Sample Size Calculator in Excel (Rev 10/13)
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 desired width of the confidence interval
δ - Maximum allowable error of the estimate
= 1/2 * tolerance
- σ - estimated standard deviation
- The Power required (80%, 85%, 90%)
β = 0.2, 0.15, 0.1 (Type II Error)
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 Anova and Analysis Tools and then Sample Size Calculator. You should see the following:
The defaults are set to standard parameters, but can be changed:
- α = 0.05 - 95% confidence level
- β = 0.1 - 90% Power (added October of 2013)
- + 0.05 (1/2 of desired tolerance) - Maximum allowable error of the estimate
- Attribute data with percent defects of 50%
- Variable data with standard deviation (σ) of (0.167)
The Population is also an input area as evidenced by its yellow shading.
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
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 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.
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.