Student's t Critical Value
Computes the critical value of Student's t distribution for the degrees of freedom and confidence level you choose, replacing the lookup in the t table at the back of statistics books. It returns both the two-sided value (for confidence intervals and two-tailed tests) and the one-sided value (for one-tailed tests). As the degrees of freedom grow, the value converges to that of the normal distribution. Enter the degrees of freedom and the confidence level.
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Student's t Critical Value
Computes the critical value of Student's t distribution for the degrees of freedom and confidence level you choose, replacing the lookup in the t table at the back of statistics books. It returns both the two-sided value (for confidence intervals and two-tailed tests) and the one-sided value (for one-tailed tests). As the degrees of freedom grow, the value converges to that of the normal distribution. Enter the degrees of freedom and the confidence level.
The t table at the back of the book, computed on the spot
Every statistics handbook carries, in its last pages, that dense table of t values organized by degrees of freedom and significance level. It's necessary for building confidence intervals and deciding hypothesis tests, but consulting it is uncomfortable and limited to the few printed levels. This tool computes the exact value for any combination.
The critical t value is the point of the distribution that bounds the rejection region or the edges of an interval. The t distribution has heavier tails than the normal, which makes the values larger when the sample is small, reflecting the extra uncertainty of estimating the variance. As the degrees of freedom increase, that difference shrinks and the t value converges to the corresponding z.
Enter the degrees of freedom and the confidence level. The tool returns the two-sided value, for intervals and two-tailed tests, and the one-sided value, for one-tailed tests. Remember that the degrees of freedom in a one-sample t-test are n minus one, and in a two-sample test with pooled variances, n1 plus n2 minus two.
Related Tools
Chi-Square Critical Value
Computes the critical value of the chi-square distribution for the degrees of freedom and confidence level you choose, dispensing with the printed table. It's the right-tail cutoff used in goodness-of-fit, independence and variance tests: if the computed statistic exceeds this value, the null hypothesis is rejected. Unlike the normal and the t, the chi-square is asymmetric and takes only positive values. Enter the degrees of freedom and the confidence level.
F Critical Value (Fisher-Snedecor)
Computes the critical value of the Fisher-Snedecor F distribution for the numerator and denominator degrees of freedom and the chosen confidence level, replacing the bulky F tables. It's the cutoff used in ANOVA and in variance-ratio tests: if the observed F statistic exceeds it, the conclusion is that the variances or means differ. The F distribution depends on two degrees of freedom, which made the printed tables enormous. Enter the two degrees of freedom and the confidence level.
Degrees of Freedom (Grübler)
Compute the degrees of freedom (mobility) of a planar mechanism by the Grübler-Kutzbach equation, DOF = 3·(n − 1) − 2·j1 − j2, where n is the number of links (including the fixed one), j1 the 1-DOF joints (pin, slider) and j2 the 2-DOF joints. A four-bar linkage (n=4, j1=4) has DOF=1: a single input motion controls the whole mechanism. The basis of mechanism and robot synthesis. Enter the number of links, 1-DOF joints and 2-DOF joints.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.