CI.tscore {psychometric} | R Documentation |
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 t.d.fletcher05@gmail.com
References
Dudek, F. J. (1979). The continuing misinterpretation of the standard error of measurement. Psychological Bulletin, 86, 335-337.
See Also
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)