Raising the bar

Chapter 14. Excel statistical functions

Unit 14.2. Excel functions for critical values

In the previous unit each function takes the argument $latex x$ (or $latex z$, $latex \lambda$, $latex \ldots$) and returns a probability (or a density value). In this unit the direction is reversed: we specify the probability of the right tail and ask Excel for the cut-off value that delivers it. The reference values that NCT puts into Tables 7$latex -$9 of its appendix are produced this way.

Cutoff points of the chi-square distribution function. For given probability of the right tail $latex \alpha$ and degrees of freedom $latex \nu$ the cut-off value $latex \chi_{\nu, \alpha}^2$ is a solution of the equation (see Figure 14.2)

$latex P(\chi_\nu^2 > \chi_{\nu, \alpha}^2) = \alpha.$

Figure 14.2: Cut-off point for chi-square distribution.

Table 14.7. Cutoff points of the chi-square distribution function.

In Mathematica, enter (on one line, without spaces)

v=9;a=0.995;InverseCDF[ChiSquareDistribution[v],1-a]

Cutoff points for the Student's $latex t$ distribution. For given probability of the right tail $latex \alpha$ and degrees of freedom $latex \nu$ the cut-off value $latex t_{\nu, \alpha}$ is a solution of the equation (see Figure 14.3)

$latex P(t_\nu > t_{\nu, \alpha}) = \alpha.$

Figure 14.3: Cut-off point for Student's t distribution.

Table 14.8. Cutoff points for the Student's $latex t$ distribution.

In Mathematica, enter (on one line, without spaces)

v=9;a=0.1;InverseCDF[StudentTDistribution[v],1-a]

Cutoff points for the $latex F$ distribution. For given probability of the right tail $latex \alpha$, degrees of freedom $latex v_1$ (numerator) and $latex v_2$ (denominator) the cut-off value $latex F_{v_1, v_2, \alpha}$ is a solution of the equation (see Figure 14.4)

$latex P(F_{v_1, v_2} > F_{v_1, v_2, \alpha}) = \alpha.$

Figure 14.4: Cut-off point for F distribution.

Table 14.9. Cutoff points for the $latex F$ distribution.

In Mathematica, enter (on one line, without spaces)

v1=9;v2=10;a=0.05;InverseCDF[FRatioDistribution[v1,v2],1-a]

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