How does a person compare to a reference group?
On this page, you can compare a test person to a sample mean. Upon displaying confidence intervals, you can investigate if confidence intervals of one person overlaps with the sample mean or with the average range. The sample mean can be set irrespective if the person is part of that sample (e. g. compare a women to a men-only sample mean).
You have to select one person in “Settings and information” to display person-level data.
Confidence interval of the sample mean
The confidence interval of the sample mean is calculated as
where
-
x is the sample mean
-
z is the critical value corresponding to the selected confidence level
-
σ is the standard deviation
-
n is the sample size
If n < 3, the confidence interval is not displayed.
The user chooses z from the available confidence levels:
|
Confidence level |
z |
α |
|---|---|---|
|
68% |
1.000 |
0.32 |
|
80% |
1.282 |
0.20 |
|
90% |
1.645 |
0.10 |
|
95% (default) |
1.960 |
0.05 |
|
99% |
2.576 |
0.01 |
The bounds of the norm-referenced score confidence intervals are restricted depending on the score type, for percentile ranks 0 ≤ CI ≤ 100, and for T scores, IQ scores, and Z scores −3σ ≤ CI ≤ +3σ with
|
Score scale |
Mean (μ) |
Standard deviation (σ) |
|---|---|---|
|
Z score |
100 |
10 |
|
T score |
50 |
10 |
|
IQ score |
100 |
15 |