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Correlation - Coggle Diagram

- - - - null hypothesis: p is less than or equal to 0
        
        the population correlation is not positive
      - alternative hypothesis: p is greater than 0
        
        the population correlation is positive
  - - - Sample is not expected to be identical to the population
      - There is always some error between the sample statistic and the corresponding population parameter
  - - - sample statistic = sample correlation (r)
      - corresponding parameter is the population correlation (p)
      - null hypothesis : p=0
      - Standard error for r = the square root of ((1 - r squared) / (n-2))
    - - df = n-2
- - - - Correlations should and can't be interpreted as proof of a cause & effect relationship between the two variables
    - - Coefficient of determination: (r squared) measures the proportion of variability in one variable that can be determined from the relationship with the other variable
- - - - as the value of the X variable increases from one individual to another, the Y variable also tends to increase
        
        When the X variable decreases, the Y variable also decreases
    - - As the X variables increases, the Y variable decreases
        
        It is inverse relationship
- - - - Definitional formula
        
        1.) Find the X deviation and the Y deviation for each individual
        
        2.) Find the product of the deviations for each individual
        
        3.) Add the products
- - - - When converting scores into ranks, may encounter two or more identical scores
      - When two scores have the same value, their ranks should also be the same
      - Completed by:
        
        1.) List the scores in order from smallest to largest, include tied values in the list
        
        2.) Assign a rank (first, second, etc) to each position in the ordered list
        
        3.) When two (or more) scores are tied, compute the mean of their ranked positions, and assign this mean value as the final rank for each score
    - - After the original X & Y values have been ranked, calculations for SS and SP can be simplified
      - Find the midpoint of the series by M = (n+1)/2
    - - a correlation between two variables where one of the variables is dichotomous
      - A variable with only two values is called dichotomous or binomial
        
        male vs female or college graduate vs non college graduate
      - Phi-coefficient : a correlation between two variable both of which are dichotomous
        
        1.) Convert each of the dichotomous variables to numerical values by assigning a ) to one category and a 1 to the other category for each of the variables
        
        2.) Use the regular Pearson formula with the converted scores