The question of how homeschooled students fare academically has been raised countless times over the past three-and-a-half decades. Numerous volunteer-based studies have compared homeschooled students’ percentile scores on standardized tests with the national average and other studies have approached the issue from other angles, but few researchers have asked a different question: Does homeschool performance vary from discipline to discipline? Do homeschooled students tend to score better in some academic subjects than others?

Frost and Morris (1988) found in a study of 74 Illinois homeschoolers that, controlling for family background variables, homeschoolers scored above average in all subjects but math. Wartes, similarly, found that homeschoolers in Washington state scored well above average in reading and vocabulary but slightly below average in math computation (Ray & Wartes, 1991). The HSLDA-sponsored studies also found that homeschoolers do comparatively less well in math than in language-based subjects (Ray, 1997a; Rudner, 1999). Likewise Belfield (2005), in a well-designed study that controlled for family background variables, found that homeschooled seniors taking the SAT scored slightly better than predicted on the SAT verbal and slightly worse on the SAT math. A similar study of ACT mathematics scores likewise found a slight mathematical disadvantage for homeschoolers (Quaqish, 2007). Given this persistent corroboration across two decades we might conclude, tentatively, that there may be at least a modest homeschooling effect on academic achievement—namely that it tends to improve students’ verbal and weaken their math capacities.

The existence of a homeschool math gap is not surprising. It is easier for the average parent to teach children to read and let them loose on the library than it is for them to teach a sequential and increasingly challenging math curriculum. Few parents are qualified to teach higher-level math, and tutors or community college classes can be expensive. In many cases, homeschooled teens are expected to teach themselves algebra or calculus out of a textbook without the aid of any kind of teacher or adult help—something most children likely cannot do successfully.

Homeschooled children were more intrinsically motivated in reading and less intrinsically motivated in math than children attending a conventional school using grades to evaluate students’ performance.

In other words, Medlin and Blackmer found that the homeschooled children they surveyed had less intrinsic motivation to learn math than other children. This is likely related to the relative difficulty homeschool parents have teaching math as compared to other subjects.

Testing data from Arkansas and Alaska, the only states to collect and release homeschool testing data, and studies of homeschool graduates enrolled in various colleges provide further verification of the homeschool math gap. In this article, we will survey the Arkansas and Alaska data, look briefly at the SAT and ACT, and then turn to how this math gap affects homeschool alumni’s college attendance and choice of major.

Arkansas, Alaska, and the Math Gap

All homeschooled students in Arkansas are tested annually, and the scores are released to the public in annual reports. In addition to providing the average homeschool scores by grade, these annual reports break down the scores by subject and compare homeschool scores to public school scores. The chart below includes homeschool percentile scores in reading and in math, listed by grade for the years 1997 to 2004. The reading scores are in blue and the math scores are in red. We find that homeschooled students regularly score ten or more percentile points better in reading than in math. This is an especially interesting finding when we consider that Arkansas public schooled students tend to score better in math than in reading (you can see this by reading the public school comparisons made in the state’s annual homeschool reports).

Alaska is another state with publicly available data. The majority of Alaska’s homeschooled students are enrolled in the state’s popular correspondence programs, which offer money for educational expenses and allow parents to homeschool just as they normally would, requiring only quarterly progress reports and annual testing. Each correspondence school releases its data to the public. In the chart below, the correspondence schools’ scores are averaged and compared to the public school average. As the graph above shows, 6% more of the homeschooled students in Alaska’s correspondence programs are proficient in reading than their public school counterparts, but 6% fewer of the homeschoolers are proficient in math. This gap persists for every demographic.

We know that homeschooled students have a harder time with math than with reading, but how do their scores compare to public school students? Are homeschoolers scoring around the same as their public school peers in math and higher in reading? Or, are they scoring lower in math and about the same or above in reading? Do we have data to address this question?

How homeschooled students’ scores compare to their public school peers is a question in demand of more research. Homeschooled students participating in studies conducted by homeschool advocacy groups, such as Rudner (1999) and Ray (2010), have tended to score thirty or forty percentage points above average, but these studies use volunteer samples and do not correct for background samples and are thus not generalizable. Further, this research has been increasingly called into question in light of new findings by other researchers. In a study published in 2011, Sandra Martin-Chang, Odette N. Gould, and Reanne E. Meuse compared a volunteer sample of 37 homeschooled children to 37 demographically matched traditionally schooled children and found that homeschooled students in structured learning environments scored slightly higher on standardized tests, those in less structured learning environments scored slightly lower. That same year, the Cardus Education Survey, which used a random sample and corrected for background factors, found that its homeschooled respondents were behind other students academically. Finally, in early 2014 a study conducted by Sharon Green-Hennessy found that homeschoolers were two or three times more likely to report being behind grade level than their traditionally schooled peers.

But how do homeschooled students’ scores compare in math and reading specifically? Does the Alaska and Arkansas data touch on this question? In Arkansas, preliminary data suggests that homeschooled students’ scores are roughly equivalent to public schoolers’ scores in math and higher in reading. However, this data is not corrected for background factors. In Alaska, preliminary data suggests that homeschooled students scores are lower than public schooled students’ scores in math and higher in reading. However, when we correct for background factors we find that some demographics’ reading scores are also below those of their public school peers. While more research needs to be done to make a determination, this data seems to suggest that homeschooled students score worse in math than their traditionally schooled peers.

But when we talk about the homeschool math gap, for the purpose of this post, we are not interested in how homeschooled students’ math scores compare to those of public school students. We are primarily interested in how homeschooled students’ math scores compare to their own reading scores—or, namely, that there is a gap between the two.

The SAT/ACT and the Math Gap

Homeschool advocates frequently point out that homeschoolers have higher SAT and ACT scores than other students in both the verbal and math sections. These claims ignore background factors—and also the oddly low numbers of homeschoolers taking the SAT and ACT. They also miss the discrepancy between verbal and math. You can see this illustrated below: In other words, homeschooled students’ SAT scores suggest a higher discrepancy between verbal and math ability than is seen among students who attend public or private schools. In fact, while homeschooled SAT-takers’ scores are higher on the verbal section than the math section, the opposite is true for public school students.

What happens to homeschooled SAT-takers’ scores when we correct for background factors—things like parental education, gender, ethnicity, and county-level poverty rate, etc.? Belfield analyzed the 2001 SAT data by dividing students based on educational method and factoring in background factors. He used these factors to predict how students in each demographic, with their background factors, should score on each section. He found that while homeschooled students scored better than predicted on the verbal section, they actually scored slightly worse than predicted on the math section. The predicted math score is higher for homeschooled students than for public schooled students because homeschool SAT-takers have background factors that typically correlate with higher SAT scores. In other words, homeschool SAT-takers’ parents were more highly educated than public school SAT-takers’ parents, so we would expect homeschoolers’ math scores to be higher than public schoolers’ math scores (based not on educational method but simply on parental education). While homeschool SAT-takers only slightly underscored their predicted math score, that they underscored it at all suggests that homeschooling does not enhance homeschool SAT-takers’ math ability.

Because taking the SAT or ACT is voluntary for homeschooled students, those homeschooled students who do take these exams are likely to be those most prepared—those who are college-bound. The same is less true for public school students, because some states and some school districts require students to take the SAT or ACT, either as another assessment or to encourage college attendance. This difference may serve to elevate homeschooled students’ scores relative to public school students.

The number of students taking the SAT or ACT can also inform us about homeschooled students’ college attendance—something that can’t help but be affected by their math ability. The College Board maintains its own school code for homeschooled students, as does the ACT. A few states allow students to be homeschooled through enrollment in private “umbrella schools,” but while some of these schools may have their own SAT and ACT codes others simply have students use the existing homeschool code. By looking at the number of students using the homeschool code when taking the SAT and ACT, then, we gain a rough idea of how many homeschooled students take these college entrance exams—and thus how many homeschooled students are college-bound.

If we assume that no homeschooled student takes the SAT or ACT more than once and that no homeschooled students take both tests, we find that at most 20% of homeschooled students take one of these exams. If some of these students take one of these exams twice, or take both of them, that percentage goes down. Nationally, 40% of high school graduates enroll in four-year colleges (another 20% enroll in two-year colleges). Virtually all four-year colleges require SAT or ACT scores. The rate at which homeschooled students take the SAT and ACT suggests that homeschooled students are underrepresented at four-year colleges. It is likely that, for at least some students, a deficiency in mathematics plays a role in the decision not to attend college.

Major Choice and the Math Gap

Studies conducted to date have tended to find that homeschool alumni have higher college GPAs than other students. This is likely at least in part a result of homeschooled students’ lower college attendance rates—the ones who do attend college are likely the most prepared, the best of the best. However, most of studies of homeschool alumni’s college performance fail break down students’ GPAs by subject area or to report on students’ choices of major. Only two studies, conducted at Austin College in Texas and Grove City College in Pennsylvania, have touched on these subjects. These studies offer an opportunity to examine possible long-term effects of the homeschool math gap.

Austin College is a four-year liberal arts college in Texas with a larger-than-average homeschool population (5% of incoming freshmen were homeschooled in 2008). In 2010, the school’s Institutional Research department carried out a study of homeschool graduates attending the school. The study found that homeschool graduates took fewer total math and science courses (0.8 and 1.9) than their traditionally schooled counterparts (1.9 and 3.2), and that while they achieved a slightly higher average GPA overall they had lower GPAs in math and science courses (2.58 and 2.62) than their conventionally schooled peers (2.72 and 2.65). Unfortunately, while the Austin College study does state the majors chosen by homeschool alumni attending Austin College (45.7% majored in social sciences, 43.5% in humanities, 7.6% in sciences, and 3.3% in interdisciplinary studies), it does not offer a similar breakdown for traditionally schooled students. However, the fact that homeschool graduates at Austin College took fewer math and science courses than traditionally schooled students clearly indicates that they were less likely to major in these fields than were other students.

To our knowledge, only one study of homeschool alumni at a college or university has ever looked specifically at homeschool alumni’s choice of college major in comparison with the major choices of other students. This study was conducted at Grove City College, a four-year Christian college in Pennsylvania. The study, which found that homeschool students were much less likely to major in math and science than other students, was published in Sociological Viewpoints in 2010. The Grove City College study found that homeschool graduates majored in the natural sciences (7.7%) and math/engineering (5.1%) at far lower rates than either public school graduates (17.8% and 15.6%) or private school graduates (17.0% and 14.3%).

There is little extant research on homeschooled students’ college major choice beyond what we can glean from these two studies. This is unfortunate, because each study looks only at one college and it is therefore possible that they are outliers and that homeschoolers at other colleges make different major choices. A recent informal study of young adults who were “unschooled,” a form of homeschooling that focuses on experiential learning in place of formal textbooks and curricula, found that an especially large portion of the participants went into the creative arts.The question of homeschool alumni’s major and career choice demands further research.

Further research on students’ GPAs by subject area is also needed. Do homeschool graduates who attend college have lower GPAs in math and science than in other subjects, or is the difference found in the Austin College study simply a result of major choice? A study of York Technical College, a community college in South Carolina, found that homeschoolers had a slightly higher math GPA than other students. However, in the qualitative component of the York Technical College study, homeschooled students verbally reported feeling unprepared for college math courses. It may be that homeschooled students can perform as well as other students in college math and science courses (perhaps because their prior math deficit was related to access rather than ability), but that a limited math education prior to high school graduation influences their career interests and thus their choice of college major.

Conclusion

There is a preponderance of evidence pointing to a homeschool math gap. There is also preliminary data pointing to some of the ways this math gap may affect homeschooled students as they graduate and begin their adult lives. In an era when STEM fields have taken on increasing importance, the homeschool math gap should be taken seriously by both homeschool parents and policymakers.

It should be noted that individual homeschooled students may excel at math. The existence of a math gap does not mean every homeschooled student has deficiencies in math. What it means is that homeschooled students on average have substantial lower math scores as compared to reading scores, a discrepancy that may follow many out of childhood into their adult lives.

The Coalition for Responsible Home Education empowers homeschooled children by educating the public and advocating for child-centered, evidence-based policy and practices for families and professionals.

Last Updated: 19 May, 2020 by Rachel Coleman

## The Homeschool Math Gap: The Data

The question of how homeschooled students fare academically has been raised countless times over the past three-and-a-half decades. Numerous volunteer-based studies have compared homeschooled students’ percentile scores on standardized tests with the national average and other studies have approached the issue from other angles, but few researchers have asked a different question: Does homeschool performance vary from discipline to discipline? Do homeschooled students tend to score better in some academic subjects than others?

In 2013, researchers Robert Kunzman and Milton Gaither reviewed the extant research on homeschooling and found evidence of a “math gap.”

Frost and Morris (1988) found in a study of 74 Illinois homeschoolers that, controlling for family background variables, homeschoolers scored above average in all subjects but math. Wartes, similarly, found that homeschoolers in Washington state scored well above average in reading and vocabulary but slightly below average in math computation (Ray & Wartes, 1991). The HSLDA-sponsored studies also found that homeschoolers do comparatively less well in math than in language-based subjects (Ray, 1997a; Rudner, 1999). Likewise Belfield (2005), in a well-designed study that controlled for family background variables, found that homeschooled seniors taking the SAT scored slightly better than predicted on the SAT verbal and slightly worse on the SAT math. A similar study of ACT mathematics scores likewise found a slight mathematical disadvantage for homeschoolers (Quaqish, 2007).

Given this persistent corroboration across two decades we might conclude, tentatively, that there may be at least a modest homeschooling effect on academic achievement—namely that it tends to improve students’ verbal and weaken their math capacities.The existence of a homeschool math gap is not surprising. It is easier for the average parent to teach children to read and let them loose on the library than it is for them to teach a sequential and increasingly challenging math curriculum. Few parents are qualified to teach higher-level math, and tutors or community college classes can be expensive. In many cases, homeschooled teens are expected to teach themselves algebra or calculus out of a textbook without the aid of any kind of teacher or adult help—something most children likely cannot do successfully.

Indeed, researchers Richard Medlin and Robin Blackmer found in a study conducted in 2000 that:

Homeschooled children were more intrinsically motivated in reading and less intrinsically motivated in math than children attending a conventional school using grades to evaluate students’ performance.

In other words, Medlin and Blackmer found that the homeschooled children they surveyed had less intrinsic motivation to learn math than other children. This is likely related to the relative difficulty homeschool parents have teaching math as compared to other subjects.

Testing data from Arkansas and Alaska, the only states to collect and release homeschool testing data, and studies of homeschool graduates enrolled in various colleges provide further verification of the homeschool math gap. In this article, we will survey the Arkansas and Alaska data, look briefly at the SAT and ACT, and then turn to how this math gap affects homeschool alumni’s college attendance and choice of major.

## Arkansas, Alaska, and the Math Gap

All homeschooled students in Arkansas are tested annually, and the scores are released to the public in annual reports. In addition to providing the average homeschool scores by grade, these annual reports break down the scores by subject and compare homeschool scores to public school scores. The chart below includes homeschool percentile scores in reading and in math, listed by grade for the years 1997 to 2004. The reading scores are in blue and the math scores are in red. We find that homeschooled students regularly score ten or more percentile points better in reading than in math. This is an especially interesting finding when we consider that Arkansas public schooled students tend to score better in

maththan inreading(you can see this by reading the public school comparisons made in the state’s annual homeschool reports).Alaska is another state with publicly available data. The majority of Alaska’s homeschooled students are enrolled in the state’s popular correspondence programs, which offer money for educational expenses and allow parents to homeschool just as they normally would, requiring only quarterly progress reports and annual testing. Each correspondence school releases its data to the public. In the chart below, the correspondence schools’ scores are averaged and compared to the public school average. As the graph above shows, 6%

moreof the homeschooled students in Alaska’s correspondence programs are proficient in reading than their public school counterparts, but 6%fewerof the homeschoolers are proficient in math. This gap persists for every demographic.We know that homeschooled students have a harder time with math than with reading, but how do their scores compare to public school students? Are homeschoolers scoring around the same as their public school peers in math and higher in reading? Or, are they scoring lower in math and about the same or above in reading? Do we have data to address this question?

How homeschooled students’ scores compare to their public school peers is a question in demand of more research. Homeschooled students participating in studies conducted by homeschool advocacy groups, such as Rudner (1999) and Ray (2010), have tended to score thirty or forty percentage points above average, but these studies use volunteer samples and do not correct for background samples and are thus not generalizable. Further, this research has been increasingly called into question in light of new findings by other researchers. In a study published in 2011, Sandra Martin-Chang, Odette N. Gould, and Reanne E. Meuse compared a volunteer sample of 37 homeschooled children to 37 demographically matched traditionally schooled children and found that homeschooled students in structured learning environments scored slightly higher on standardized tests, those in less structured learning environments scored slightly

lower. That same year, the Cardus Education Survey, which used a random sample and corrected for background factors, found that its homeschooled respondents were behind other students academically. Finally, in early 2014 a study conducted by Sharon Green-Hennessy found that homeschoolers were two or three times more likely to report being behind grade level than their traditionally schooled peers.But how do homeschooled students’ scores compare in math and reading specifically? Does the Alaska and Arkansas data touch on this question? In Arkansas, preliminary data suggests that homeschooled students’ scores are roughly

equivalentto public schoolers’ scores in math and higher in reading. However, this data is not corrected for background factors. In Alaska, preliminary data suggests that homeschooled students scores arelower thanpublic schooled students’ scores in math and higher in reading. However, when we correct for background factors we find that some demographics’ reading scores arealsobelow those of their public school peers. While more research needs to be done to make a determination, this data seems to suggest that homeschooled students score worse in math than their traditionally schooled peers.But when we talk about the homeschool math gap, for the purpose of this post, we are not interested in how homeschooled students’ math scores compare to those of public school students. We are primarily interested in how homeschooled students’ math scores compare

to their own reading scores—or, namely, that there is a gap between the two.## The SAT/ACT and the Math Gap

Homeschool advocates frequently point out that homeschoolers have higher SAT and ACT scores than other students in both the verbal and math sections. These claims ignore background factors—and also the oddly low numbers of homeschoolers taking the SAT and ACT. They also miss the discrepancy between verbal and math. You can see this illustrated below: In other words, homeschooled students’ SAT scores suggest a higher discrepancy between verbal and math ability than is seen among students who attend public or private schools. In fact, while homeschooled SAT-takers’ scores are higher on the verbal section than the math section,

the oppositeis true for public school students.What happens to homeschooled SAT-takers’ scores when we correct for background factors—things like parental education, gender, ethnicity, and county-level poverty rate, etc.? Belfield analyzed the 2001 SAT data by dividing students based on educational method and factoring in background factors. He used these factors to predict how students in each demographic, with their background factors, should score on each section. He found that while homeschooled students scored better than predicted on the verbal section, they actually scored slightly

worsethan predicted on the math section. The predicted math score is higher for homeschooled students than for public schooled students because homeschool SAT-takers have background factors that typically correlate with higher SAT scores. In other words, homeschool SAT-takers’ parents were more highly educated than public school SAT-takers’ parents, so we would expect homeschoolers’ math scores to be higher than public schoolers’ math scores (based not on educational method but simply on parental education). While homeschool SAT-takers only slightly underscored their predicted math score, that they underscored it at all suggests that homeschooling does not enhance homeschool SAT-takers’ math ability.All this said, comparatively few homeschoolers take the SAT or ACT. While 2% of all students were homeschooled in 2001, only 0.5% of students who took the SAT were homeschooled. The same is true of the ACT. In 2011, when 3.4% of all students were homeschooled, only 0.8% of those taking the ACT were homeschooled. This is relevant to the homeschool math gap in several ways.

Because taking the SAT or ACT is voluntary for homeschooled students, those homeschooled students who do take these exams are likely to be those most prepared—those who are college-bound. The same is less true for public school students, because some states and some school districts require students to take the SAT or ACT, either as another assessment or to encourage college attendance. This difference may serve to elevate homeschooled students’ scores relative to public school students.

The number of students taking the SAT or ACT can also inform us about homeschooled students’ college attendance—something that can’t help but be affected by their math ability. The College Board maintains its own school code for homeschooled students, as does the ACT. A few states allow students to be homeschooled through enrollment in private “umbrella schools,” but while some of these schools may have their own SAT and ACT codes others simply have students use the existing homeschool code. By looking at the number of students using the homeschool code when taking the SAT and ACT, then, we gain a rough idea of how many homeschooled students take these college entrance exams—and thus how many homeschooled students are college-bound.

If we assume that no homeschooled student takes the SAT or ACT more than once and that no homeschooled students take both tests, we find that at most 20% of homeschooled students take one of these exams. If some of these students take one of these exams twice, or take both of them, that percentage goes down. Nationally, 40% of high school graduates enroll in four-year colleges (another 20% enroll in two-year colleges). Virtually all four-year colleges require SAT or ACT scores. The rate at which homeschooled students take the SAT and ACT suggests that homeschooled students are underrepresented at four-year colleges. It is likely that, for at least some students, a deficiency in mathematics plays a role in the decision not to attend college.

## Major Choice and the Math Gap

Studies conducted to date have tended to find that homeschool alumni have higher college GPAs than other students. This is likely at least in part a result of homeschooled students’ lower college attendance rates—the ones who do attend college are likely the most prepared, the best of the best. However, most of studies of homeschool alumni’s college performance fail break down students’ GPAs by subject area or to report on students’ choices of major. Only two studies, conducted at Austin College in Texas and Grove City College in Pennsylvania, have touched on these subjects. These studies offer an opportunity to examine possible long-term effects of the homeschool math gap.

Austin College is a four-year liberal arts college in Texas with a larger-than-average homeschool population (5% of incoming freshmen were homeschooled in 2008). In 2010, the school’s Institutional Research department carried out a study of homeschool graduates attending the school. The study found that homeschool graduates took fewer total math and science courses (0.8 and 1.9) than their traditionally schooled counterparts (1.9 and 3.2), and that while they achieved a slightly higher average GPA overall they had lower GPAs in math and science courses (2.58 and 2.62) than their conventionally schooled peers (2.72 and 2.65). Unfortunately, while the Austin College study does state the majors chosen by homeschool alumni attending Austin College (45.7% majored in social sciences, 43.5% in humanities, 7.6% in sciences, and 3.3% in interdisciplinary studies), it does not offer a similar breakdown for traditionally schooled students. However, the fact that homeschool graduates at Austin College took fewer math and science courses than traditionally schooled students clearly indicates that they were less likely to major in these fields than were other students.

To our knowledge, only one study of homeschool alumni at a college or university has ever looked specifically at homeschool alumni’s choice of college major in comparison with the major choices of other students. This study was conducted at Grove City College, a four-year Christian college in Pennsylvania. The study, which found that homeschool students were much less likely to major in math and science than other students, was published in Sociological Viewpoints in 2010. The Grove City College study found that homeschool graduates majored in the natural sciences (7.7%) and math/engineering (5.1%) at far lower rates than either public school graduates (17.8% and 15.6%) or private school graduates (17.0% and 14.3%).

There is little extant research on homeschooled students’ college major choice beyond what we can glean from these two studies. This is unfortunate, because each study looks only at one college and it is therefore possible that they are outliers and that homeschoolers at other colleges make different major choices. A recent informal study of young adults who were “unschooled,” a form of homeschooling that focuses on experiential learning in place of formal textbooks and curricula, found that an especially large portion of the participants went into the creative arts.The question of homeschool alumni’s major and career choice demands further research.

Further research on students’ GPAs by subject area is also needed. Do homeschool graduates who attend college have lower GPAs in math and science than in other subjects, or is the difference found in the Austin College study simply a result of major choice? A study of York Technical College, a community college in South Carolina, found that homeschoolers had a slightly higher math GPA than other students. However, in the qualitative component of the York Technical College study, homeschooled students verbally reported feeling unprepared for college math courses. It may be that homeschooled students can perform as well as other students in college math and science courses (perhaps because their prior math deficit was related to access rather than ability), but that a limited math education prior to high school graduation influences their career interests and thus their choice of college major.

## Conclusion

There is a preponderance of evidence pointing to a homeschool math gap. There is also preliminary data pointing to some of the ways this math gap may affect homeschooled students as they graduate and begin their adult lives. In an era when STEM fields have taken on increasing importance, the homeschool math gap should be taken seriously by both homeschool parents and policymakers.

It should be noted that individual homeschooled students may excel at math. The existence of a math gap does not mean

everyhomeschooled student has deficiencies in math. What it means is that homeschooled studentson averagehave substantial lower math scores as compared to reading scores, a discrepancy that may follow many out of childhood into their adult lives.Category: Blog, Research Tags: academics, math, original research

## Search

The Coalition for Responsible Home Education empowers homeschooled children by educating the public and advocating for child-centered, evidence-based policy and practices for families and professionals.## Find Your State

ALAKAZARCACOCTDEFLGAHIIDILINIAKSKYLAMEMDMAMIMNMSMOMTNENVNHNJNMNYNCNDOHOKORPARISCSDTNTXUTVTVAWAWVWIWYDC