Study of the Standard Deviation

Scope: continuous metric (Y) following a normal distribution. For example: duration, temperature, size, etc.

Here we determine the 1-α confidence interval of the standard deviation σ from what is observed in a sample.

Enter the following data:

• α: risk that the true value of the standard deviation lies outside the confidence interval. For a 95% confidence interval, indicate α = 5%
• s: standard deviation of the sample Y
• n: sample size

Scope: continuous metric (Y) following a normal distribution. For example: duration, temperature, size, etc.

Here we determine the minimum sample size to be taken to know the standard deviation σ with a desired margin of error (statistical precision).

Enter the following data:

• s: standard deviation of the sample Y
• Margin of error: half the 1-α confidence interval of the desired mean
• α: the risk that the true value of the standard deviation lies outside the confidence interval. It therefore determines the 1-α confidence level of the margin of error. For a 95% confidence interval, indicate α = 5%.

Scope: continuous metric (Y) following a normal distribution. For example: duration, temperature, size, etc.

Here we determine the target standard deviation reduction, with constant mean, required to achieve the target defect rate reduction.

Enter the following data:

Summary calculation (if you already know the initial defect rate):

• Di: initial defect rate
• DC: Target Defective Rate

Detailed calculation:

• LS: Specification limit on the Y (lower or upper)
• LSI: Lower specification limit of Y
• LSS: upper specification limit of Y
• µ: average
• σi: initial (current) standard deviation
• τred.(%): desired reduction rate of the defective rate

Scope: continuous metric (Y) following a normal distribution. For example: duration, temperature, size, etc.

Here we determine the minimum sample size needed to detect the standard deviation reduction effect that would allow us to achieve, with a constant mean, the objective of reducing the defective rate.

To do this:

1/ Calculate the required standard deviation reduction effect using the ‘Target effect according to project objective’ tab.
2/ Enter this effect into the sample size calculator here .

Scope: continuous (Y) metric following a normal distribution. For example: duration, temperature, size, etc.

Here, we determine whether we can conclude that there is a reduction or increase effect of the standard deviation below or above a given threshold, based on the differences in standard deviations 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 used here is the test of two variances (F-test) .

Enter the following data:

• n1 and n2: the sizes of each sample
• s1 and s2: the standard deviations of Y in each sample
• α: risk that the actual effect lies outside the calculated confidence interval; enter 5% if a 95% confidence interval is desired.
• Emin: the threshold of the desired effect

Scope: continuous (Y) metric following a normal distribution. For example: duration, temperature, size, etc.

Here, within the framework of implementing a two-variance test (F-test), we determine:
– The minimum sample size required to detect a standard deviation reduction effect below or above a given threshold
– The smallest detectable standard deviation reduction effect (resolution) using given samples

The calculations are performed for a power = 79.16% and α = 5%.

Enter the following data:

1/ For determining the sample size:
E _min to detect: minimum (useful) effect that we want to detect

2/ For determining the minimum detectable effect:
n1 and n2: the sizes of each sample

Scope: continuous metric (Y) following a normal distribution. For example: duration, temperature, size, etc.

Here we determine whether a standard deviation differs from its hypothesized value, based on the standard deviation observed in a sample. The test used here is the test of variance (F-test).

Enter the following data:

• σ0: value of the hypothesized standard deviation
• n: the sample size
• Xbar: the average of Y calculated in the sample
• s: the standard deviation of Y calculated in the sample
• α: risk that the actual standard deviation lies outside the calculated confidence interval; indicate 5% for a 95% confidence interval

Under construction…