Select the analysis options for 1 Variance

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Specify the confidence level for the confidence interval or define the alternative hypothesis.

In This Topic

Confidence level
Alternative hypothesis

Confidence level

In Confidence level, enter the level of confidence for the confidence interval.

Usually, a confidence level of 95% works well. A 95% confidence level indicates that, if you take 100 random samples from the population, the confidence intervals for approximately 95 of the samples will contain the population parameter.

For a given set of data, a lower confidence level produces a narrower confidence interval, and a higher confidence level produces a wider confidence interval. The width of the interval also tends to decrease with larger sample sizes. Therefore, you may want to use a confidence level other than 95%, depending on your sample size.

If your sample size is small, a 95% confidence interval may be too wide to be useful. Using a lower confidence level, such as 90%, produces a narrower interval. However, the likelihood that the interval contains the population standard deviation or population variance decreases.
If your sample size is large, consider using a higher confidence level, such as 99%. With a large sample, a 99% confidence level may still produce a reasonably narrow interval, while also increasing the likelihood that the interval contains the population standard deviation or population variance.

Alternative hypothesis

Standard deviation or variance < hypothesized standard deviation or variance

Use this one-sided test to determine whether the population standard deviation or the population variance is less than the hypothesized standard deviation or the hypothesized variance, and to get an upper bound. This one-sided test has greater power than a two-sided test, but it cannot detect whether the population standard deviation or the population variance is greater than the hypothesized value.

For example, a logistics analyst uses this one-sided test to determine whether the standard deviation of shipping weights is less than 8.8 kg. This one-sided test has greater power to determine whether the standard deviation is less than 8.8, but it cannot detect whether the standard deviation is greater than 8.8.

Standard deviation or variance ≠ hypothesized standard deviation or variance

Use this two-sided test to determine whether the population standard deviation or the population variance differs from the hypothesized standard deviation or the hypothesized variance, and to get a two-sided confidence interval. A two-sided test can detect differences that are less than or greater than the hypothesized value, but it has less power than a one-sided test.

For example, a quality analyst tests whether the variance of fill volumes is different from the target of 2.5. Because any difference from the target is important, the analyst tests whether the difference is greater than or less than the target.

Standard deviation or variance > hypothesized standard deviation or variance

Use this one-sided test to determine whether the population standard deviation or the population variance is greater than the hypothesized standard deviation or the hypothesized variance, and to get a lower bound. This one-sided test has greater power than a two-sided test, but it cannot detect whether the population standard deviation or the population variance is less than the hypothesized standard deviation or the hypothesized variance.

For example, an analyst uses this one-sided test to determine whether the standard deviation of pipe diameters is greater than 2 mm. This one-sided test has greater power to determine whether the variance is greater than 2 mm, but it cannot determine whether the variance is less than 2 mm.

For more information on selecting a one-sided or two-sided alternative hypothesis, go to About the null and alternative hypotheses.