Select the analysis options for 2 Variances (Options tab)

On the Options tab of the 2 Variances dialog box, specify the confidence level for the confidence interval or define the alternative hypothesis.

Hypothesized ratio

Enter a value in Hypothesized ratio. The Hypothesized ratio defines your null hypothesis. Think of this value as a target value or a reference value. For example, a cereal manufacturer will purchase a new filling machine only if the variance of fill weights for the new machine is 0.8 of the variance of the current machine (H0: σ2new / σ2current = 0.8).

Alternative hypothesis

From Alternative hypothesis, select the hypothesis that you want to test:
Ratio < hypothesized ratio

Use this one-sided test to determine whether the population ratio of the variances or the standard deviations of sample 1 and sample 2 is less the hypothesized ratio, and to get an upper bound. This one-sided test has greater power, it cannot detect when the population ratio is greater than the hypothesized ratio.

For example, an analyst uses this one-sided test to determine whether the ratio of the standard deviation of a new machine's performance to the standard deviation of an old machine's performance is less than 0.8. This one-sided test has greater power to detect whether the ratio in standard deviations is less than 0.8, but it cannot determine whether the ratio is greater than 0.8.

Ratio ≠ hypothesized ratio

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

For example, a healthcare consultant wants to compare the variances of patient satisfaction ratings from two hospitals. Because any difference in the variances is important, the consultant uses this two-sided test to determine whether the variance at one location is greater than or less than the other location.

Ratio > hypothesized ratio

Use this one-sided test to determine whether the population ratio of the variances or the standard deviations of sample 1 and sample 2 is greater the hypothesized ratio, and to get a lower bound. This one-sided test has greater power than a two-sided test, but it cannot determine whether the difference is less than the hypothesized ratio.

For example, an analyst tests whether the ratio of the variance in an old extrusion machine to the variance of a new machine is greater than 1. This one-sided test has greater power to detect whether the ratio is greater than 1, but it cannot determine whether the ratio is less than 1.

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

Confidence level

From Confidence level, select 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 ratio.

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, as follows:
  • 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 ratio 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 ratio.

Use test and confidence intervals based on normal distribution

Select Use test and confdience intervals based on normal distribution to display results for the test based on the normal distribution, also called the F-test. The results for the F-test are displayed if you enter summary data for the size and variance (or standard deviation) for each sample. With the F-test, results for Bonett's method or Levene's method are not displayed.

The F-test is accurate only for normally distributed data. Even small departures from normality can cause the F-test to be inaccurate, even with large samples. However, if the data conform to the normal distribution, then the F-test is typically more powerful than either Bonett's method or Levene's method.

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