Stats: Chi-Square
Definitions
Chi-square distribution
A distribution obtained from the multiplying the ratio of
sample variance to population variance by the degrees of freedom when random
samples are selected from a normally distributed population
Contingency Table
Data arranged in table form for the chi-square independence
test
Expected Frequency
The frequencies obtained by calculation.
Goodness-of-fit Test
A test to see if a sample comes from a population with the
given distribution.
Independence Test
A test to see if the row and column variables are
independent.
Observed Frequency
The frequencies obtained by observation. These are the
sample frequencies.
Stats: Chi-Square Distribution
The
chi-square distribution is obtained from the
values of the ratio of the sample variance and population variance multiplied
by the degrees of freedom. This occurs when the population is normally
distributed with population variance sigma^2.
Properties
of the Chi-Square
- Chi-square is non-negative. Is the ratio of two non-negative values, therefore must be non-negative itself.
- Chi-square is non-symmetric.
- There are many different chi-square distributions, one for each degree of freedom.
- The degrees of freedom when working with a single population variance is n-1.
The Chi- square Test
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