Study of The Average

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

Here we determine the 1-α confidence interval of the mean µ from what is observed in a sample.

Enter the following data:

• α: the risk that the true value of the mean lies outside the confidence interval. For a 95% confidence interval, indicate α = 5%
• n: sample size
• Xbar: sample mean
• σ or s: true standard deviation (if known) or sample standard deviation

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 mean µ with a desired margin of error (statistical precision).

Enter the following data:

• σ or s: true standard deviation (if known) or sample standard deviation
• Margin of error: half the 1-α confidence interval of the desired mean
• α: the risk that the true value of the mean 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 mean shift, with constant standard deviation, required to achieve the objective of reducing the defective rate.

Enter the following data:

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

• Di: initial defect rate
• DC: Target Defective Rate
• σ: standard deviation of Y

Detailed calculation:

• LSI: Lower Specification Limit
• LSS: upper specification limit
• µi: initial (current) mean
• σ: standard deviation of Y
• 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 mean shift effect which would allow us to achieve, at constant standard deviation, the objective of reducing the defect 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: continuous metric (Y) following a normal distribution. For example: duration, temperature, size, etc.

Here, we determine whether a mean shift effect exists below or above a given threshold, based on the differences in means 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 two-sample t-test.

Enter the following data:

• n1 and n2: the sizes of each sample
• Xbar1 and Xbar2: the means of Y in 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 metric (Y) following a normal distribution. For example: duration, temperature, size, etc.

Here we determine whether a mean differs from its hypothesized value, based on the mean observed in a sample. The test used here is the one-sample t-test.

Enter the following data:

• µ0: value of the hypothesized mean
• n: the sample size
• Xbar: the average of Y calculated in the sample
• s or σ: the standard deviation of Y calculated in the sample or the actual standard deviation if known
• α: risk that the true mean lies outside the calculated confidence interval; enter 5% for a 95% confidence interval