Academic Achievement and Demographic Traits of Homeschool Students: A Nationwide Study

11,739 homeschooled students (grades 1-11) with matched questionnaire and standardized test scores, from 23,182 parents; response rate a minimum of 19% for the four main testing services (71.5% of the sample) and an estimated 11.0% for the remaining sources

US homeschool families who PAID a fee-for-service testing organisation (BJU Press, Family Learning Organization, Piedmont Education Services, Seton Testing Services, plus several smaller Christian/state homeschool bodies) to administer the ITBS or CAT in Spring 2008. 91.7% White/non-Hispanic; 97.9% married-couple families; 81% of mothers out of the labour force; median annual spend on materials $400-599.

Cross-sectional descriptive survey with NO comparison group of children: home-school scores are compared to the ITBS/CAT national norming sample only. The author is the founder and president of NHERI, the home-education advocacy research institute, and the study's design is the same convenience-testing-service design as Rudner 1999 with more testing services bolted on. HSLDA supplied the state-regulation ratings used in the regulation analysis AND was one of the organisations recruiting participants. Two genuine design improvements over Rudner: 69.4% of parents did not know their child's scores before completing the questionnaire (and knowing made no difference, F=.06, p=.812), and non-participants' scores at the major testing services were only 2-4 percentile points lower than participants'. Alpha was set at .01 a priori, which is the standard against which the regulation nulls below are declared non-significant.

Mean scores sat at the 84th-89th national percentile on every subtest (Reading 89th, Core 88th, Science 86th, Composite 86th, Language/Math/Social Studies 84th). The internal comparisons are the informative part and they cut hard against the standard causal story: the degree of state regulation of homeschooling had no significant relationship to scores in three separate analyses (p=.045, .041, .084 against a pre-set alpha of .01), and the pattern was NON-MONOTONIC — medium-regulation states scored highest (z=1.171) and low-regulation states scored lowest (z=1.121), with high-regulation states in between (z=1.131). Being homeschooled the entire academic life made no difference (F=.78, p=.378), contradicting Rudner's dose-response reading. Full-service packaged curriculum made no difference. Parents who had EVER been certified teachers had children who did WORSE (variance explained <0.1%). Of every variable examined, only parental education level explained a practically meaningful share of variance — and that share was 2.5%.

Maximal, and structurally unfixable in this design. The sample is defined by parents who pay for standardized testing and then volunteer their data — a selection on exactly the heritable parental traits (education, conscientiousness, income stability, valuing academics) that predict child achievement. Ray states plainly that the study "is not an experiment and readers should be careful about assigning causation to anything", then closes by inviting the causal reading anyway. Range restriction at the top of the distribution is Ray's own explanation for why nothing inside the sample predicts anything, which is another way of saying the sample is selected.

Never replicated against a comparison group, because no replication of a paid-testing-service convenience sample can produce one. Rudner 1999 is the same design with one testing service; Ray & Hoelzle 2026 is the same design a generation later and returns notably LOWER percentiles (75-79 raw), which is the closest thing to a within-programme replication and it moves toward the mean. The regulation null has never been tested by anyone using a design that could detect a regulation effect — state aggregates and self-selected testers cannot.