The Chi Square distribution is commonly used to test the difference amongst proportions. It is also used directly or indirectly in many tests of significance and it is a mathematical distribution. The Chi Square distribution has one parameter and it is denoted as df (degrees of freedom). All these points are taken care of by the experts providing Statistic homework help and assignment help at transtutors.com.
Chi Square distribution has a positive skew. The Skew is less with more df. The Chi Square distribution approaches a normal distribution as the degrees of freedom increases. The df is the mean of Chi Square distribution, df – 2 is the mode, the median is around df – 0.7.
Sample 2 scores from a standard normal distribution, square each score, and add the squares. Define the probability of the addition to be 6 or higher?
By using Chi Square distribution with two degrees of freedom the answer can be found because 2 scores are sampled.
The probability is 0.050, which can be found by using Chi Square calculator.
As mentioned above, df is the mean of Chi Square distribution. The distributions are positively skewed, where when the degree of skew decreases, the df increases and as df increases the Chi Square Distribution reaches a normal distribution.
Figure A shows three Chi square distributions and their density function. This will show the inverse relation of the skew and degrees of freedom (df).
Figure A with 2, 4 and 6 degrees of freedom (df)
Many test statistics are approximately distributed as Chi Square therefore Chi Square distribution is very vital. Tests of deviations in frequencies between theoretically expected and observed & relation between the contingency tables (categorical variables), are two of the more commonly tests using the Chi Square distribution. All such methods are covered in Statistic Homework help, Assignment help at transtutors.com.
Expected Value, Variance, and the role of the parameters
The Chi-Square distribution is a type of the Gamma distribution. Most of the treatments of the Chi-Square are based on the common results about the Gamma to affirm the characteristics of the special-case Chi-square. There are two parameter distribution in Gamma distribution, i.e. G(α, β), with parameters shape (α) and scale (β).
The probability density would be to the Chi-square distribution with degrees of freedom equal to N, if in Gamma distribution the shape parameter is N/2 & the scale parameter is equivalent to 2.
The known fact is that the variance is αβ2, and expected value of a Gamma distribution is αβ, which means that anticipated value of a Chi-square for N observations is:
E(x) = N
and noted variance of a Chi-square variable is:
Now we understand, that has a distribution, if any variable is proportional to Chi – Square , and the probability density is
For N > 2, the mode is:
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