CHIINV in WPS Spreadsheet: Invert a Chi-Square Right Tail

=CHIINV(probability, degrees_freedom)

Original controls use probabilities strictly between zero and one and small positive integer degrees of freedom. The published probability-error inequality is incomplete, so this guide does not infer exact endpoint behavior or error tokens from that damaged statement.

The lesson defines the inverse through CHIDIST(x, degrees_freedom)=probability. The forward and inverse calculations describe the same right-tail model. Use the independent probability checks below to distinguish a correct tail convention from a plausible-looking threshold.

For degrees of freedom 2, right-tail probability is exp(−x/2). Solving it for x gives −2*ln(probability).

1. Enter 0.25 in A2 and 2 in B2.
2. Use =CHIINV(A2,B2) in C2.
3. Independently calculate −2*ln(0.25), approximately 2.77258872223978.
4. Substitute it into exp(−x/2) to recover 0.25.

The probability input is 25% above the threshold. The lower-tail probability at the same threshold is 75%. Passing 0.75 would answer a different upper-tail question.

The last two decimal inputs approximate probabilities obtained independently from even-degree survival formulas. Their expected thresholds are known mathematical roots within numerical rounding, not assertions of exact stored application values.

For a candidate x with four degrees of freedom, independently evaluate exp(−x/2)*(1+x/2). At x=2 this is 2/e, approximately 0.735758882342885. With six degrees, include the quadratic term (x/2)^2/2; at x=6 the survival is 8.5*exp(−3).

These checks assess the actual tail probability rather than merely comparing decimal digits of a threshold. A small x difference has different implications depending on the distribution’s local density. Rounded display values should not be used to claim a precise significance boundary without examining the underlying value and model assumptions.

The vendor example probability 0.000235642 and degrees of freedom 4 displays 21.64653138. Independent calculation gives approximately 21.64653230362246, so the vendor’s historical display is not a precision benchmark or an application execution for this guide. Original controls stay away from extreme probabilities.

A threshold may be useful within a properly specified statistical procedure, but it does not construct the test statistic, determine appropriate degrees of freedom or establish a hypothesis as true. The source’s broad validity language is therefore interpreted narrowly as distribution evaluation.

Check that probability is a fraction, not a whole percentage, and that the intended tail is right-sided. Fractional-degree truncation, endpoints, malformed arguments and convergence outside these examples remain untested. For comparison, NORMINV uses a different distribution and a lower-tail quantile contract.

The official WPS lesson is dated 2019-06-20 and leaves its edition/platform applicability field blank. Its numeric build is unspecified. This documents the function by that date; it does not establish first introduction, the last functioning build, other-platform parity or a retirement/deprecation history.

The official lesson was rechecked on October 19, 2026. Original examples are documentation-derived independent calculations, not WPS or other spreadsheet-engine executions. Numeric reference values do not certify application precision or statistical model suitability.