CI.tscore {psychometric}

Confidence Intervals for Test Scores

Description

Computes the CI for a desired level for observed scores and estimated true scores

Usage

CI.tscore(obs, mx, s, rxx, level = 0.95)

CI.obs(obs, s, rxx, level = 0.95)

Arguments

obs

Observed test score on test x

mx

mean of test x

s

standard deviation of test x

rxx

reliability of test x

level

Significance Level for constructing the CI, default is .95

Details

CI.tscore makes use of Est.true to correct the observed score for regression to the mean and SE.Est for the correct standard error. CI.tscore also requires entry of the mean of the test scores for correcting for regression to the mean.
CI.obs is much simpler in construction as it only makes use of the observed score without any corrections. CI.obs uses SE.Meas, the SEM that appears in most test manuals and text books.

Value

Both functions return a table with 4 elements

SE.

Standard Error of the Estimate or SE of Measurement

LCL

lower confidence limit of the CIDescription of 'comp2'

T.Score

(or OBS) Estimate True Score or Observed score

UCL

upper confidence limit of the CI

Warning

Be Cautious in construction and interpretation of CIs
To obtain percent for 1 SEM
1-((1-pnorm(1))*2)
To obtain percent for 2 SEM
1-((1-pnorm(2))*2)

95 percent CI corresponds to 1.96 * SE
1 * SE corresponds to .6827
2 * SE corresponds to 0.9772499
so, for two-sided, 2 * SE corresponds to 0.9544997

Note

It is not in error to report any one of these. The misinterpretation is in taking the observed score and making inferences about the true score without (1) using the correct standard error and (2) correcting for regression toward the mean of the observed scores.

Author(s)

Thomas D. Fletcher [e-mail]

References

Dudek, F. J. (1979). The continuing misinterpretation of the standard error of measurement. Psychological Bulletin, 86, 335-337.

See Also

SE.Meas

Examples

# Examples from Dudek (1979)
# Suppose a test has mean = 500, SD = 100 rxx = .9
# If an individual scores 700 on the test
CI.tscore (700, 500, 100, .9, level=.68)
CI.obs(700, 100,.9, level=.68)