The document discusses sources of error in measurement including random error and systematic error. Random error affects individual scores but not the overall mean, while systematic error consistently biases scores in one direction. The document provides an example of how to calculate the confidence interval for a population mean using a sample's mean, standard deviation, sample size, and desired confidence level (e.g. 95%). Ways to reduce standard error include pilot testing instruments, thorough examiner training, and double checking data entry.

1. Estimating Standard Error of
Measurement
Dr. Carlo Magno
Counseling and Educational
Psychology Department

2. X=Observed Score
T=True Score
E=measurement error

3. SE
• What is random error?
• Random error is caused by any factors that
randomly affect measurement of the variable
across the sample.
• Person's mood can inflate or deflate their
performance
• RE only affects individual not the entire
sample, does not affect the mean of the group
• Sometime called noise

4. Random Error

5. SE
• What is Systematic Error?
• Systematic error is caused by any factors that
systematically affect measurement of the variable
across the sample.
• Ex. loud traffic going just outside of a classroom where
students are taking a test, this noise is liable to affect
all of the children's scores -- in this case, systematically
lowering them
• systematic errors tend to be consistently either
positive or negative -- because of this, systematic error
is sometimes considered to be bias in measurement.

6. Systematic Error

7. Estimating True Scores
• A confidence interval gives an estimated
range of values which is likely to include an
unknown population parameter, the
estimated range being calculated from a given
set of sample data.

8. Example
Suppose that 10 students took the OLMAT with
their scores 102.5, 101.7, 103.1, 100.9, 100.5,
and 102.2 respectively.
what is the confidence interval for the
population mean at a 95% confidence level?

9. what is the confidence interval for the population
mean at a 95% confidence level?
Translation: What is the band of score, you are
confident that the scores are not affected by
standard errors?  δ 
To estimate the Confidence interval: X ± z  
 N

10. • Mean= ∑X
N
• Standard Error
δ
SE=
N
δ=
∑x 2
N
• Z=point in a distribution that determines 95%
or 99% above the distribution.

11. Areas of the normal curve

12. 99% of the distribution = 2.57
95% of the distribution = 1.96
1.96 1.96

13. Confidence intervals for two
means
• X 1 = 15.4 σ=.95
• X 1 = 20.4 σ=.50

14. Reducing SE
• Pilot test your instruments,
– Getting feedback from your respondents regarding
how easy or hard the measure was and information
about how the testing environment affected their
performance.
• Make sure to train examiners thoroughly so that
they aren't inadvertently introducing error.
• Double-check the data thoroughly when
encoding