Estimating Standard Error of Measurement

Dr. Carlo MagnoCounseling and Educational

Psychology Department

X=Observed ScoreT=True ScoreE=measurement error

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

Random Error

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.

Systematic Error

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.

ExampleSuppose 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?

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?

To estimate the Confidence interval:

N

zX

• Mean=• Standard Error

SE=

• Z=point in a distribution that determines 95% or 99% above the distribution.

N

X

N

N

x2

Areas of the normal curve

99% of the distribution = 2.5795% of the distribution = 1.96

1.96 1.96

Confidence intervals for two means

• = 15.4 σ=.95

• = 20.4 σ=.501X

1X

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