1. ## Finding Standard Deviation

I have been working through a problem in which I am given 4 means from four different conditions, and I am also given the between, within, and total SS, df, MS and F.

I used this set of on-line directions to try to figure it out. The answer was in response to this question:

Q: The sum of 50 observations in the sample is 400. The sum of the squares is 3544. That is all I know.

How do I find variance and Standard Deviation? Do I even have enough information?

A:

The Standard Deviation (σ) is a measure of how spread out numbers are.

σ = the square root of the Variance
so Variance (v) is the square of the standard deviation, ie: σ^2
To solve the problem, you first calculate v which will then give σ

v = The average of the squared differences from the Mean (m)
= (1/m)(sum (Xi - m)^2)
= (1/m)(sum (s)^2)

You have the number of samples (N) and their sum (T)
So you have m=(T/N) = (400/50) = 8

You have the sum of the squares(S),
S = 3544

but not the sum of the squared differences (sum (s)^2)

If you do the algebra, you can calculate σ^2 anyway by using

σ^2 = (S - (sum (s))^2/N) )/N

= ( 3544 -(160000/50) )/50

= ( 3544 - 3200 )/50 = 6.88

and the standard deviation is the square root.
________

Since used the average score of the four means and multiplied by the total number of subject to get an estimate of the sum of scores. I then used my sum of squares total and subtracted it from my sum of scores squared divided by my total number of subjects. After the subtraction I divided the number again by my total number of subjects and then sq rooted that number. So is this right? When I graph it, it seems as if the standard dev is way too large. Help, please.

2. Originally Posted by PabloZzzz

Why not just compute the standard deviation (S) for all the data as:

S = Sqrt[ Total Sums of Squares / df ]

where df = N - 1. (N is the total sample size).

3. I am not given the data, the question asks that I guess about the stand dev, but I was thinking that I could actually work backwards from the data at hand to find a general estimate. I am assuming homogeniety of variance. Is there a way to work backwards in order to make a guess?

4. Ok, I went back and read your response again. I think I get it. The results surprise me a bit, again, however. Since I am getting an F of 6 with an F critical of 2.7 and the distance between the lowest and highest mean is 7 points, and st dv is comes out to be around 5--meaning the .05 line would be drawn 15 points out. Does this mean I have fairly steep curves? or am I even reading this correctly?

5. Originally Posted by PabloZzzz
Ok, I went back and read your response again. I think I get it. The results surprise me a bit, again, however. Since I am getting an F of 6 with an F critical of 2.7 and the distance between the lowest and highest mean is 7 points, and st dv is comes out to be around 5
The overall S is not a good statistic to use if you're wondering why the F statistic is 6. A better statistic to consider at would be the MS_within...it's the average of the variances for each group. Also, if you take the
Sqrt[MS_within] it is the "standard error of the estimate". In other words, if you conducted this ANOVA via Regression (with dummy codes) it would be the standard of the regression.

--meaning the .05 line would be drawn 15 points out. Does this mean I have fairly steep curves? or am I even reading this correctly?
I am not familiar with what it is you're looking at here.

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