Has two answers, #-1# and #1#, which can raise a question much like your own, can square roots be negative?
The answer to this, is no. Conventionally when taking the square root we only take the positive value. The concept that a negative value appears come from a frequently omitted step and/or a not very known fact.
#x^2 = a# #sqrt(x^2) = sqrt(a)#
So far so good, but you see, the definition of the absolute value function is #sqrt(x^2)#, so we have
#|x| = sqrt(a)#
And since we now have an equation dealing with a modulo, we must put the plus minus sign
#x = +-sqrt(a)#
But you see, despite using #s# or #sigma# for standard deviation and #s^2# or #sigma^2#for the variance, they came to be the other way around!
Standard deviation was defined as the square root of variance and square roots are by convention always positive. Since we're not using the standard deviation as an unknown value, that plus minus sign won't show up.
Whenever, there are two unequal terms in the observations, the standard deviation is positive, that means greater than zero. If all the observations are exactly equal, then the standard deviation is exactly zero.So, under no circ*mstances, the standard deviation can be negative or less than zero.
Standard errors (SE) are, by definition, always reported as positive numbers. But in one rare case, Prism will report a negative SE. This happens when you ask Prism to report P1^P2 where P1 and P2 are parameters and P1 < 1 and P2 > 0.
One common question students often have about variance is: Can variance be negative? The answer: No, variance cannot be negative. The lowest value it can take on is zero.
The standard deviation is found by taking the positive square root of the variance. Therefore, the standard deviation and variance can never be negative. Squared deviations can never be negative.
So you can't say that the variance is bigger than or smaller than the standard deviation. They're not comparable at all. Nothing is amiss: you can happily work with values above 1 or below 1; everything remains consistent.
The standard deviation is also overused at the expense of other measures of dispersion. For example, its use with the arithmetic mean (as mean ± SD) is misleading for data with a skewed distribution. This is because errors are no longer distributed symmetrically around the mean.
Negative values in VC matrix may indicate: A not positive definite input covariance matrix may signal a perfect linear dependency of one variable on another.
Introduction: My name is The Hon. Margery Christiansen, I am a bright, adorable, precious, inexpensive, gorgeous, comfortable, happy person who loves writing and wants to share my knowledge and understanding with you.
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