TECHNOLOGY OVERVIEW

# Hypothesis testing for the difference of two binomial probabilities and ppms

The following applies to difference in proportions. The same principle is applied to ppms where n1 and n2 are each equal to one million and R1 and R2 are the parts per million.

One option is to calculate a confidence interval using sample information. If the confidence interval covers the reference value, then the null hypothesis is accepted. If it does not include the reference value, the null hypothesis is rejected.

Alternatively, randomly sample n1 items from population 1 and n2 items from population 2, then:

• Count the number of occurrences (successes) of the variable in question in both samples e.g. number of red marbles, number of defectives, number of voters voting for your party.
• Specify a level of significance
• Specify an equality (<. > or <>)
• Specify a reference value for the difference in the two proportions to test against.
• Determine the test statistic with the following expression
• (((R1 / N1 - R2 / N2) – Reference Value) / Sqrt(p * q * (1 / N1 + 1 / N2)))
• Where p= (R1+R2)/(N1+N2)
• Q=1-p
• R1 is successes in the first sample of sample size n1 and R2 is the number of successes in the second sample of sample size n2
• 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

The online BIS.Net Analyst.com service uses the above mainstream technology.

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