Download Calculating Sampling Error for a percentage

3/6/2015
CalculatingSamplingError
forapercentage
sometimes called MOE (“Margin of Error”)
Estimation error
Focus:

Difference between a Parameter
and a Statistic

What is sampling error

How to calculate sampling error

Finite population
Rememberthedifferencebetween
a…
•Parameter
•Statistic
Describes a population
Describes a sample
Whatdoessamplingerrormean?
• It represents the approximate amount of variance you can expect if you ran the same poll with a different sample.
• The error caused by observing a sample rather than measuring the whole population.
Example: Do you think violence on television causes violence amongst teens?
‐ 4.9% + 4.9%
Yes
50%
50%
45.1%
No
50%
54.9%
If sampling error is less than +/‐ 4.9% (at the 95% confidence level), the actual percentage saying “yes” in the “real” population would likely be within +/‐ 4.9% of the 50%:
Between 45.1% and 54.9%
1
3/6/2015
Confidenceinterval(CI)
A range of values so defined that there is a specified probability that the value of a parameter lies within it.
‐ 4.9% + 4.9%
45.1%
50%
54.9%
WhatdoesSamplingErrornot mean?
• It does not represent any other possible errors in the survey
•
•
•
•
Measurement error (coding errors, poor questions)
Poor sampling design
Coverage error
Non‐response errors
• It only says:
If we do this survey again, exactly the same, but with a different sample drawn from the same population, 19 times out of 20 (95% of the time), the data we would get would be within +/‐ x.x% of the data we got this time.
Whatdoyouneedtocalculate
basicsamplingerror?
• Number of respondents answering the question (n)
• The results of the question (p and q)
• The confidence level you are using (e.g., 95%) so you can identify the associated z‐score (e.g., 1.96) (z)
2
3/6/2015
Z = x – x
SD
MemoryLane:Z‐score
• “The standard score used most frequently by researchers.”
• “A standard score (or standard normal deviates) that provide a common unit of measurement that indicates how far any particular score is away from its mean.”
• Most z‐score
common Confidence Area between Area in one
Level
0 and z‐score
tail (alpha/2)
z‐scores:
Most commonly
used in commercial
surveys
50%
0.2500
0.2500
80%
0.4000
0.1000
0.674
1.282
90%
0.4500
0.0500
1.645
95%
0.4750
0.0250
1.960
98%
0.4900
0.0100
2.326
99%
0.4950
0.0050
2.576
Whythesez‐scores?
Z‐scores:
1.65 = 90% confidence level
1.96 = 95% confidence level
2.58 = 99% confidence level
68%
95%
99%
Unusual
Values
‐3
Unusual
Values
Ordinary Values
‐2
‐1
0
1
2
3
Sampling Error
BasicFormula

p * q
n
* z
p = proportion or percentage (e.g., 30% said “Yes”) q = 1 – p (e.g., 70% did not say “Yes”)
n = sample size
z = z‐score for the confidence level you want
1.65 = 90% confidence level
1.96 = 95% confidence level
2.58 = 99% confidence level
3
3/6/2015
Let’sPlugItIn
n answering question: 400
Results of question: 50% (p) = Yes
50% (q) = Not yes
Confidence Level:
95% meaning z‐score of 1.96

50 * 50
* 1.96
400
+/‐ 4.9%
Why50/50issocommon
/
= 2500
50 50
* p
q
Calculatingpandq
Yes p
No q
Excellent
Good
Fair
Poor
45%
30%
13%
12%
p
65%
q
4
3/6/2015
Sampling Error
Morepractice
n answering question:
Results of question: 300
50% (p) = Yes
50% (q) = Not yes
99% (look up z‐score)
Confidence Level:
2.58
n answering question:
Results of question: 400
10% (p) = Yes
90% (q) = Not yes
90% (look up z‐score)
Confidence Level:
1.65
n answering question:
Results of question: 100
60% (p) = Yes
40% (q) = Not yes
95% (look up z‐score)
Confidence Level:
1.96
Customer Base = 200
Completed interviews = 100
Whatabouta
100 / 200 = 50%
small(finite)population?
• “Population” refers to the “real” population, not the survey population (N)
• Consider using when the sampling fraction exceeds 5% n / N > 5%
• Finite population correction (FPC) formula:
Alternatively:
CalculatingSamplingError
foraFinitePopulation
• Calculate sampling error
as usual
• Calculate FPC
• Multiply
(
)( )
*
5
3/6/2015
Sampling Error for Finite Population
Let’sPlugItIn
n answering question: 100
N of population:
200
Results of question: 50% (p) = Yes
Confidence Level: 95% meaning z‐score of 1.96
(
) ( )
50 * 50
* 1.96 * 1 ‐
100
100
200
Processing Time!
• Why is sampling error important?
• What do you need to calculate sampling error?
• What would you do if you are dealing with a small population?
(
) *(
p * q
* z
n
)
6