Sample Size Calculator in the QI Macros for Excel

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To calculate a sample size you need to know:

1. The confidence level required (90%, 95%, 99%)
2. The desired width of the confidence interval (+5%)
3. The variability of the characteristic (e.g., mean)

The QI Macros Sample Size Calculator is designed to work with both variable (measured) and attribute (counted) data.

When you click on QIMacros-Sample Size Calculator for Lean Six Sigma and Analysis Tools and select Sample Size Calculator, you should see the following:

The defaults are set to standard parameters:

• 95% confidence level
• +5% (0.05) confidence interval
• Variable data with standard deviation of (0.167). (Change this value to 0.5 for attribute data.)

Confidence Level
In sampling, you want to know how well a sample reflects the total population. The 95% confidence level means you can be 95% certain that the sample reflects the population within the confidence interval.

Step 1 - Select a confidence level
(Typically 95%)

Confidence Interval
The confidence interval represents the range of values which includes the true value of the population parameter being measured.

Step 2 - Set the confidence interval
(Typically + 5% or .05)

Attribute (Counted) Sampling
If 95 out of 100 are good and only 5 are bad, then you wouldn't need a very large sample to estimate the population. If 50 are bad and 50 are good, you'd need a much larger sample to achieve the desired confidence level. Since you don't know beforehand how many are good or bad, you have to set the attribute field to (50% or 0.5).

Step 3 - Attribute data - Set percent defects to 0.5

Variable (Measured) Data
If you know the standard deviation of your data (from past studies), then you can use the standard deviation.

If you know the specification tolerance, then you can use (maximum value - minimum value)/6 as your standard deviation. (The default is 1/6=.167).

Step 3 - Variable Data - Enter Standard Deviation
Use the Percent Defects/Standard Deviation field for either attribute or variable samples.

Step 4 - Enter the total population (if known)

Step 5 - Press Calculate
Using the default values (95%, +5%, Stdev=0.167), you would get:

Step 6 - Read the Sample Size
Use the sample size calculated for your type of data: Attribute or Variable.

In this case, we're using variable data so the sample size would be 43.

Attribute Example:
What if you were using attribute data, (e.g., counting the number of defective coins in a vat at the Denver Mint)? Change 0.167 to 0.5 (worst case).

Here you'd need 384 coins to be 95% confident that the coins fell within the 5% interval.

What if you knew there were 1000 coins in the vat (population known)?

You only need 278 to be confident.

What if you changed the confidence interval to be +10% (0.1)?

You only need 88 to be 95% confident.

Variable Example
A sample must be selected to estimate the mean length of a part in a population. Almost all production falls between 2.009 and 2.027 inches.

Estimated standard deviation = (2.027-2.009)/6 = .003

And you want to be 95% confident that the sample is within 0.001 of the true mean. Enter the data as shown below:

You need 35 samples.

The Sample Size Calculator is just one of the tools included in the QI Macros for Excel SPC Software for Excel.

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