Standard Deviation with Formula
  Count (x) = n is the number of elements in the list.
  Sum (x) = Σx
  Sum (x²) = Σx²
  Mean (x) = x is the average of the data in a list.
  SVari (x) = Sx²
  SStDev (x) = Sx
  Standard Deviation Graph
    

fig. 1  Standard Deviation
Reference: The Little Handbook of Statistical Practice
  Summary Statistics: Location & Spread - Statistics are summaries derived from data.
  The most commonly reported measure of spread is the standard deviation (SD)
fig. 2  Standard Deviation
Reference: e-Handbook of Statistical Methods
Reference: HyperStat Statistics Textbook

 Standard Deviation with Frequency List
 
  The standard deviation measures how much each reading differs from the mean (mathematic average) of all of the readings.
  A frequency distribution is a table of values of one or more variables that make a sample. Each entry in the table contains the frequency (or count) of the occurrences of values within a particular group, and this way the table summarizes the distribution of values in the sample.

from Red Crab Manual:
  A list starts with a bracket ( [ ) and ends with a bracket ( ] ) and has commas between the elements of the list.

n=sum(y) is the number of the elements in the list.
SVari(x) is the variance of sample values in a list
SStDev(x) is the sample standard deviation of values in a list.
Mean(x) is the mathematical average value of a list.

fig. 3  Standard Deviation
Reference: Computational Statistics Handbook With MATLAB
Reference: Statistics: Methods and Applications
fig. 4  Standard Deviation
Reference: StatSoft electronic statistics textbook
Reference: Statistical handbook free download

 Standard Deviation Sum of Squares

   In measuring how spread out a set of measures are, the sum of the squares, often indicated as SS, is calculated as the square of the sum of differences between each measure and the average.
SS = SUM(Xi - AVERAGE(X))

  in statistics, many formulas require the calculation of sums of squares; i.e., squaring all of the elements in a set and then taking the sum of those squares.
Reference: Standard Deviation Formulas
  
  ∑ ( x-x)² = sum(x)-(x mean) squared
  N = number of elements in the list

fig. 5  Standard Deviation
Reference: Applied Statistics Handbook
Reference: Statistical Methods in Biological and Medical Sciences
fig. 6  Standard Deviation
Reference: Calculate Standard Deviation
Reference: Standard Deviation Tutorial


 Two Sample T Test
Assumptions:
   each group is considered to be a sample from a distinct population
   the responses in each group are independent of those in the other group
   the distributions of the variable of interest are normal
Purpose:
  A 't' test compares the means of two groups.

    The null hypothesis is that the two population means are equal to each other. To test the null hypothesis, you need to calculate the following values: (x1, x2)(the means of the two samples), s1², s2² (the variances of the two samples), n1, n2 (the sample sizes of the two samples), and k (the degrees of freedom).
            

fig. 7  Two Sample T Test
Reference: graphpad
The t test compares one variable between two groups.
fig. 8  Two Sample T Test
Reference: acastat
A two-sample t-test is used to test the difference (d0) between two population means.

 Pearson r

Pearson r (product-moment correlation coefficient) is a measure of the correlation (linear dependence) between two variables X and Y, giving a value between +1 and -1 inclusive

Example:
    
   Example: Pearson r Graph




Reference:
   √ = Crtl + 1
   x² (or exponent 2) = F3 + 2
   π = Ctrl + P
 
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