Confidence Interval for Variance

R / RStudio

R does not ship a dedicated one-line function for a variance confidence interval, but it is straightforward to build directly from the chi-square quantiles, since qchisq() is a base R function.

# Example data
x <- c(12.5, 14.2, 13.8, 15.1, 12.9, 13.4, 14.0)

n     <- length(x)
s2    <- var(x)              # sample variance
df    <- n - 1
alpha <- 0.05

chi_lower <- qchisq(alpha / 2, df)
chi_upper <- qchisq(1 - alpha / 2, df)

ci_lower <- (df * s2) / chi_upper
ci_upper <- (df * s2) / chi_lower

cat("Sample variance:", s2, "\n")
cat(paste0(100 * (1 - alpha), "% CI for variance: (",
           round(ci_lower, 4), ", ", round(ci_upper, 4), ")\n"))

If you prefer a packaged function, the EnvStats package includes varTest(), which returns a confidence interval for variance alongside a chi-square hypothesis test:

install.packages("EnvStats")   # once
library(EnvStats)

varTest(x, conf.level = 0.95)

The varTest() output reports the sample variance, degrees of freedom, the chi-square statistic, and the confidence interval bounds directly.

IBM SPSS

SPSS's built-in Explore procedure reports a confidence interval for the mean, not the variance, so a variance CI has to be assembled from the pieces SPSS gives you plus a chi-square lookup.

Step 1 — Get the sample variance and n:

Analyze → Descriptive Statistics → Explore, move your variable into the Dependent List, and request the Descriptives output. Note the Variance and N values.

Step 2 — Get the chi-square critical values:

SPSS can compute chi-square quantiles via the Compute Variable dialog using the inverse CDF function. In Transform → Compute Variable, use an expression such as:

<

IDF.CHISQ(0.025, df)
IDF.CHISQ(0.975, df)

(substitute your own df = n − 1 and adjust the two probabilities to match your chosen α).

Step 3 — Combine by hand or with a Compute Variable expression:

Lower = (df * variance) / IDF.CHISQ(0.975, df)
Upper = (df * variance) / IDF.CHISQ(0.025, df)

Alternatively, the values from Explore's descriptives can simply be plugged into this calculator to get the same interval without the manual SPSS syntax.

JASP

JASP's standard Descriptives and Frequentist modules do not include a direct "confidence interval for variance" option, so the same two-step approach is used: obtain the sample variance from Descriptives, then compute the chi-square bounds.

Step 1 — Descriptives:

Descriptives → move your variable to the Variables box → enable Variance and N under Statistics.

Step 2 — Chi-square critical values:

JASP does not expose a chi-square quantile calculator in its interface, so the critical values are typically obtained from R, a chi-square table, or this page's calculator, using df = n − 1 and the same α as your desired confidence level.

Step 3 — Combine:

Apply the same formula used throughout this page:

Users who work mainly in JASP and want the chi-square step handled automatically can enter their sample variance and n directly into this calculator's manual-entry mode alongside a raw data list to get the same bounds.