A review of how to calculate a sample size using a Sample Size Calculator.

1. Section & Lesson #:
Pre-Requisite Lessons:
Complex Tools + Clear Teaching = Powerful Results
Calculating a Sample Size
Six Sigma-Measure – Lesson 19
A review of how to calculate a sample size using a Sample Size Calculator.
Six Sigma-Measure #18 – Rational Sub-Grouping
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted by any means
(electronic, mechanical, photographic, photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.

2. Sample Size Calculator Defined
o What is a sample size calculator?
• It helps determine how much data to collect in order to be confident in your results.
• It is one of the easiest, most powerful and yet most neglected tools for basic data analysis.
o What is the purpose of a sample size calculator?
• Tells how much confidence or risk there is of accuracy in a given sample size.
• Determines the amount of data necessary to sustain a certain level of confidence and accuracy.
• Shows the amount of accuracy for a given sample size and confidence/risk level.
o Example of a sample size calculator:
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Estimated Population Size 100,000
Discrete Data Inputs Answer
Defect Rate (can't exceed 50%) 14.0%
Confidence Level (e.g. 95%) 95.0%
Precision (e.g., ± 2 units) 1.0%
Sample Size (per lowest level) 4625
Adjusted Minimum Sample Size 4625
Continuous Data Inputs Answer
Standard Deviation 5.0
Confidence Level (e.g. 95%) 95.0%
Precision (e.g., ± 2 units) 1.0
Sample Size (per lowest level) 96
Adjusted Minimum Sample Size 96
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.

3. Sample Size Calculator Components
o What are the different components of a sample size calculator?
• There are actually two sample size calculators each having four key components:
 Discrete Data – use this calculator if the key metric you’re evaluating is a discrete value.
– For example, polling which candidates are favored to win an election, measuring %’s or proportions of data, etc.
– Components are 1) Defect Rate, 2) Confidence Level, 3) Precision, and 4) Sample Size.
 Continuous Data – use this calculator if the key metric you’re evaluating is a continuous value.
– For example, polling the age of customers, measuring call handle time, measuring average billing adjustments, etc.
– Components are 1) Standard Deviation, 2) Confidence Level, 3) Precision, and 4) Sample Size.
• Each calculator shares 3 of the same components; below is a breakdown of all components:
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Estimated Population Size 100,000
Discrete Data Inputs Answer
Defect Rate (can't exceed 50%) 14.0%
Confidence Level (e.g. 95%) 95.0%
Precision (e.g., ± 2 units) 1.0%
Sample Size (per lowest level) 4625
Adjusted Minimum Sample Size 4625
Continuous Data Inputs Answer
Standard Deviation 5.0
Confidence Level (e.g. 95%) 95.0%
Precision (e.g., ± 2 units) 1.0
Sample Size (per lowest level) 96
Adjusted Minimum Sample Size 96
Two calculators depending on if you’re
measuring Discrete or Continuous dataDefect Rate: % of defects expected.
Must be <50%; if unknown,
use (1 / # of discrete values).
Confidence Level: % of
confidence desired (alpha risk)
Precision: % pt margin
of error desired
Sample Size: minimum samples
required to reflect the given
confidence level & precision
Standard Deviation: estimated
std deviation for the continuous
value being measured.
A smaller population size can
reflect an adjusted sample size
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.

4. How To Use the Calculator
o How do you use the sample size calculator?
• This particular sample size calculator allows you to enter any 3 of each calculator’s required
components and it returns the answer for the 4th missing value.
 This makes this calculator extremely effective for not only determining the necessary sample size, but to
also return the confidence level or precision for an existing sample size.
 Simply type in a value in any 3 of the 4 yellow boxes for each calculator and keep any one yellow box
empty. The answer will display at right in green for the missing, unknown value.
• NOTE: The sample size it returns is the minimum sample size for the lowest level measured.
 For example, if you want to measure the average transactional errors at each of 100 stores, then the
sample size should not reflect the total transactions collected across all stores, but for each store.
o Sample size calculator steps:
1. Determine what data element to measure
and it’s data type (discrete vs. continuous).
2. Identify the estimated population size.
3. Based on the data type…
– Discrete Data – What is the defect rate? E.g., if the
metric is 85%, then 1 – 85% is 15% as the defect rate.
Or, if polling for 3 candidates, then 1 / 3 = 33%.
– Continuous Data – What is the metric’s standard
deviation? You may need to guess at first or pull a
small sample to calculate a baseline.
4. How confident do you want to be in your
sampled results? This is your alpha risk.
5. How precise do you want to be in your
sampled results? This is your margin of error.
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Estimated Population Size 100,000
Discrete Data Inputs Answer
Defect Rate (can't exceed 50%) 14.0%
Confidence Level (e.g. 95%) 95.0%
Precision (e.g., ± 2 units) 1.0%
Sample Size (per lowest level) 4625
Adjusted Minimum Sample Size 4625
Continuous Data Inputs Answer
Standard Deviation 5.0
Confidence Level (e.g. 95%) 95.0%
Precision (e.g., ± 2 units) 1.0
Sample Size (per lowest level) 96
Adjusted Minimum Sample Size 96
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Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.

5. Examples Using a Sample Size Calculator
o Example 1: Polling for a local election in a city with 40,000 people
• Scenario 1: If 2 candidates are running for local office, how many people should be surveyed of
who they’ll vote for in order to be 95% confident with +/- 3% margin (precision)?
 After 300 surveys you find candidate A has 75% of votes; how does this change the total # to survey?
 What if there were 3 candidates running for office; how does this change the total # to survey?
 What if the city only had 12,000 people and you want 1% precision; how does this change the sample size?
• Scenario 2: If 4 candidates are running for local office, how many people should be surveyed to
find the age of the average voter and be 95% confident with +/- 1 year?
 After 300 surveys you find the average so far is 42 with standard deviation of 12; what does that mean and
how does this change the total # to survey?
 What if you could only survey 400 people; how does this affect your confidence level and precision?
o Example 2: Call duration measurement at a Call Center
• Scenario: How many samples are needed to measure each employee’s call duration per month
with 95% confidence and within 10 seconds of duration?
 What if we only have 300 samples per employee; how does that affect our confidence or precision?
o Example 3: Compare efficiency between two systems
• Scenario: 90 similar transactions were each run through two different systems. System Alpha’s
time was 45 seconds and System Beta’s time was 27 seconds (each had std dev of 1/3). Is System
Beta statistically faster?
 What is the best/worst case difference in efficiency for System Beta?
 What if we only had 24 samples and System Alpha was at 180 seconds and System Beta at 160 seconds?
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Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.

6. Practical Application
o Identify at least 2 metrics used by your organization that are based on sampled data.
• What is the ideal sample size for each metric to have 95% confidence (use the existing metric to
determine the ideal precision typically used and the defect rate or standard deviation)?
 How does this compare to the actual sample size used for that metric?
– If the organization does not meet the ideal sample size, then what affect does that have on the confidence level and/or
precision for each metric?
• Determine how the organization typically applies rational sub-grouping for the metric.
 How many levels exist for each type of sub-group?
 Does the organization have at least the ideal sample size calculated above for each sub-group level?
– If not, then what affect does this have on the confidence level and/or precision?
Copyright © 2011-2019 by Matthew J. Hansen. All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted by any means (electronic, mechanical, photographic,
photocopying, recording or otherwise) without prior permission in writing by the author and/or publisher.
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