Measuring Students’ Sense of School Catholic Identity Measuring Students’ Sense of School Catholic Identity

: As a min is try of the Cath o lic Church, Cath o lic schools are charged with edu cat ing stu dents’ hearts and minds. Multiple stan dard ized aca demic tests and other stu dent assess ments are avail able for mon i tor ing both stu dent and teacher out comes in Cath o lic schools, but fewer mea sures exist for con sid er ing the school’s faith-related mis sion. Although tests of stu dent reli gious knowl edge and bench marks related to spe cific Cath o lic ele ments of the school are avail able, we do not yet have a robust set of instru ments that pro vide teach ers and lead ers an under stand ing of their prog ress in pro vid ing a school envi ron ment per me ated by Cath o lic cul ture and faith. To con sider how stu dents in Cath o lic schools per ceive the Catholicity of their school and how these per cep tions vary among dif er ent stu dent groups, we devel oped, piloted, and val i dated the Sense of School Cath o lic Identity Survey (SSCI). This 20-item sur vey mea sures Grade 5 through 8 stu dents’ per cep tions of their Cath o lic school as per sonal and invi ta tional, sac ra men tal, uni tive, and eucha ris tic. Findings from the pilot study sug gest that responses dif er by stu dent grade level, reli gious tra di tion, and gen der. Future test ing of the scale will exam ine school-level dif er ences in Cath o lic iden tity.


Measuring Students' Sense of School Catholic Identity Measuring Students' Sense of School Catholic Identity
Cover Page Footnote Cover Page Footnote infused with faith in a com mu nity envi ron ment informed by faith (Groome, 1996;Heft, 2004;Joseph, 2004).
Within the larger edu ca tional field, school-level account abil ity has increased steadily over the last two decades (Mittleman & Jennings, 2018), and schools are encour aged to use data to inform school-wide deci sions and improve ment (Goldring & Berends, 2008). Although Cath o lic schools do not face the same level of account abil ity as pub lic schools, they do face the need to dem on strate to the par ish and dioc e san com mu nity that they are fulfilling their mis sion. The use of stu dent-and school-level data can pro vide evi dence to con sider what Cath o lic schools are doing well and where they may need addi tional sup port. Currently, stan dard ized achieve ment and interim test ing can pro vide some mea sure of how well the school is doing from an aca demic per spec tive, but Cath o lic schools still strug gle to under stand their prog ress on their reli gious mis sion.
Assessing the lived expe ri ence of reli gious mis sion in Cath o lic schools is impor tant for sev eral rea sons. First, as a cen tral min is try of the Cath o lic Church, faith for ma tion is of pri mary impor tance-par tic u larly for school lead ers and teach ers charged with pro vid ing an envi ron ment con du cive to aca demic and spir i tual growth as well as inte grat ing faith into the aca demic cur ric u lum (Congregation for Cath o lic Education [CCE], 1977[CCE], , 1988. Second, research sug gests that trans mis sion of the faith con tin ues to be impor tant to reli gious par ents, includ ing Cath o lic par ents (Smith et al., 2019), and that one of the main rea sons par ents choose Cath o lic schools is because of the reli gious instruc tion and envi ron ment that they pro vide (Cohen-Zada & Sander, 2008;Lockwood, 2014;Lopez Arends, 2021). In addi tion, recent demo graphic data on Cath o lic schools show that more non-Cath o lic stu dents and fam i lies are choos ing Cath o lic schools (Smith & Huber, 2022), mak ing it increas ingly impor tant to under stand how stu dents of other faith tra di tions are expe ri enc ing the Cath o lic nature of the com mu nity to ensure that all stu dents feel wel come and included.
While mea sur ing aca demic out comes in schools is fairly straight for ward, mea sur ing reli gious and spir i tual growth in stu dents can be dif cult. Although quan ti ta tive mea sures of Church atten dance and fre quency of prayer ofer some per spec tive on the per sonal reli gi os ity of chil dren and fam i lies, the faith for ma tion that Cath o lic schools seek to pro vide goes beyond dis crete check lists of prac tices. Similarly, tests of reli gious knowl edge pro vide an assess ment of what stu dents have learned about their faith, but this infor ma tion is more aca demic and speaks less to the entirety of the school envi ron ment. Other resources for Cath o lic schools focus on the décor, rit u als, and sym bols within the school. These tools get closer to defin ing the Cath o lic cul tural ele ments within the school, but to grasp the extent of a school's Catholicity, we need to under stand how stu dents expe ri ence the Cath o lic nature of the school in its entirety. Measures that tar get stu dent per cep tions can help school lead ers and teach ers under stand what aspects of their Cath o lic iden tity have an impact on stu dents and where edu ca tors should focus fur ther atten tion. Finally, as Cath o lic schools begin to use school-and stu dent-level data to mon i tor and track aca demic prog ress and oper a tional health (Dallavis, this issue), Cath o lic school lead ers have also expressed the desire to bet ter assess and improve the reli gious envi ron ment and faith for ma tion in their schools (Dallavis & Ponisciak, 2022).
To this end, this study con sid ered the fol low ing two research ques tions: (1) How do mid dle-grade stu dents per ceive the Cath o lic iden tity of the Cath o lic school envi ron ment? (2) To what extent do these per cep tions vary by dif er ent stu dent char ac ter is tics, namely aca demic grades, stu dent grade level, race/eth nic ity, reli gion, and gen der? To explore these ques tions and to pro vide addi tional met rics for use in Cath o lic schools and dio ceses, we devel oped, piloted, and val i dated a set of stu dent sur vey mea sures-the Sense of School Cath o lic Identity (SSCI)-draw ing on writ ings related to the phi los o phy and mis sion of Cath o lic schools. In a pilot study using these mea sures, we found that stu dent per cep tion varies by grade level, reli gious tra di tion, and (in some cases) aca demic suc cess and gen der. Future use of the sur vey will inves ti gate school-level aggre gate dif er ences in the per cep tions of Cath o lic iden tity, with the goal of devel op ing school-level met rics.

Cath o lic School Identity
For sev eral decades, the pres ence of vowed reli gious sis ters, broth ers, and priests in U.S. Cath o lic schools-indi vid u als who had com pleted exten sive reli gious for ma tion within their respec tive orders or dio ceses-ensured the Cath o lic iden tity of schools, a char ac ter is tic that went largely unex am ined by Cath o lic school lead ers, teach ers, and fam i lies. Over the last 100 years, the com po si tion of the national Cath o lic school teach ing force has changed from 92% vowed reli gious men and women in 1920 to 97% lay men and women in 2022 (Smith & Huber, 2022). With the tran si tion to a pri mar ily lay teach ing force and school lead er ship, Cath o lic school lead ers and teach ers have had to become inten tional regard ing what makes their school Cath o lic. The broader Cath o lic com mu nity can no lon ger take for granted that all of the adults in the build ing have the same level of knowl edge and prac tice of the Cath o lic faith to share with stu dents and to inform the cul ture of the school envi ron ment (Convey, 2012;Heft, 2004). Despite a con certed focus, Cath o lic iden tity remains an elu sive con struct that research ers and prac ti tion ers strug gle to con cep tu al ize (Baker, 2019;Convey, 2012;Fuller & Johnson, 2013;Nuzzi, 2001). Cath o lic edu ca tors agree that Cath o lic iden tity is at the heart of a school and can be felt and expe ri enced, even if it is not eas ily artic u lated (Schuttlofel, 2012). Convey (2012) sur veyed over 3,000 Cath o lic school edu ca tors to explore their under stand ing of the con cept of Cath o lic iden tity. In the sur vey data, school lead ers and teach ers iden ti fied the school's faith com mu nity and cul ture, reli gious con tent and ele ments, as well as stu dent par tic i pa tion in prayer, lit urgy, and ser vice as most cen tral to the Cath o lic iden tity of the school. Other Cath o lic writ ers and edu ca tors dis cuss the Cath o lic nature of schools as more than its ele ments, with faith per me at ing every aspect of the Cath o lic school edu ca tion and envi ron ment (Groome, 1996;Heft, 2004;Joseph, 2004). Convey (2012) has con cep tu al ized Cath o lic iden tity as made up of con tent and cul ture for which school lead ers, teach ers, clergy, and par ents are respon si ble. Within con tent is the reli gion pro gram and other cur ric u lum, and cul ture is com prised of the school faith com mu nity, ser vice to oth ers, and rit u als-includ ing lit urgy, prayer, and the sac ra ments. Beyond struc ture, how ever, doc u ments from the Vatican (see CCE, 1977CCE, , 1982CCE, , 1988CCE, , 1997CCE, , 2022Vatican II, 1965) and the U.S. Bishops (see National Conference of Cath o lic Bishops [NCCB], 1972[NCCB], /2012USCCB, 2005USCCB, /2012 sug gest sev eral com mon themes that should inform a Cath o lic school iden tity. These include a focus on the holis tic for ma tion of the indi vid ual that rec og nizes their human dig nity; a robust faith com mu nity char ac ter ized by the norms and val ues of the Gospel; coop er a tion between lead ers, teach ers, clergy, and par ents in the edu ca tional endeavor; and the inte gra tion of faith and rea son, with faith infus ing all ele ments of the school envi ron ment and cur ric u lum.

Academic Achievement
Schools use a num ber of dif er ent instru ments to mea sure aca demic prog ress. In Cath o lic schools, these include annual stan dard ized achieve ment tests (e.g., the Iowa Test of Basic Skills or Terra Nova) and an increas ing num ber of interim assess ments taken two to three times per year (e.g., NWEA MAP Growth, Renaissance Star, and ACT Aspire). In some states, such as Indiana, stu dents in Cath o lic schools also take the state stan dard ized achieve ment test. A sub set of Cath o lic schools par tic i pates in the National Assessment of Educational Progress (NAEP) and other national stud ies conducted by the National Center for Education Statistics (NCES). Although the avail abil ity of these instru ments does not ensure com pa ra ble data among Cath o lic schools or between Cath o lic and other pub lic, char ter, and pri vate schools (Dallavis, this issue), these stan dard ized assess ments do pro vide Cath o lic school edu ca tors some mea sure of how well Cath o lic schools are pre par ing their stu dents aca dem i cally. The assess ment of a school's Cath o lic iden tity, how ever, is more dif cult to mea sure in its total ity.

Religious Knowledge
The imme di ate par al lel to stu dent aca demic test scores would be met rics that seek to assess stu dent out comes related to faith, includ ing their knowl edge of the faith. One such tool is the National Cath o lic Educational Association's (NCEA) Information for Growth (IFG) Assessment for Child/Youth Religious Education (ACRE), which is "a tool to help Cath o lic schools and parishes assess how well their reli gious edu ca tion pro grams are forming com mit ted Chris tian dis ci ples" (NCEA, 2022). A help ful mea sure of reli gious con tent knowl edge, this assess ment speaks to the qual ity of the reli gious courses and cur ric u lum within the school, a pri mary objec tive that may not encom pass stu dent under stand ings concerning the full nature of their school's Cath o lic iden tity. Although this instru ment also includes sur vey mea sures on atti tudes, prac tices, and beliefs, it is a pro pri e tary model of assess ment that may not be avail able to all Cath o lic schools.

Religiosity
Other stu dent-level met rics seek to quan tify how reli gious indi vid u als are in prac tice (e.g., how often they pray, attend reli gious ser vices, etc.), mea sur ing an indi vid ual's reli gious expe ri ence using a set of indi vid ual prac tices or devo tions that may be sub ject to overreporting (Christiano et al., 2008). Several sur vey instru ments cur rently exist to assess spir i tu al ity, reli gi os ity, and reli gious iden tity (see Austin et al. [2018] for a scop ing review of avail able mea sures) that could be used over time to con sider the school's efect on indi vid u als. However, chil dren and ado les cents' reli gi os ity is greatly informed and influ enced by their par ents' level of reli gi os ity (Pearce & Thornton, 2007), and par ents and teens report shar ing sim i lar reli gious beliefs and ser vice atten dance (Pew Research Center, 2020). As par ents who are more reli gious are more likely to choose a reli gious school for their chil dren (Cohen-Zada, 2006;Greeley & Rossi, 1966;Sander, 2005), it can be dif cult to sep a rate out the school's efect from the fam ily's efect on a stu dent's own reli gi os ity. In addi tion, some research sug gests that fam ily upbring ing has a greater influ ence on chil dren's reli gi os ity than reli gious school ing (Smith et al., 2014). Thus, when con sid er ing the qual ity of the Cath o lic iden tity of the school envi ron ment, we are more inter ested in mea sur ing stu dents' expe ri ences in their school rather than their lev els of reli gious ness.

School Culture and Climate
In choos ing to focus more on stu dents' expe ri ences in the Cath o lic school, we con sid ered established school cul ture and cli mate mea sures within gen eral edu ca tion research. A large, sec u lar lit er a ture dem on strates pos i tive cor re la tions between a strong school cli mate and stu dent aca demic achieve ment. The U.S. Department of Education has placed a high pri or ity on these mea sures, as the Every Student Succeeds Act (2015) requires fed er ally funded schools to col lect and report data related to school cli mate. Researchers have operationalized school cli mate to include safe and sup port ive envi ron ments and pos i tive school cul tures, and a pleth ora of instru ments are avail able to mea sure school cli mate var i ables such as school con nect ed ness, cul tural com pe tence, per sonal safety, trust in teach ers, and many more (National Center on Safe and Supportive Learning Environments, 2017). While Cath o lic schools cer tainly care about all of these out comes, and some school cli mate mea sures have been val i dated in Cath o lic school con texts (Ponisciak, 2021;Ponisciak & Kowalski, 2019), these cli mate mea sures are not suf cient to encom pass the uniquely Cath o lic cul ture pres ent in Cath o lic schools. Research indi cates that the school com mu nity expe ri ences school cli mate and aca demic empha sis dif er ently in reli gious schools com pared to pub lic schools (Sikkink, 2012), which sug gests that we need addi tional mea sures spe cific to the Cath o lic school envi ron ment to fully under stand its Cath o lic iden tity.

Cath o lic School Characteristics
The National Standards and Benchmarks for Efective Cath o lic Elementary and Secondary Schools (NSBECS) artic u late nine defin ing char ac ter is tics of Cath o lic schools, includ ing being cen tered on Jesus Christ, con trib ut ing to evan ge li za tion, being steeped in a Cath o lic world view, and being shaped by com mu nion and com mu nity (Ozar & Weitzel-O'Neill, 2012;Ozar et al., 2019). The defin ing char ac ter is tics serve as the foun da tion for 13 stan dards and 70 bench marks across 4 domains, 1 of which is enti tled Mission and Cath o lic Identity (Ozar & Weitzel-O'Neill, 2012). The NSBECS efort has included the devel op ment of rubrics and sur veys that can be used to mea sure align ment with the stan dards and bench marks, such as the Defining Characteristics Survey. These are use ful and well-designed tools that allow school lead ers and teach ers to assess their school's align ment with national stan dards related to Cath o lic iden tity. However, some items could be con sid ered as an inven tory of school prac tices rather than a mea sure of how stu dents per ceive Cath o lic iden tity enacted in the school (e.g., "There are crucifixes and other Cath o lic sym bols in the school"). Beyond sim ple rec og ni tion of the tan gi ble Cath o lic ele ments in the school, we are inter ested in how stu dents expe ri ence the Cath o lic ethos or essence of the school. We believe such a mea sure would be dis tinct from but com ple men tary to the instru ments avail able through the NSBECS.

Student Sense of Cath o lic Identity Survey
Taken together, each of the afore men tioned tools have strengths for mea sur ing spe cific aspects of the Cath o lic iden tity of the school. To approach more closely a mea sure of the school's Cath o lic iden tity among mul ti ple dimen sions, we exam ined stu dent per cep tions. Students are the pri mary con sum ers of a school's expres sion of its Cath o lic iden tity. Although teach ers and lead ers expe ri ence the cul ture and com mu nity, they also play an inte gral role in shap ing the school's Cath o lic iden tity. Students expe ri ence the Catholicity of the school in its entirety, so the sur vey instru ment is designed for them.
The SSCI defi nes Cath o lic iden tity based on the writ ten guid ance of the Vatican (CCE, 1977, 1988, 1997 and U.S. Bishops (NCCB, 1972(NCCB, /2012USCCB, 2005USCCB, /2012, as well as a frame work of the con stit u ent ele ments of a Cath o lic edu ca tion described in four domains: per sonal and invi ta tional, sac ra men tal, eucha ris tic, and uni tive (DelFra et al., 2018). These writ ings express both the phi los o phy and the ide als on which Cath o lic schools are established. In this sec tion, we describe each of the four iden ti fied domains trans lated to the stu dent expe ri ence and share exam ples of the ques tions on the scale. The full set of ques tions is avail able in the Appendix.

Personal and Invitational
The per sonal and invi ta tional dimen sion of Cath o lic edu ca tion encompasses the extent to which a stu dent senses a Cath o lic school and/or class room as wel com ing the indi vid ual stu dent into a liv ing rela tion ship with Christ, and in doing so engag ing the stu dent in heart and mind. Questions in this domain seek to under stand both the per sonal care of the teach ers and lead ers in the school (e.g., "Adults at my school care about me as a child of God"), as well as the school as a wel com ing and invi ta tional space (e.g., "My teach ers invite me to build my rela tion ship with God").

Sacramental
The sac ra men tal dimen sion refers to the extent to which stu dents sense God in all things, such as the peo ple, orga ni za tion, activ i ties, rou tines, and pro ce dures of their school. This domain asks stu dents to reflect on the adults in the build ing (e.g., "I can see God in the actions of the adults in my school") as well as aspects of the school day ("There are daily events at my school that remind me of God's pres ence").

Eucharistic
The eucha ris tic dimen sion includes the extent to which stu dents sense their school as a faith com mu nity ded i cated to the com mon good and the dig nity of the human per son. These ques tions focus on stu dents' per cep tion of the school com mu nity (e.g., "People in this school help each other") and their prep a ra tion for help ing oth ers (e.g., "My school pre pares me to help peo ple in need."

Unitive
The uni tive dimen sion encompasses stu dents' sense that faith and reli gion are inte grated through out their aca demic edu ca tion and the school is ded i cated to devel op ing the whole per son. Questions in this domain ask about their under stand ing of the rela tion ship between aca dem ics and faith in the school (e.g., "In my school, aca dem ics and faith are impor tant"; "At school, I am taught to use my heart and my mind").

Cath o lic School and Student Context
Cath o lic schools enroll close to 1.7 mil lion stu dents in nearly 6,000 schools, and recently expe ri enced an increase in enroll ment for the first time in sev eral decades (Smith & Huber, 2022). The stu dent com po si tion in today's Cath o lic schools is both more and less diverse than pre vi ous gen er a tions of Cath o lic school stu dents. From the per spec tive of reli gious tra di tion, in 1970, only 3% of stu dents were non-Cath o lic whereas cur rently (in 2022), non-Cath o lic stu dents com prise 20% of the Cath o lic school pop u la tion (Smith & Huber, 2022). Over time, Cath o lic schools have gone from serv ing stu dents from all social clas ses to serv ing fewer stu dents at the mid dle of the socio eco nomic dis tri bu tion, likely due to ris ing tuition costs for Cath o lic schools and sub se quent school clo sures (Murnane et al., 2018). In some dio ceses, state-funded paren tal choice options such as tax-credit schol ar ships and vouch ers pro vide addi tional means for low-income stu dents to attend Cath o lic schools. Currently, 20% of Cath o lic schools in the United States par tic i pate in paren tal choice pro grams and just over 7% of Cath o lic school stu dents use these funds to attend Cath o lic schools. When con sid er ing racial diver sity, roughly 22% of Cath o lic school stu dents iden tify racially as other than White, an increase from just over 10% in 1970, and nearly 19% iden tify as Latinx (Smith & Huber, 2022).
Understanding how dif er ent stu dent groups expe ri ence Cath o lic iden tity is impor tant infor ma tion that schools can use to assess their cur rent school cul ture. As Cath o lic schools attempt to bal ance an atmo sphere of inclusivity with the more overtly reli gious aspects of the school, such as Mass and reli gion courses, non-Cath o lic stu dent per spec tives can pro vide impor tant insight. Similarly, under stand ing dif er ences by stu dent grade level and level of achieve ment as well as gen der and race/eth nic ity can help edu ca tors con sider what aspects of the school's Cath o lic iden tity may need atten tion. At the school level, low aggre gate scores in one or more domains may also pro vide impor tant infor ma tion for reflec tion and change.

Methods
We gen er ated an ini tial list of 62 items based on doc u ment anal y sis of the guid ing frame work text (DelFra et al., 2018). Through inter nal dis cus sions, redun dant or poten tially con fus ing items were elim i nated, lead ing to a list of 30 items. These items were then assessed for con struct validity in two ways. First, we conducted an expert review, consisting of a con ven ing of fac ulty in a Cath o lic edu ca tion pro gram. The instru ment was presented and fac ulty engaged in dis cus sion of the items, at some points suggesting rewording or clar i fi ca tion. As a result of this review, six items were deleted, and sev eral oth ers had slight changes made to the word ing.
Next, we conducted cog ni tive inter views (Willis, 2004) with 10 stu dents at a Cath o lic school in the local area will ing to part ner with the research ers. Students were selected based on teacher rec om men da tions for stu dents who would be able to artic u late their thought pro cesses while tak ing the sur vey. We used a con cur rent ver bal prob ing method (Willis, 2004) in which a researcher asked ques tions like "What does this mean to you?" and "Can you explain your think ing?" as each stu dent read the sur vey items aloud. This pro cess was designed to con firm that stu dents accu rately comprehended the ques tions and that the items were mea sur ing what was intended. Students in the pilot study included one stu dent in each of sec ond, third, fifth and sev enth grades, and two stu dents in each of Grades 4, 6, and 8. The cog ni tive inter views lasted between 11 and 25 min utes; these con ver sa tions were audio recorded and tran scribed for anal y sis.
We first reviewed the cog ni tive inter view tran scripts by indi vid ual stu dent to deter mine over all lev els of com pre hen sion. The data from stu dents in Grades 2 through 4 had much lower over all com pre hen sion than older stu dents, lead ing us to elim i nate those responses and decide that the sur vey should be lim ited to Grades 5 and above. Next, we com piled the remaining tran scripts together by item and coded each item as keep, revise, or delete based on whether or not stu dents seemed to com pre hend the item as intended. After this anal y sis, 16 items were deemed accept able as writ ten, 4 items were deleted, and 4 items were slightly revised. For exam ple, an orig i nal item read, "My school encour ages me to be part of the Church." Cognitive inter views revealed that stu dents asso ci ated the word "Church" with the phys i cal build ing, thus interpreting this ques tion to nar rowly refer to serv ing as an altar server or oth er wise being phys i cally pres ent in the build ing. The ques tion was revised to "My school encour ages me to be part of the Cath o lic com mu nity" to bet ter reflect the invi ta tional call to belong to the uni ver sal Church. The final revised instru ment consisted of 20 items, included in the Appendix.
We then piloted the sur vey in the Diocese of Fort Wayne-South Bend. Principals of all schools were sent an email invi ta tion to par tic i pate in the pilot study. Three schools volunteered to par tic i pate in spring 2021, and two in fall 2021. Four of the five schools had an aca demic per for mance in 2019 that was bet ter than the state aver age, while the fifth was above aver age in read ing and below aver age in math (Indiana Department of Education, n.d.). Schools ranged in size from 63 to 422 stu dents in 2020-21. Four of the five schools had stu dent pop u la tions that were 30 to 40% eco nom i cally dis ad van taged, while the remaining school had fewer than 5% of such stu dents. One school had 15% of its pop u la tion denoted as English Language Learners, while the other 4 each had fewer than 5%, and each school had between 6 and 10% of its stu dents in spe cial edu ca tion pro grams.
Participating schools were pro vided with a let ter to send home to par ents, and then class room teach ers admin is tered the sur vey through Qualtrics to stu dents with paren tal con sent. Teachers were instructed to read each sur vey ques tion aloud as stu dents responded on their devices. Students were prom ised ano nym ity in order to achieve the most accu rate responses.
Schools par tic i pated at vary ing rates, with 184, 63, 41, 16, and 5 stu dents, so we can not yet deter mine the extent to which the sur vey is a good mea sure of dif er ences between schools; how ever, we expect to exam ine that aspect of mea sure ment in the next round of ana ly ses. Our ini tial anal y sis was there fore focused on mea sur ing dif er ences between stu dents.

Results
We used Rasch anal y sis to cre ate aggre gate mea sures of Cath o lic iden tity in each of the five domains described ear lier. Rasch anal y sis is a method of com bin ing sur vey, assess ment, or other data that is flex i ble to the pos si bil ity of miss ing data, and places items ("dif culty") and respon dents ("agree abil ity") on the same scale, represented by the fol low ing equa tion: This is known as the "par tial credit" model (Masters, 1982), as the D jk term allows for dif er ences in categories between sur vey items.
We implemented the Rasch model so that we do not have to assume that the dif er ence between "agree" and "strongly agree" is the same as the dif er ence between "neu tral" and "dis agree" (for exam ple)-so that we mea sure the under ly ing "latent" agree abil ity of the per son and dif culty of the item. We want to com bine items to pro duce a scale that is reli able, that allows us to mea sure mean ing ful dif er ences between respon dents, between schools, and between other group ings of respon dents. The Rasch model gen er ates a mea sure of reli abil ity, the degree to which the order ing of the mea sures is repro duc ible; it is a ratio of the true var i ance to the observed var i ance. An accu rate mea sure of changes over time requires a sta ble mea sure of item dif culty, which the Rasch model can pro vide. The Rasch model also pro vi des an indi ca tion of the rel a tive pre ci sion of each mea sure, in the form of a stan dard error.
Very few stu dents responded "strongly dis agree" and only slightly more responded "dis agree." We there fore com bined "strongly dis agree" and "dis agree" for all items. For most items, we also had to com bine "strongly dis agree" and "dis agree" with "neu tral" so that we did not esti mate dis or dered or poorly mea sured cat e gory cut ofs, due to low fre quen cies of response in some categories (Linacre, 2002). Using the TAM pack age in R soft ware (Robitzch et al., 2018), we com bined sur vey responses into mea sures for each stu dent. We then used the SIRT pack age in R (Robitzch et al., 2018) to exam ine the results of the Rasch ana ly ses.
As described above, we the o rized that our items would fit into four mea sures: per sonal and invi ta tional, sac ra men tal, eucha ris tic, and uni tive. We included items from a fifth mea sure, con nect ed ness, that was pre vi ously val i dated and used in sev eral school dis tricts and dio ceses (Goodenow, 1993;University of Chicago, 2018), in order to exam ine the con sis tency of the new mea sures with an existing mea sure of school cli mate and cul ture.
When we com bine items into mea sures as described the o ret i cally, we find that one mea sure does not fit well, as shown in Table 1. The fit sta tis tic that we use is a mean-squared resid ual, mea sur ing the ratio of observed to expected var i ance in the sur vey items, so val ues above 1 indi cate more than expected var i a tion, while those below 1 indi cate less than expected var i a tion (Wright and Linacre, 1994). Values greater than one pres ent more of a con cern than those less than one, although val ues far below one-espe cially those below 0.5-indi cate items that do not pro vide addi tional infor ma tion, and are not help ful for mea sure ment. Measures with fit that we labeled as "poor" had val ues of 0.5 or less for the fit sta tis tic for all or most of their items. Due to the poor fit and unre li abil ity of the "uni tive" mea sure, we sought to keep these items, but include them in other mea sures if appro pri ate. We there fore exam ined the cor re la tions among these mea sures. We found that the highest cor re la tion of "uni tive" was with "eucha ris tic" (0.65). However, a mea sure that com bined "uni tive" with "eucha ris tic" also suf ered from poor model fit. We there fore com bined with "uni tive" with "sac ra men tal, " as these mea sures had a cor re la tion of 0.58. The resulting com bined mea sures improved reli abil ity, and accept able model fit. The com bined "uni tive + sac ra men tal" mea sure had a reli abil ity of 0.71. This com bi na tion is con sis tent with the the o ret i cal frame work, as well, as the mea sures cover sim i lar rhe tor i cal ground. Our resulting final mea sures are shown in Table 2. While these reliabilities are not objec tively high, this is likely due to the rel a tively small size of the sam ple.
We then exam ined dif er ences in these mea sures by stu dent grades, school open ing sta tus, grade level, race/eth nic ity, reli gion, and gen der. Nearly all stu dents reported their school was pri mar ily open in per son, so we were unable to make use ful com par i sons of mea sures across school open ing sta tus. We used t-tests for dichot o mous var i ables, and ANOVA (followed by paired t-tests when needed) for polytomous var i ables. We found sig nifi cant asso ci a tions between stu dent grade level and each sur vey mea sure. Students in eighth grade reported the low est lev els of all mea sures (includ ing con nect ed ness), while stu dents in fifth grade reported the highest lev els. Diferences between fifth grad ers and eighth grad ers were at least 0.88 for each of the new mea sures, as shown in Table 4; because these are mea sured in stan dard devi a tion units, these dif er ences are quite large. There was no asso ci a tion between stu dent race/eth nic ity and the sur vey mea sures. The asso ci a tion between stu dent grades and the eucha ris tic mea sure was sig nifi cant; stu dents who reported that their grades were Bs and Cs, or Cs and lower (who are com bined into "Bs and lower" due to the small num ber of stu dents reporting Cs and lower), reported lower lev els of the eucha ris tic mea sure than stu dents who reported their grades as "Mostly As" or "As and Bs." Non-Cath o lic stu dents reported sig nifi cantly lower lev els of all mea sures than Cath o lic stu dents. The only sig nifi cant asso ci a tion between a sur vey mea sure and schools attended was for the eucha ris tic mea sure; this asso ci a tion was driven by one large dif er ence of more than half a stan dard devi a tion between two schools. Diferences between male and female stu dents were min i mal, but the nine stu dents who did not report a gen der indi cated lower lev els of all mea sures than stu dents who did report their gen der, and the eucha ris tic mea sure for these stu dents was sig nifi cantly lower than for those who reported a gen der.
The resulting sur vey mea sures were pos i tively related to each other, but not per fectlysuggesting that they are mea sur ing some what dif er ent aspects of Cath o lic iden tity. Each of the pairwise cor re la tions among the three Cath o lic iden tity mea sures was at least 0.72, while each of the Cath o lic iden tity mea sures had a cor re la tion of at least 0.56 with con nect ed ness, as shown in Table 3.

Discussion
In an increas ingly com pet i tive edu ca tional mar ket place, Cath o lic schools seek to dem on strate their value to poten tial fam i lies (Foundations and Donors Interested in Cath o lic Activities, 2018). While many Cath o lic schools are dis tin guished by aca demic excel lence, which can be quan ti fied via stu dent achieve ment out comes, the Cath o lic iden tity of the school may be just as impor tant to high light. Existing tools and sur veys mea sure spe cific aspects of Cath o lic iden tity in schools, but a pub licly avail able, val i dated mea sure of how Cath o lic iden tity is expe ri enced by stu dents has been lacking. We sought to cre ate a mea sure of stu dent per cep tions of a school's Cath o lic iden tity among mul ti ple dimen sions. We suc cess fully piloted and val i dated a sur vey cov er ing four domains of Cath o lic iden tity, and found that stu dents' responses dif ered across domains and by stu dent grade level, reli gion, and gen der.
This ini tial phase of anal y sis has yielded reli able indi vid ual mea sures in a small sam ple of Cath o lic schools. However, due to the small sam ple, we were unable to deter mine whether the school-level aggre gate mea sures can reli ably dis tin guish between Cath o lic schools. To address this issue, and oth ers presented by the small sam ple, we hope to exam ine sur vey results from a larger num ber of Cath o lic schools in future years. In a larger sam ple, sur vey mea sures are likely to be more pre cise; school-level results should be more reli able; and it would be pos si ble to ana lyze a wider range of stu dent out comes in a more com pre hen sive man ner. When we are able to reach more schools, we will be able to exam ine the extent to which the sur vey items fit in the same way in dif er ent types of schools (whether by region, level of stu dent achieve ment, stu dent demo graph ics, etc.); how these mea sures change over time; and poten tially how these sur vey mea sures are related to stu dent and school out comes (pend ing data avail abil ity). We will also be able to fur ther explore the dif er ences between stu dent groups. Of par tic u lar inter est will be dif er ences between Cath o lic and non-Cath o lic stu dents. For instance, the frame work-based on the evan ge liz ing mis sion of Cath o lic schools-assumes that all stu dents should per ceive the school as per sonal and invi ta tional, regard less of their reli gion. If there are sig nifi cant dif er ences between the way that Cath o lic and non-Cath o lic stu dents per ceive the invi ta tion to be part of the Cath o lic com mu nity, for exam ple, schools may want to refine their mes sag ing to the school com mu nity, to ensure that all stu dents are con sis tently told that they are invited to belong.
Cath o lic schools and pro grams partnering with Cath o lic schools, such as through uni ver si ties or foun da tions, may wish to use the SSCI as part of a com pre hen sive strat egy to assess school efec tive ness. Those already using the NSBECS may want to sup ple ment the Defining Characteristics Survey with the SSCI to gain a more robust under stand ing of stu dent per cep tions related to their expe ri ence of a school's Cath o lic iden tity. Through deter min ing how stu dents expe ri ence the Cath o lic iden tity of the school, schools and pro grams can iden tify spe cific areas of strength and needs for improve ment to cre ate targeted ini tia tives and inter ven tions. For instance, a school that stu dents rate low in the Personal and Invitational domain may con sider increas ing their empha sis on stu dent-teacher rela tion ships or adding pro fes sional devel op ment oppor tu ni ties related to adult faith for ma tion to enhance adult faith mod el ing, aligned with the results of the sur vey.
In the near future, the SSCI can be used to com pare indi vid ual schools and to assess changes over time when used lon gi tu di nally. With more data, research ers can develop addi tional tools and resources, such as a guide for interpreting results. Cath o lic schools exist in order to form chil dren in the faith, and this for ma tion is strength ened when stu dents per ceive their school as an envi ron ment per me ated by Cath o lic cul ture and faith. The devel op ment and val i da tion of the SSCI rep re sents a step toward help ing Cath o lic schools bet ter dem on strate their suc cess in achiev ing their com mon mis sion.