TECHNOLOGY OVERVIEW

# Hypothesis testing for the standard deviation from a normal variate

Hypothesis testing for the standard deviation is strictly a hypothesis test for the variance which requires the following steps:

• Sample n items randomly
• Calculate standard deviation
• Specify a level of significance
• Specify an equality (<. > or <>)
• Specify a reference value for the standard deviation
• Determine the test statistic with the following expression
• (n-1)*standard deviation^2/reference value ^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.