A guideline based on large-sample normal approximation is often used to decide whether a specific sample autocorrelation is within sampling error of zero. (This is equivalent to testing if the population autocorrelation of lag k is zero). If the population autocorrelation of lag k is zero for k = 1,2 ... then, for adequately large n, r_{k} will be approximately normally distributed, with mean (μ) zero and standard deviation (σ) . Since approximately 95% of a normal population is within 2 standard deviations of the mean, a test that rejects the hypothesis that the population autocorrelation of lag k equals zero when | r_{k} | is greater than has a significance level (α) of approximately 5%.

A guideline based on large-sample normal approximation is often used to decide whether a specific sample partial autocorrelation is within sampling error of zero. (This is equivalent to testing if the population partial autocorrelation of lag k is zero). If the population autocorrelation of lag k is zero for k = 1,2 ... then, for adequately large n, r_{kk} will be approximately normally distributed, with mean (μ) zero and standard deviation (σ) . Since approximately 95% of a normal population is within 2 standard deviations of the mean, a test that rejects the hypothesis that the population autocorrelation of lag k equals zero when | r_{kk} | is greater than has a significance level (α) of approximately 5%.

A guideline based on large-sample normal approximation is often used to decide whether a specific sample cross correlation is within sampling error of zero. (This is equivalent to testing if the population cross correlation of lag k is zero). If the population autocorrelation of lag k is zero for k = 1,2 ... then, for adequately large n, r_{xy}(k) will be approximately normally distributed, with mean (μ) zero and standard deviation (σ) . Since approximately 95% of a normal population is within 2 standard deviations of the mean, a test that rejects the hypothesis that the population autocorrelation of lag k equals zero when | r_{xy}(k) | is greater than has a significance level (α) of approximately 5%.