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Chi-squared 11-30-06

# Chi-squared 11-30-06 - A Chi-squared and Non-parametric...

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A. Chi-squared and Non-parametric Tests B. C. Non-parametric Measures I. Do not depend on estimation of population values and do not follow population distributions a. Instead of coming up with clean regression lines, which assumes normality of the distribution, it comes up with choppy lines that best fit the data at each point in the line D. Chi-square Distributions I. A family of different types of distributions (multiple types of functions as opposed to a normal distribution) that are chosen depending upon the degrees of freedom (which changes how the distribution is skewed) where the df ranges from 1 to 4 a. It has only one parameter (degrees of freedom) b. Mean = degrees of freedom; Variance = degrees of freedom * 2 c. It is a distribution of squared z scores i. chi-squared(1 df) = χ 2 (1) = z 2 = (x – X) 2 /s 2 ii. This will create a distribution that has no negative values, so the distribution will be positively skewed iii. χ 2 (2) = z 2 1 + z 2 2 = (x 1 – X) 2 /s 2 + (x 2 – X) 2 /s 2 (just summing together pairs of z scores)
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