Statistics Equations Flashcards
Average Equation
xbar = Sigma(x)/n
Standard Deviation
s = sqrt(sigma((x-xbar)^2)/n-1
Degrees of freedom
n-1
Variance
s^2
Relative standard deviation (coefficient of cariation)
s/xbar
Gaussian Curve equation
y = 1/(ssqrt(2pi))e^[-(x-xbar)^2/2s^2]
y = 1/(ssqrt(2pi))e^(-z^2/2)
What is the equation for multiples of standard deviation
z = x-xbar/s
Percentage of 1s, 2s, and 3s
68.3, 95.5, and 99.7
Equation for standard deviation of the mean
u = s/sqrt(n)
What is the f-test
F = s1^2/s2^2 (where s1>s2
confidence interval equation
Interval = xbar +- ts/sqrt(n)
Equation for comparing a result to a standard
same as the confidence interval
What is the t-test equation when s’s are not significantly different
t = |xbar1 - xbar2|/spooled * sqrt (n1n2/(n1+n2))
spooled = sqrt((sigma(x-xbar)^2) + (sigma(x-xbar)^2)/(n1+n2-2))
spooled = sqrt(s1^2(n1-1)+s2^2(n2-1)/(n1+n2-2))
T-test when standard deviations are significantly different
t =|xbar1-xbar2|/sqrt(s1^2/n1+s2^2/n2)
DoF = (s1^2/n1+s2^2/n2)^2/[(s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1)]
DoF = (u1^2+u2^2)^2/[u1^4/(n1-1)+u2^4/(n2-1)]
Standard Deviation and t value for paired t-test with no duplicates
s = sqrt(sigma[(d-dbar)^2]/(n-1))
t = |dbar|*sqrt(n)/s
One tailed t=tests
t = |xbar - threshold|*sqrt(n)/s
Grubbs Test Equation
G = |value - xbar|/s
Vertical deviation equation
di = yi-y
Deteminant of 2x2 matrices
|a b| = ad - bc
|c d|
Slope equation
m = |Sigma(x*y) Sigma(x)|/D
|Sigma(y) n |
Intercept equation
b = |Sigma(x^2) Sigma(x*y)|/D
|Sigma(xi) Sigma(y) |
What does D equal
D = |Sigma(x^2) Sigma(x)|
|Sigma(x) n |
How to take the inverse of a matrix
make a, b, c, and d to d, -b, -c, and a, and multiply each by 1/det of abcd
How to multiply matrices
The first matrix columns must match the second’s rows
Then multiply the rows of the first by the second’s columns and add together
