3.2 sourced of error

1. 1
Sources of error
• Random error
– Random error plays a role in all epidemiologic studies
– We use statistics to quantify the role of chance (to be
discussed in statistical inference module)
– Random error relates to the concept of precision

2. 2
Sources of error
• Random error
– Random error based on the concept of hypothetical
study repetitions
– Even if you conduct your study perfectly, your
measure of association can still differ from the true
measure of association in the source population due
to chance
– This is because your sample is only one of
innumerable samples you could have selected by
chance

3. Sources of error
Source population with RR = 1
20%
10%
30%
60%
Repeating random samples of 30 participants…
50%
40%
3
R
R

4. Sources of error
Many of the samples
found RR much different
from truth in source
population of RR = 1
If you could repeat your study many hundreds of times with
new random samples of 30 participants these are the
measures of association you would observe
Obviously you never get to do this in real life, but this is
conceptually what random error captures
10%
20%
30%
40%
50%
60%
Source population with RR = 1
4
R
R

5. 5
Sources of error
• Systematic error or bias
– Systematic error also plays a role in all epidemiologic
studies
– Systematic error or bias is a systematic difference
between association observed and causal effect
– It is difficult to quantify the exact effect of bias on
study findings
– Therefore must try to design studies and collect data
in a manner that avoids/minimizes introducing bias
– Systematic error relates to the concept of validity

6. 6
Sources of error
• Random error
– Precision is the lack of random error
– If there is only random error, over many study
repetitions your estimates of association will center
around the truth in the source population
• Systematic error or bias
– Validity is the lack of systematic error
– If there is systematic error, over many study
repetitions your estimates of association will not
center around the truth in the source population

7. Sources of error
X
XXX
X X
X
X X XX
X
X
Precise and
valid
Not precise but
valid
Precise but
not valid
Not precise and
not valid
X XXX
Describe each figure with respect to precision and validity
X
X
Truth
7

8. Sources of error
• Since it is impossible to avoid bias entirely, we
carefully consider potential biases (and their
direction) when we present results
– Underlines importance of minimizing at the design
and data collection phases
8

9. Sources of error
• Like associations between variables, bias has a
direction and a magnitude
– Direction refers to how the bias changes the effect
estimate
• Bias toward the null (conservative bias)
• Bias away from the null exaggerates the association
– Magnitude refers to the strength of the bias – the
extent to which it distorts the association
9

10. 1
0
Sources of error
• Direction (either towards or away from null)
– Towards the null
• For relative measures, closer to 1 than true measure
• For absolute measures, closer to 0 than true measure
• Examples:
– Study RR = 2.0, true RR = 3.0
– Study RR = 0.7, true RR = 0.5
– Study RD = 0.011, true RD = 0.022
– Study RD = -0.03, true RD = -0.09

11. 1
1
Sources of error
• Direction
– Away from the null
• For relative measures farther from 1 (in either direction) than
true measure
• For absolute measures, farther from 0 (in either direction)
than true measure
• Examples:
– Study RR = 4.0, true RR = 3.0
– Study RR = 0.3, true RR = 0.5
– Study RD = 0.044, true RD = 0.022
– Study RD = -0.15, true RD = -0.09

12. Sources of error
• Magnitude
– Strong bias – major distortion of the true association
• Example: study RR = 10.0, true RR = 1.0
– Weak bias – minor distortion of the true association
• Example: study RD = 0.011, true RD = 0.012
– Extremes are obvious but middle range is subjective
1
2

13. Sources of error
• Typically epidemiologic associations will
represent a combination of causal association
and error (random and systematic)
1
3

14. 1
4
Sources of error
• Example illustrating bias/validity versus random
error/precision
– A tape measure with only hash-marks for feet (not
inches or any smaller unit) will give imprecise
measures of height
– You would be unable to measure people’s height with
more precision than feet: 5 to 6 feet, 4 to 5 feet, etc.
– The instrument would not introduce a systematic error
in any direction—just random error around the true
value

15. Sources of error
• Example illustrating bias/validity versus random
error/precision
– A tape measure that has only 11 inches to a foot will
yield biased estimates of height
20

16. 1
6
Sources of error
– Any height greater than 11 inches will be incorrect,
and the error introduced is systematic – it has a
direction and a magnitude
• For example, someone who is 5’10” will be measured
on average as 6’4” whenever you use this tape
measure, systematically