One Sample Standard Deviation Example | JMP 13.2

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Design of Experiments Guide • Prospective Sample Size and Power • One Sample Standard Deviation • One Sample Standard Deviation Example

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One Sample Standard Deviation Example

One example from the NIST manual states a problem in terms of the variance and difference to detect. The variance for resistivity measurements on a lot of silicon wafers is claimed to be 100 ohm-cm squared. The buyer is unwilling to accept a shipment if the variance is greater than 155 ohm-cm squared for a particular lot (55 ohm-cm squared above the baseline of 100 ohm-cm squared).

In the Sample Size and Power window, the One Sample Standard Deviation computations use the standard deviation instead of the variance. The hypothesis to be tested is:

H0: σ = σ0, where σ0 is the hypothesized standard deviation. The true standard deviation is σ0 plus the difference to detect.

In this example the hypothesized standard deviation, σ0, is 10 (the square root of 100) and σ is 12.4499 (the square root of 100 + 55 = 155). The difference to detect is 12.4499 – 10 = 2.4499.

You want to detect an increase in the standard deviation of 2.4499 for a standard deviation of 10, with an alpha of 0.05 and a power of 0.99. To determine the necessary sample size:

1.

Select DOE > Design Diagnostics > Sample Size and Power.

2.

Click the One Sample Standard Deviation button in the Sample Size and Power Window.

3.

Leave Alpha as 0.05.

4.

Enter 10 for Hypothesized Standard Deviation.

5.

Select Larger for Alternate Standard Deviation.

6.

Enter 2.4499 as Difference to Detect.

7.

Enter 0.99 for Power.

8.

Leave Sample Size blank. (See the left of Window To Compare Single-Direction One-Sample Standard Deviation.)

9.

Click Continue.

The Sample Size is calculated as 171. (See the right of Window To Compare Single-Direction One-Sample Standard Deviation.) This result is the sample size rounded up to the next whole number.

Note: Sometimes you want to detect a change to a smaller standard deviation. If you select Smaller from the Alternative Standard Deviation menu, enter a negative amount in the Difference to Detect field.

Window To Compare Single-Direction One-Sample Standard Deviation

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Help created on 9/19/2017