Search results
Results from the WOW.Com Content Network
The chi-squared distribution has numerous applications in inferential statistics, for instance in chi-squared tests and in estimating variances. It enters the problem of estimating the mean of a normally distributed population and the problem of estimating the slope of a regression line via its role in Student's t-distribution .
Chi-squared distribution, showing χ2 on the x -axis and p -value (right tail probability) on the y -axis. A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical ...
Usage. Pearson's chi-squared test is used to assess three types of comparison: goodness of fit, homogeneity, and independence. A test of goodness of fit establishes whether an observed frequency distribution differs from a theoretical distribution. A test of homogeneity compares the distribution of counts for two or more groups using the same ...
Unbiased estimation of standard deviation. In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the ...
Test statistic is a quantity derived from the sample for statistical hypothesis testing. [1] A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or ...
Reduced chi-squared statistic. In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating [1] and variance of unit weight in the context of weighted least squares. [2][3] Its square root is called regression standard error, [4 ...
The predicted response distribution is the predicted distribution of the residuals at the given point xd. So the variance is given by. The second line follows from the fact that is zero because the new prediction point is independent of the data used to fit the model. Additionally, the term was calculated earlier for the mean response.
It is remarkable that the sum of squares of the residuals and the sample mean can be shown to be independent of each other, using, e.g. Basu's theorem.That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic: