UConn Statistics Experts Trash the Document that Started It All, the Child Advocate’s Report Urging Homeschool Regulation in Connecticut
They say it can't be used!

Review of Children Withdrawn From School For Equivalent Instruction Elsewhere: A Statistical
Perspective
Eric Bae & Timothy E. Moore
September 28, 2025
Disclaimer
This report is intended solely for informational and internal evaluative purposes. The analyses and conclusions herein are based on available data and statistical modeling assumptions that may not account for all contextual factors. This report does not
constitute legal advice, expert testimony, or a certified audit. It is not intended to be used, cited, or relied upon in any legal proceeding, litigation, or regulatory action. The authors and affiliated institutions expressly disclaim any liability for decisions made or actions taken based on the contents of this report.
Question Responses 3
In a normal statistical analysis, what should one typically do? 3
Was the gold standard used by the OCA in her report? 4
Did she propose a hypothesis or take the necessary steps to reach her conclusions? 4
Did the OCA conduct a statistical analysis? 4
How would you describe her report? 4
What are the differences between a statistical analysis and a descriptive report? 4
What are some of the problems you see with her report? 5
Did the OCA conduct a normal analysis? 6
What did the OCA do regarding the numbers she chose and any inferences she
made from them? 6
What should be done for an appropriate statistical analysis, given the facts in the report? 6
Is there any way to check the figures for accuracy in her report to see if they are correct?7 Can one make reasonable or accurate inferences from a descriptive report versus a statistical analysis? 7
Conclusion 8
Recommendations 8
Note that text of some of the questions has been adjusted for clarity.
Statistical analysis does not adhere to a singular "normal" approach; rather, it varies according to several factors, including the research questions, the nature of the data (e.g., categorical, binary, continuous), sample size, underlying distributions, the number of variables involved, and the specific research context and hypotheses being tested.
However, statistical analyses generally include the following:
Clearly defined variables (of interest) that are used to address the research questions.
Description of the statistical methodology used.
Conclusions based on the analysis.
Hypothesis testing is one of the most common forms of statistical analyses, where an alternative hypothesis, typically of a specific effect/association, is contrasted with a null hypothesis, typically of there being no effect/association.
Null hypothesis: there is no difference in DCF report rates between children Withdrawn from school.
Alternative hypothesis: children withdrawn from school tend to have higher DCF report rates than children not withdrawn from school.
The goal of a hypothesis-testing statistical analysis would be to identify whether the data analyzed are consistent with the alternative hypothesis.
Was the gold standard used by the OCA in her report?
No. There was no statistical methodology. There is no formal descriptive analysis, nor any hypothesis testing.
Is there a hypothesis or are the necessary steps to reach the reports conclusions presented?
No, the hypothesis is unclear.
On page 2 under the brief summary of findings section in the report, it is stated that “While Connecticut has robust procedures for following up on children who are not attending school, once children are withdrawn for the purpose of enrolling in private school in Connecticut or to be homeschooled, nothing is in place to ensure those children are, in fact, receiving educational services.”
Did the OCA conduct a statistical analysis?
No. The OCA report does not contain any statistical analyses. There is no formal descriptive analysis, nor any hypothesis testing.
How would you describe her report?
It is a descriptive report aimed at providing information on rates of DCF referrals for children withdrawn from traditional schooling over different time periods. The reason we refer to this as not a formal descriptive analysis or hypothesis testing is that no contrast is made to rates of DCF referrals for children who remain in traditional schooling environments.
What are the differences between a statistical analysis and a descriptive report?
A statistical analysis has a clearly defined research question, hypotheses, and a statistical test to answer the research question. A descriptive report contains descriptive statistics (sample size, means, medians, variances, and distributions of variables). Statistical analyses usually include descriptive statistics, as performing the latter is key to determining the approach for the former. However, descriptive reports (as is the case of OCA) often do not include statistical analyses or formal hypothesis statements.
What are some of the analytical problems you see with this report?
See the response to the question “Is there a hypothesis or are the necessary steps to reach the reports conclusions presented?”
Additional analytical challenges include:
No attempt to control for the various covariates that are present and can explain the discrepancy in DCF referrals better than the homeschooling vs. traditional schooling.
The pupils who were withdrawn from traditional schools for homeschooling may have already had higher rates of abuse and neglect even before the withdrawal than those who were not withdrawn from traditional schools. This implies that there were some other factors that better explain the difference in DCF referrals between the two groups, but homeschooling itself is not what explains it (Lurking variable). The OSA’s own report seems to suggest this by stating that “[of] the children aged 7 to 11, 31% were chronically absent and 19% were children identified as students with special education needs prior to their withdrawal from public school (page 2).” It is important to factor in covariates, such as parental occupations, income, gender, ethnicity, disability status, types of schools (public, private, magnet, etc.) the pupils attend or have attended, geographic area where they live, and many more, that explain the difference in abuse rates between the two groups.
The footnote #8 of the OCA report states that “OCA randomly selected a sample of 250 children who were withdrawn for the stated purpose of attending private school and cross referenced those children with DCF records. OCA found that 10.4% had at least one accepted report, 3% had four or more accepted reports…” OCA report does not mention pupils who are attending other school types.
There may be biases in sampling or data collection. If DCF referrals are filed as a result/retaliation of students taken out of traditional schools for homeschooling, then the DCF referral is not an appropriate representation for abuse and neglect, hence does not represent the true rates of abuse and neglect in the traditional-to-homeschooling population. There is also no distinction in the types of DCF referrals, or the timing of the referrals based on when children were withdrawn. This makes even conclusions based on this data problematic, and potentially biased.
The OCA report does not conduct any statistical analyses. See responses for “Is there a hypothesis or are the necessary steps to reach the reports conclusions presented?” and “What are some of the analytical problems you see with this report?” for more information.
What did the OCA do regarding the numbers chosen and any inferences made from them?
OCA reported the sample size of the “withdrawn to homeschooling” group (unclear if 774 or 747; the latter must be a typo) and the “withdrawn to private schools” group (250), and that they were “randomly sampled.” OCA also report that 22.9% of pupils in the “withdrawn to homeschooling” group and 10.4% of pupils in the “withdrawn to private school” group had at least one accepted DCF referral; 7.9% of pupils in the “withdrawn to homeschooling” group and 4.0% of pupils in the “withdrawn to private schools” had 4 or more accepted DCF referrals; 9.6% in the “withdrawn to homeschooling” group and 4.4% in the “withdrawn to private schools” group lived in families with at least one substantiated DCF referrals; and 3.8% of pupils in the “withdrawn to homeschooling” group and 2.0% of pupils “withdrawn to private schools” had a caregiver in the DCF Central Registry. In
contrast to the “withdrawn to homeschooling” group, which were measured over the 3-year timeframe, it is unclear what the timeframe of the DCF referrals for the “withdrawn to private schools” is because it is not mentioned in the report.
The OCA also reports that “[in] 2023, DCF received 69,562 reports. Of those, 32,462 were accepted. Of the 32,462 accepted, 3,733 (11.4%) were substantiated.” However, these numbers are not useful without the total number of students in the state and linking the accepted DCF referrals to the pupils. In addition, the DCF reports for the “withdrawn to homeschooling” are obtained across a three-year timeframe (2021-2024), but the total statewide DCF reports is only for a single year 2023. This is not an apple-to-apple comparison.
Given the information provided in the report, the only inference that can be made is between “withdrawn to homeschooling” group and “withdrawn to private schools” groups. However, this does not seem to be the primary focus of the OCA report.
What should be done for an appropriate statistical analysis, given the facts in the report?
The report is missing crucial information to conduct appropriate statistical analysis. First, the report is missing and formally stated hypotheses and any description of the data used to support any conclusions. Second, and relatedly, the same set of values that are provided for the “withdrawn to homeschooling” and “withdrawn to private schools” groups should
be provided for the general population of students (those who are not homeschooled). Additional information that would be helpful includes:
Number of students across the entire state.
This could be used as a denominator to convert counts to proportions, e.g., what proportion of children in the state are homeschooled?
DCF referrals data across the same timeframe for which the homeschooling DCF referral data are presented (e.g. 2021-2024).
This would allow for a more direct comparison, e.g., X% of children who were homeschooled between 2021 and 2024 had DCF referrals vs Y% of children who are in traditional school had DCF referrals between 2021 and 2024.
Proportion of traditional school pupils with at least 1 DCF referrals in the timeframe.
Proportion of traditional school pupils with 4 or more DCF referrals in the timeframe.
Proportion of traditional school pupils living in families with at least one substantiated DCF investigation.
Proportion of traditional school pupils living in families with a caregiver on the DCF central registry.
Having data on both home-schooled and traditionally schooled children would strengthen the argument that there are different rates of DCF referrals between them. Without them, there is no comparison group.
Is there any way to check the figures for accuracy in her report to see if they are correct?
There is no access to DCF records to see if the figures in the report are correct. Therefore, it is not possible to tell whether the OCA numbers are correct.
Can one make reasonable or accurate inferences from a descriptive report versus a statistical analysis?
In some descriptive reports, some reasonable or accurate inferences can be made.
However, in the OCA report, this is not possible due to lack of information, specifically the lack of information on rates of referrals, etc. in children attending traditional schools (see above).
There is no differentiation between types of reports, e.g., physical abuse vs mental health.
There is no information on the timing of the reports, i.e., pre- vs post-withdrawal for homeschooling.
There is no discussion about the overlap of characteristics. For example, what are the frequencies of DCF accepted reports for Special Ed vs non-Special Ed students?
Ultimately, there is no statistical analysis in this report that could be used to make any inference about the impact of homeschooling on DCF referral rates and whether the rates differ between homeschooled children and traditionally schooled children.
Our overall impression after reviewing this report is that, while the report provides some details about DCF referral rates, these rates are not put into the broader context of referrals for the general school-going population. If these data exist, they should be included so that more formal hypothesis testing, and thus inference, can be conducted.
More detailed comparison of CT to other New England states (with different regulatory requirements) to see whether rates of reports are different (again with matched comparisons). This is challenging due to other differences between states (in reporting requirements, etc.)










