How many samples do i need part 1
This presentation is the property of its rightful owner.
Sponsored Links
1 / 45

How Many Samples do I Need? Part 1 PowerPoint PPT Presentation


  • 103 Views
  • Uploaded on
  • Presentation posted in: General

DQO Training Course Day 1 Module 4. How Many Samples do I Need? Part 1. Presenter: Sebastian Tindall. 60 minutes (15 minute 1st Afternoon Break). Topics to Discuss in Module 4. How many samples based on Census Sampling Types of decision error Definitions of common statistical terms.

Download Presentation

How Many Samples do I Need? Part 1

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


How many samples do i need part 1

DQO Training Course

Day 1

Module 4

How Many Samples do I Need?Part 1

Presenter: Sebastian Tindall

60 minutes

(15 minute 1st Afternoon Break)


Topics to discuss in module 4

Topics to Discuss in Module 4

  • How many samples based on

    • Census

    • Sampling

  • Types of decision error

  • Definitions of common statistical terms


How many samples do i need

How Many Samples do I Need?

n = (total $)  ($ per sample)

Quick & Dirty Method

n = 5

Budget Method


How many samples do i need1

How Many Samples do I Need?

How will the

data be used?

It depends!

What is the decision?

What is the

tolerance for

mistakes?

What is the

underlying variation

in the material

being sampled?


How many samples do i need2

How Many Samples do I Need?

(The Real Answer)

Just Enough!


How many samples do i need3

How Many Samples do I Need?

REMEMBER:

HETEROGENEITY

IS THE RULE!


Decisions with absolute certainty

Decisions with Absolute Certainty

  • Requires knowing the “true condition” of the population in question

    • Perform a census

      • Collect and analyze every possible member of the population in question


Decisions with absolute certainty cont

Decisions with Absolute Certainty (cont.)

  • Population

    • Universe of items (elements) within the spatial boundary

      • All the possible soil samples in the Smith’s backyard

      • All the people in the U.S.A.

    • Translation: you have to count/measure (sample) EVERY single member of the population


Football field

Football Field

One-Acre

30'0"

Football Field


Number of samples in a one acre field

Number of Samples in a One-Acre Field

How many surface

soil samples can

I take from a

one-acre field?

The perimeter of a

one-acre field measures

272.25 feet by 160 feet.

If one surface soil

sample = 2.5” x 2.5” x 6”

deep, then….

...there are = 1,000,000 possible

surface soil samples in a one-acre field.


Cost of sampling entire one acre field

Cost of Sampling Entire One-Acre Field

How much would it

cost to know the

true condition of

the one-acre field?

If it costs $3000 to test

one surface soil sample,

it would cost$3,000,000,000

to test all possible population

units.


Testing all possible samples

Testing All Possible Samples

CENSUS

  • Testing all possible population units (samples) is the ONLY way to know the true condition of the site with absolute certainty

  • However, time and money considerations usually prevent us from doing this


Decisions with absolute certainty1

Decisions with Absolute Certainty

  • Perform a census

    • totally impractical

  • Therefore, we can never make a decision with absolute certainty

  • So what’s left to do?


Testing a few samples from the larger population

Testing a Few Samples(from the larger population)

ESTIMATION

  • Estimates of the true condition of the site are usually made from a few (representative) samples

    • Taking a few samples (making a few measurements) and using them to represent the site

    • Make inferences (even sweeping claims) about the population of interest based on these few samples


The process of estimation

The Process of Estimation

  • An estimate is just an educated guess based on incomplete information

  • Educated guesses will be wrong, to some degree

  • In other words, the process of estimation contains inherent errors


Estimation errors

Estimation Errors

Are unavoidable!

  • Are NOT mistakes. They do not suggest that anything was done improperly

  • Are an inherent part of the process of estimation

  • Are simply deviations from the true condition of the site

  • Introduce uncertainty into the decision-making process


Consequences of uncertainty

Consequences of Uncertainty

Estimation Errors

Decision Errors

  • Decision errors are true mistakes

  • Examples:

    • Walking away from a dirty site

    • Cleaning up a clean site

  • Decision errors can be managed


Decision errors

Decision Errors

  • Are acceptable or tolerable …within limits

  • We set tolerable limits on the percentage of time we are willing to:

    • Walk away from a dirty site

    • Clean up a clean site


Where do errors occur

Where do errors occur?

Planning

Sampling

Analysis

Data Vs

Decision


Definition of terms

Population

Everyone or everything of interest

Example: All the people in this class

Sample

Some subset of the population

Example: Five people randomly chosen from the class

Definition of Terms


Definition of terms1

Population Parameter

The true value of the population characteristic (e.g., age) that can only be known if all possible samples are measured

Example: true mean age of all the people in the class, calculated using data from every member of the population

Sample Statistic

The estimated value of the population characteristic that is calculated from sample data

Example: estimate of the true mean age of all people in the class, calculated using data from a subset (sample) of the population

Definition of Terms


Comparison

Population Parameter

Represents “true condition” of the population

Decisions can be made with 100% certainty (0% uncertainty)

Sample Statistic

Represents “estimated condition” of the population

Decision cannot be made with 100% certainty

Comparison


Class question

What is the true mean age in this class?

What is the estimated mean age in this class?

Randomly select 5 ages

2nd estimated mean age in this class?

Randomly select 15 ages

(See Computer Age Demo)

Class Question?


True mean age of all the people in this class

True Mean Age of All the People in This Class

  • In this case - where we are only interested in measuring a small group of people who are all in the same room at the same time - it is not too difficult to determine the true mean age with 100% certainty. But:

    • What if some people failed to respond?

    • What if some people “fudged” a little?

    • What if some of the response forms got lost?


Types of decision errors

Types of Decision Errors

  • Before we can talk about acceptable limits for making decision errors, we must first understand what correct decisions and decision errors look like and define some terms

  • There are two types of correct decisions and two types of decision errors that can be made


How many samples do i need part 1

Graph of Perfect Decision Making

1.0

0.5

0.0

Ideal Decision Rule

Chance of Deciding Site is Dirty

6 pCi/g

Action Level

Low True Mean 226Ra concentration High


How many samples do i need part 1

Graph of Typical Decision Making

1.0

0.5

0.0

Typical Curve

Chance of Deciding Site is Dirty

6 pCi/g

Action Level

Low True Mean 226Ra Concentration High


How many samples do i need part 1

Null Hypothesis:

The Site is dirty.

True State of Site

Site is clean

Site is dirty

The Gray Region

1.0

Probability of deciding that the site is dirty

Typical Curve

0.5

0.0

75

100

Lower Bound of Gray Region

Action Level

True mean COPC Concentration

Decision

Performance

Goal

Diagram

Walk away from site

Clean up site

Alternative Action


How many samples do i need part 1

Action Level

UCL 1A

UCL 1B

X A

75

110

100

95

Decision-Making Procedure:

Apply Decision Rule

PSQ

Is Site clean?

Is Site dirty?

DL

95 UCL% COPC Concentration

Walk away from site

Clean up site

Alternative Action


How many samples do i need part 1

Action Level

X B

UCL B

110

120

100

Decision-Making Procedure:

Apply Decision Rule

PSQ

Is Site clean?

Is Site dirty?

DL

95 UCL% COPC Concentration

Walk away from site

Clean up site

Alternative Action


How many samples do i need part 1

True Mean

Sample Mean UCL

Deviation

Decision-Making Procedure: Apply Decision Rule

PSQ

Conclusion:

Site is dirty.

Is Site clean?

Is Site dirty?

Action:

Clean up a

dirty site.

A correct

decision.

DL

100

Action Level

95 UCL% COPC Concentration

Walk away from site

Clean up site

Alternative Action


How many samples do i need part 1

True Mean

Sample Mean UCL

Deviation

Decision-Making Procedure: Apply Decision Rule

PSQ

Conclusion:

Site is clean.

Is Site clean?

Is Site dirty?

Action:

Walk away from a dirty site.

An incorrect

decision.

DL

100

Action Level

95 UCL% COPC Concentration

Walk away from site

Clean up site

Alternative Action


How many samples do i need part 1

True Mean

Sample Mean UCL

Deviation

Decision-Making Procedure: Apply Decision Rule

Conclusion:

Site is clean.

PSQ

Is Site clean?

Is Site dirty?

Action:

Walk away

from a

clean site.

A correct

decision.

DL

100

Action Level

95 UCL% COPC Concentration

Walk away from site

Clean up site

Alternative Action


How many samples do i need part 1

True Mean

Sample Mean UCL

Deviation

Decision-Making Procedure: Apply Decision Rule

PSQ

Conclusion:

Site is dirty.

Is Site clean?

Is Site dirty?

Action:

Clean up a

clean site.

An incorrect

decision.

DL

100

Action Level

95 UCL% COPC Concentration

Walk away from site

Clean up site

Alternative Action


How many samples do i need part 1

True Mean

Sample Mean UCL

Deviation

The Gray Region

Null Hypothesis:

The Site is dirty.

True State of Site

Site is clean

Site is dirty

When the True Mean is

well above the Action

Level...

1.0

Probability of deciding that the True Mean is greater that or equal to the Action Level

... then there should be high a

probability that the Sample

Mean UCL will also be above

the Action Level...

0.5

... and it is highly likely that we

will correctly decide to clean

up a dirty site.

0.0

Lower Bound of GrayRegion

75

100

Action Level

True mean COPC Concentration

Walk away from site

Clean up site

Alternative Action


How many samples do i need part 1

True Mean

Sample Mean UCL

Deviation

Null Hypothesis:

The Site is dirty.

The Gray Region

True State of Site

If the True Mean

is well below the Lower

Bound of the Gray

Region...

... then there should

be a very low

probability that the

Sample Mean UCL

will be above the

Action Level...

Site is clean

Site is dirty

1.0

Probability of deciding that the site is dirty

0.5

0.0

Lower Bound of GrayRegion

75

100

Action Level

True mean COPC Concentration

... and it is highly unlikely

that we will incorrectly

decide to clean up a clean site.

Walk away from site

Clean up site

Alternative Action


How many samples do i need part 1

True Mean

Sample Mean UCL

Deviation

Null Hypothesis:

The Site is dirty.

The Gray Region

True State of Site

... then there is an

increased probability that

the Sample Mean UCL will

be above the Action Level...

When the True Mean

is IN the gray region…..

Site is clean

Site is dirty

1.0

Probability of deciding that the site is dirty

0.5

... and that we will agree to

incorrectly decide to clean up

a clean site.

0.0

Lower Bound of GrayRegion

75

100

Action Level

True mean COPC Concentration

Walk away from site

Clean up site

Alternative Action


How many samples do i need part 1

Null Hypothesis:

The Site is dirty.

True State of Site

Site is clean

Site is dirty

1.0

Typical Curve

The Gray Region

0.5

Probability of deciding that the site is dirty

0.0

Lower Bound of Gray Region

75

100

Action Level

True mean COPC Concentration

Decision

Performance

Goal

Diagram

Walk away from site

Clean up site

Alternative Action


How many samples do i need part 1

Unnecessary Disposal and/or Cleanup Cost

Threatto Public Healthand Environment

Sampling and Analyses Cost

Sampling and Analyses Cost

$

$

$

$

Managing Uncertainty is a Balancing Act

PRP 1 Focus

Regulatory 1 Focus


Key points

Key Points

  • We will never know the true condition of the site - time and money prevent this

  • Therefore we must estimate the true condition through sampling

  • Estimates based on samples are not factual statements about the site. They are educated guesses

  • Estimates must be in error - because they use incomplete information


Key points cont

Key Points (cont.)

  • Errors are not mistakes - just deviations from the truth

  • Errors (deviations) introduce uncertainty into the decision-making process

  • Errors and uncertainty can be managed so that you can still get the job done and prove that you did it


Key points cont1

Key Points (cont.)

  • The DQO Process is designed to help you manage uncertainty and:

    • Get the job done efficiently

    • Prove that you did it defensibly


Primary benefit of the dqo process

Primary Benefit of the DQO Process:

Managing uncertainty through

systematic planning.

“FAILING TO PLAN…..

IS PLANNING TO FAIL”


How many samples do i need4

How Many Samples do I Need?

REMEMBER:

HETEROGENEITY

IS THE RULE!


Summary of parts 1 2 3 will be at the end of module 6

End of Module 4

Thank you

Summary of Parts 1, 2, 3 will be at the end of Module 6

Questions?

We will now take a 15 minute break.

Please be back in 15 minutes.


  • Login