Please enable JavaScript.

Coggle requires JavaScript to display documents.

Statistics Week8 - Coggle Diagram

- - - - you only have one standard normal value squared (Z^2)
      - Chi Squared R.V = Sum of Squared Std Normals
      - Substitute P(Chi Squared ... > ) = P(Z^2 > ...)
        
        this equals to P(Z > ) + P(Z < - ) = 2 * P(Z > ) as symmetric
- - - - meaning, you can create a confidence interval to estimate the true population proportion with a margin of error of 3% (eg: 55% is the true population proportion, so the confidence interval is 52% to 58%) and you are 95% confident that the true population proportion will fall within this bounds
- - - - note, the sum of the expected values should add up to n, because the various probabilities should add up to 1
      - if Ho is true, we expect the chi squared random variable to be very small due to formula. however, if it is larger than chi squared crit value with (m-1 dof and alpha), then we reject Ho because it is a very unlikely event to occur, but it still occurred anyway, which means its not due to chance, and that Ho is probably false.
      - in excel, to calculate the chi squared value with the dof, you can use chisq.inv (1-prob, dof) OR chisq.inv.rt(prob,dof)
    - - Discrete Cases
        
        want to see if data approximates x distribution
        
        MUST specify what distribution you are testing against before you commence the test, to avoid a multiple test fallacy where we make something that is not statistically significant into something that is
        
        remember to reduce degree of freedom according to how many parameters you estimate.
      - CONTINUOUS CASES
        
        steps to take
        
        find what is lambda/sample mean /standard deviation
        
        use integration thru using the cdf of the distribution, and the lambda you calculate, to calculate the expected probability that the data falls within the range
        
        note, you have to subtract two integrals as 20 - 40 = (0 - 40) - (0 - 20)
        
        find the expected values
        
        take the difference between the observed and the expected
        
        sum the value up to give the chi squared value and compare that with the critical value
        
        note that you need to -1 if you estimate 1 parameter from the dof
    - - calculated expected value using formula (row sum *column sum)/grand sum
      - sum all the values for the matrix into chi square
      - degree of freedom is just use the formula (row - 1) * (column - 1)
      - compare chi squared with critical value