
Mean = 15.84 and SD = 7.614
Estimated SD from the range = ...
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My biologist colleagues do similar research, but no-one so far could explain to me why they do it according to this schema: 3 'biological replications' $\times$ 3 'technical replications'. It seems to be the standard procedure that no-one questions, but also no-one really understands.
So, without knowing the reasons, I can only offer my more-or-less '...
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In the comments on Paul's answer Whuber commented that the case of a Bernoulli variable with $p=1/2$ contradicts with his argument. In this question we look further into the Delta method with a graphic. This will provide some intuition and explanation about the (multivariate) Delta method and it explains why the Bernoulli variable is an exception (the only ...
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We have a statistical consultant on the study that has said typically compliance is calculated the latter way (as a percentage figure for each individual patient). It is not relevant to show the numerator and denominator for compliance here, and instead they recommended giving the interquartile range (IQR) alongside the mean percentage and standard deviation ...
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