TECHNOLOGY OVERVIEW

# Hypothesis testing for the difference in the ratio of two standard deviations from two normally distributed population

Hypothesis testing for the ratio of two standard deviations is based on hypothesis testing for the ratio of two variances according to the following steps.

• Randomly sample n1 items from population 1 and n2 from population 2. N1 can be equal to n2.
• Calculate standard deviations of both samples.
• Specify a level of significance
• Specify an equality (<. > or <>)
• Specify a reference value for the ratio of the two standard deviations.
• Determine the test statistic with the following expression
• Sd1^2/sd2^2
• Sd1 and Sd2 are the sample standard deviations for population 1 and population 2
• Determine the critical region for the test statistic. The critical region depends on the equality i.e. < or > or <>.
• Compare the test statistic with the Critical region and conclude significance if the test statistic falls outside the critical region.

Alternatively, a p-value can be calculated and if the p-value falls below the specified level of significance the Null Hypothesis is rejected and the Alternative Hypothesis is accepted

BIS.Net Analyst and the BIS.Net Inferences APP both use p-values for hypothesis testing as these are more flexible than imposing a predefined level of significance on users. To place perspective on the p value a P Curve is provided for the analyst.