# Sample Size Calculator in Excel (Rev 10/13)

### What's Cool About the QI Macros Sample Size Calculator?

The QI Macros * Sample Size Calculator* works with both variable (measured) and attribute (counted) data.

Just click on the QI Macros menu, then Calculators, then Sample Size Calculator. You should see the following:

To calculate a sample size you need to know:

- The confidence level required (90%, 95%, 99%)

α = 0.1,**0.05**, 0.01 (Type I Error) - The Power required (80%, 85%, 90%)

β = 0.2, 0.15,**0.1**(Type II Error) - The desired width of the confidence interval

δ - Maximum allowable error of the estimate

= 1/2 * tolerance - σ - estimated standard deviation (
**0.167**= 1/6)

The defaults are set to standard parameters, but can be changed.

**Confidence Level**

In sampling, you want to know how well a sample reflects the total population. The α = 0.05 - 95% confidence level means you can be 95% certain that the sample reflects the population within the confidence interval.

**Step 1 - Choose alpha α = 0.05 - 95% Confidence Level
**

**Step 2 - Choose beta β =
0.1 - 90% Power
**

**Confidence Interval**

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

**Step 3 - Set the confidence interval to half the tolerance or maximum allowable error of the estimate.
(e.g., + 0.05, 2, etc.)**

**Step 4 - Attribute data (pass/fail, etc.) - Set percent defects to 0.5**

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 can set the attribute field to (50% or 0.5).

**Step 5 - Variable Data - Enter Standard Deviation**

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 = 0.167).

**Step 6 - Enter the total population (if known)**

Using the default values (95%, + 0.05, Stdev = 0.167)

**Step 7- Read the Sample Size**

Use the sample size calculated for your type of data: Attribute or Variable.

**
Variable Sample Size:** If we are using variable data and just α the sample size would be 43.

Using α and β the sample size would be 118.

### Attribute Example

**Attribute Sample Size:** What if you were using attribute data, (e.g., counting the number of defective coins in a vat at the Denver Mint) but didn't know how many coins were in the vat? 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 + 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 = 0.003.

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 using α alone and 95 using α and β together.