Like the Student's t-Distribution, the Chi-square distribtuion's shape is determined by its degrees of freedom. The animation above shows the shape of the Chi-square distribution as the degrees of freedom increase (1, 2, 5, 10, 25 and 50). For examples of tests of hypothesis which use the Chi-square distribution, see Statistics in crosstabulation tables in the Basic Statistics and Tables chapter as well as the Nonlinear Estimation chapter. See also, Chi-square Distribution. As shown in the illustration below, the values inside this table are critical values of the Chi-square distribution with the corresponding degrees of freedom. To determine the value from a Chi-square distribution (with a specific degree of freedom) which has a given area above it, go to the given area column and the desired degree of freedom row. For example, the .25 critical value for a Chi-square with 4 degrees of freedom is 5.38527. This means that the area to the right of 5.38527 in a Chi-square distribution with 4 degrees of freedom is .25.
F Distribution Tables The F distribution is a right-skewed distribution used most commonly in Analysis of Variance (see ANOVA/MANOVA). The F distribution is a ratio of two Chisquare distributions, and a specific F distribution is denoted by the degrees of freedom for the numerator Chi-square and the degrees of freedom for the denominator Chi-square. An example of the F(10,10) distribution is shown in the animation above. When referencing the F distribution, the numerator degrees of freedom are always given first, as switching the order of degrees of freedom changes the distribution (e.g., F(10,12) does not equal F(12,10)). For the four F tables below, the rows represent denominator degrees of freedom and the columns represent numerator degrees of freedom. The right tail area is given in the name of the table. For example, to determine the .05 critical value for an F distribution with 10 and 12 degrees of freedom, look in the 10 column (numerator) and 12 row (denominator) of the F Table for alpha=.05. F(.05, 10, 12) = 2.7534.
Source: http://www.statsoft.com/textbook/stathome.html?sttable.html&1 ... As shown in the illustration below, the values inside this table are critical values of the ...
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