Study of the Proportion

Under construction…

Under construction…

Scope: binary metric (Y) following a binomial distribution. For example: abandoned calls, erroneous invoices, defective parts, etc.

Here we determine the target reduction proportion required to achieve the objective of reducing the defective rate.

Enter the following data:

• πi: initial defect rate
• τred.: desired reduction rate of the defective rate

Scope: binary metric (Y) following a binomial distribution. For example: abandoned calls, erroneous invoices, defective parts, etc.

Here we determine the minimum sample size needed to detect the effect of reducing the proportion that would achieve the objective of reducing the defective rate.

Enter the following data:

• α: risk of falsely concluding that the required effect exists
• β: risk of not detecting the required effect
• Di: initial defect rate
• DC: Target Defective Rate

Scope: binary metric (Y) following a binomial distribution. For example: abandoned calls, erroneous invoices, defective parts, etc.

Here, we determine whether we can conclude that there is a decrease or increase in proportion, below or above a given threshold, based on the differences in proportions observed in two samples. We typically test the effect associated with two different operating conditions (effect of an X, effect of a solution, etc.). The test implemented here is the two-proportion test .

Enter the following data:

• n1 and n2: the sizes of each sample
• D1 and D2: the number of defective units counted in each sample
• α: risk that the actual effect lies outside the calculated confidence interval; indicate 5% for a 95% confidence interval
• Emin: the threshold of the desired effect π2 – π1

Scope: binary metric (Y) following a binomial distribution. For example: abandoned calls, erroneous invoices, defective parts, etc.

We determine here, within the framework of implementing a test of two proportions:

• The minimum sample size required to detect a decrease or increase in proportion exceeding a given threshold
• The smallest detectable effect of decreasing or increasing the proportion (resolution) using given samples
• The power to detect an effect on the proportion below or above a given threshold, using given samples

Enter the following data:

1/ For determining the sample size:

• α: risk of falsely detecting an effect
• β: risk of not detecting the effect
• π1: the reference proportion
• π2: the comparison proportion corresponding to the effect threshold to be detected E _min = π2 – π1

2/ For determining the minimum detectable effect:

• α: risk of falsely detecting an effect
• β: risk of not detecting the effect
• n1 and n2: the sizes of each sample
• π1: the reference proportion

3/ For determining the power:

• n1 and n2: the sizes of each sample
• π1: the reference proportion
• π2: the comparison proportion corresponding to the effect threshold to be detected E _min = π2 – π1

Scope: Binary quality metric (Y) following a binomial distribution. Examples: abandoned calls, incorrect invoices, defective parts, etc.

Here we determine whether a proportion differs from its hypothesized value, based on the proportion observed in a sample. The test implemented here is the test of a proportion.

Enter the following data:

• π0: value of the hypothesized occurrence rate
• n: the sample size
• D: the number of defective units counted in the sample
• α: risk that the true mean lies outside the calculated confidence interval; enter 5% for a 95% confidence interval

Scope: Binary quality metric (Y) following a binomial distribution. Examples: abandoned calls, incorrect invoices, defective parts, etc.

We determine here, within the framework of implementing a proportion test:

• The minimum sample size required to be able to detect whether the proportion is higher or lower than its hypothesized value
• The smallest detectable difference between the proportion and its hypothesized value using a given sample
• The power to detect a discrepancy between the proportion and its hypothesized value, using a given sample

Enter the following data:

1/ For determining the sample size:

• α: risk of falsely detecting a discrepancy
• β: risk of not detecting the discrepancy
• π0: the hypothesized proportion
• π: the comparison proportion such that ε _min = π – π0

2/ For determining the minimum detectable deviation:

• α: risk of falsely detecting a discrepancy
• β: risk of not detecting the discrepancy
• n: the sample size
• π0: the hypothesized proportion

3/ For determining the power:

• n: the sample size
• π0: the hypothesized proportion
• π: the comparison proportion such that ε _min = π – π0