npe recognizes that test reliability is defined as the degree to which the test gives consistent results each time it is given.
In other words, reliability answers the following questions:
npe uses the Kuder-Richardson 21 formula to calculate reliability coefficients:
r (reliability) = (K)(SD2)-M(K-M)⁄(SD2)(K-1)
K = the number of items in the list
SD =
the standard deviation of the scores
M = the mean of the scores
The scores of reliability are judged against a perfect score of 1.00. The closer the reliability coefficient is to 1.00, the better it is. The relationship between variables is commonly considered strong over .7. Most standardized tests usually have a reliability coefficient of .90 or above.1
| Population Size | Number of Questions (K) | Mean Score (M) | Standard Deviation (SD) | Reliability Coefficient (r) | |||
|---|---|---|---|---|---|---|---|
| Level Name | Category Name | Exam Part | |||||
| Level 1 | Bilingual | Grammar | 18.0 | 20.0 | 15.277778 | 1.994591 | 0.098199 |
| Listening | 18.0 | 11.0 | 24.333333 | 1.490712 | 1.000000 | ||
| Reading | 18.0 | 14.0 | 33.000000 | 2.054805 | 1.000000 | ||
| Vocabulary | 18.0 | 20.0 | 18.944444 | 1.268079 | 0.398121 | ||
| Total | 18.0 | 65.0 | 91.555556 | 4.462463 | 1.000000 | ||
| Classroom Experience | Grammar | 137.0 | 20.0 | 13.138686 | 3.491768 | 0.663484 | |
| Listening | 136.0 | 11.0 | 20.316176 | 4.827468 | 1.000000 | ||
| Reading | 135.0 | 14.0 | 28.237037 | 6.255318 | 1.000000 | ||
| Vocabulary | 137.0 | 20.0 | 15.452555 | 3.457713 | 0.743291 | ||
| Total | 137.0 | 65.0 | 76.583942 | 16.255102 | 1.000000 | ||
| Outside Experience | Grammar | 31.0 | 20.0 | 15.064516 | 2.793258 | 0.551087 | |
| Listening | 31.0 | 11.0 | 23.516129 | 1.811629 | 1.000000 | ||
| Reading | 31.0 | 14.0 | 30.967742 | 3.084654 | 1.000000 | ||
| Vocabulary | 31.0 | 20.0 | 17.483871 | 2.045782 | 0.499411 | ||
| Total | 31.0 | 65.0 | 87.032258 | 7.186384 | 1.000000 | ||
| Level 2 | Bilingual | Grammar | 20.0 | 20.0 | 16.300000 | 3.729611 | 0.824435 |
| Listening | 21.0 | 11.0 | 23.190476 | 2.195646 | 1.000000 | ||
| Reading | 21.0 | 14.0 | 26.428571 | 5.350313 | 1.000000 | ||
| Vocabulary | 20.0 | 20.0 | 16.700000 | 2.431049 | 0.561849 | ||
| Total | 21.0 | 65.0 | 81.047619 | 14.079625 | 1.000000 | ||
| Classroom Experience | Grammar | 104.0 | 20.0 | 13.144231 | 4.191150 | 0.782627 | |
| Listening | 102.0 | 11.0 | 19.127451 | 4.190726 | 1.000000 | ||
| Reading | 103.0 | 14.0 | 23.563107 | 6.545835 | 1.000000 | ||
| Vocabulary | 104.0 | 20.0 | 13.980769 | 3.914914 | 0.763647 | ||
| Total | 104.0 | 65.0 | 69.221154 | 16.502888 | 1.000000 | ||
| Outside Experience | Grammar | 27.0 | 20.0 | 13.851852 | 4.494472 | 0.830740 | |
| Listening | 27.0 | 11.0 | 20.777778 | 4.763545 | 1.000000 | ||
| Reading | 27.0 | 14.0 | 25.407407 | 6.870545 | 1.000000 | ||
| Vocabulary | 27.0 | 20.0 | 14.592593 | 4.348344 | 0.832987 | ||
| Total | 27.0 | 65.0 | 74.629630 | 18.589420 | 1.000000 | ||
| Level 3 | Bilingual | Grammar | 24.0 | 20.0 | 16.875000 | 1.985625 | 0.348676 |
| Listening | 25.0 | 11.0 | 23.200000 | 2.019901 | 1.000000 | ||
| Reading | 25.0 | 14.0 | 26.440000 | 4.758823 | 1.000000 | ||
| Vocabulary | 24.0 | 20.0 | 19.083333 | 1.037492 | 0.197284 | ||
| Total | 25.0 | 65.0 | 84.160000 | 11.962207 | 1.000000 | ||
| Classroom Experience | Grammar | 76.0 | 20.0 | 10.592105 | 3.391854 | 0.596756 | |
| Listening | 76.0 | 11.0 | 18.026316 | 4.400878 | 1.000000 | ||
| Reading | 76.0 | 14.0 | 20.973684 | 6.474593 | 1.000000 | ||
| Vocabulary | 76.0 | 20.0 | 13.486842 | 4.200543 | 0.790610 | ||
| Total | 76.0 | 65.0 | 63.078947 | 14.750346 | 1.000000 | ||
| Outside Experience | Grammar | 20.0 | 20.0 | 12.250000 | 3.176082 | 0.557295 | |
| Listening | 20.0 | 11.0 | 22.550000 | 1.961505 | 1.000000 | ||
| Reading | 20.0 | 14.0 | 25.550000 | 3.993432 | 1.000000 | ||
| Vocabulary | 20.0 | 20.0 | 16.550000 | 2.854383 | 0.683791 | ||
| Total | 20.0 | 65.0 | 76.900000 | 8.938121 | 1.000000 | ||
| Level 4 | Bilingual | Grammar | 17.0 | 20.0 | 15.941176 | 2.645097 | 0.565907 |
| Listening | 17.0 | 11.0 | 23.529412 | 1.499712 | 1.000000 | ||
| Reading | 17.0 | 14.0 | 27.235294 | 4.988568 | 1.000000 | ||
| Vocabulary | 17.0 | 20.0 | 16.882353 | 2.517757 | 0.615634 | ||
| Total | 17.0 | 65.0 | 83.588235 | 8.029789 | 1.000000 | ||
| Classroom Experience | Grammar | 41.0 | 20.0 | 10.414634 | 3.728438 | 0.674672 | |
| Listening | 41.0 | 11.0 | 18.585366 | 5.971377 | 1.000000 | ||
| Reading | 41.0 | 14.0 | 21.609756 | 7.091314 | 1.000000 | ||
| Vocabulary | 41.0 | 20.0 | 13.097561 | 3.434437 | 0.649239 | ||
| Total | 41.0 | 65.0 | 63.707317 | 16.601857 | 1.000000 | ||
| Outside Experience | Grammar | 9.0 | 20.0 | 12.666667 | 2.494438 | 0.266917 | |
| Listening | 9.0 | 11.0 | 22.666667 | 2.211083 | 1.000000 | ||
| Reading | 9.0 | 14.0 | 23.333333 | 5.617433 | 1.000000 | ||
| Vocabulary | 9.0 | 20.0 | 14.555556 | 1.640536 | 0.000000 | ||
| Total | 9.0 | 65.0 | 73.222222 | 8.416621 | 1.000000 | ||
| Level 5 | Bilingual | Grammar | 1.0 | 20.0 | 17.000000 | 0.000000 | NaN |
| Listening | 1.0 | 11.0 | 17.000000 | 0.000000 | NaN | ||
| Reading | 1.0 | 14.0 | 33.000000 | 0.000000 | NaN | ||
| Vocabulary | 1.0 | 20.0 | 17.000000 | 0.000000 | NaN | ||
| Total | 1.0 | 65.0 | 84.000000 | 0.000000 | NaN |
1John A. Kaufhold, Basic Statistics for Educational Research (New York: iUniverse, Inc., 2007) pp. 43-46.