Achievement and Demographics of Home School Students: 1998

20,760 K-12 students in 11,930 families (drawn from 39,607 tested; the remaining 18,847 could not be disaggregated from private-school testers and were never analysed)

US home-school families who paid the Bob Jones University Press Testing and Evaluation Service to administer the ITBS/TAP in Spring 1998. ~58% of mothers identified as Independent Fundamental, Baptist or Independent Charismatic; 6% non-Christian; 98% married-couple families.

Convenience sample with NO comparison group of any kind — home-school scores are compared to the ITBS/TAP national norming sample, not to matched children. Welner & Welner estimate the sample at 1.28-2.08% of the US home-school population, selected on (a) willingness to pay a testing service, (b) willingness to use a testing service run by Bob Jones University. Funded by a grant from the Home School Legal Defense Association, whose president conceived the study; HSLDA distributed it to members of Congress. Two mitigating design choices Rudner made: parents did not know their scores before completing the questionnaire, and current rather than age-appropriate grade placement was used for percentiles.

Median composite scores fell between the 70th and 80th national percentile at every grade and skill area. The internal comparisons are the interesting part and cut against the headline: parental TEACHING CERTIFICATION made no difference (F=2.9, n.s., controlling for grade and parent education), and enrolment in a full-service packaged curriculum made no difference (F=0.24, n.s.), but parental EDUCATION produced a large gradient (F=566.4, p<.01) — children of two college graduates sat at the 83rd-98th percentile, children of non-graduates mostly at the 66th-69th. Children home-schooled their entire academic life outscored partial home-schoolers by a gap widening from 2 to 15 scale-score points by grade 10, which Rudner reads as a dose-response and which is equally consistent with families returning struggling children to school.

Maximal. The sample is defined by parental commitment, income and education — precisely the traits that are heritable and transmitted alongside alleles. Rudner states the problem himself and refuses the causal reading.

Never replicated with a comparison group, because no such replication is possible from a testing-service sample. Ray's NHERI surveys reproduce the same design and the same result, which is repetition rather than replication — the shared selection mechanism is the thing under suspicion.