Maximum Available DesktoEye Distance for Students in Grades One and Two:
Regional Norms and Statistical Comparison to Distance Used for Near Point Screening
Chapter IV:
Data Analysis and Results
Presentation and Analysis of Data
The primary purpose of this study was to establish normative tables of the maximum available desktoeye distance for students in Grades 1 and 2 who were less than 10 years of age. Additionally, this study analyzed the significant differences between the mean lengths of the Side or Across MADEDs and the target distances used in nearpoint vision screening. A second analysis was of significant differences between the diopter equivalent of the Side and Across MADED means (D_{S}, D_{A}) and the sum of D_{S} or D_{A} and each power of plus lens used as fogging lens (D_{FL}) to screen for hyperopia (D_{S} + D_{FL} = D_{SFL}, or (D_{A} + D_{FL} = D_{AFL}). A third analysis was of the significant differences between the means of the remeasured Side MADED and measured Side MADED and between the means of the remeasured Across MADED and measured Across MADED. The multiple analysis of variance (MANOVA) procedure examined the interaction between the variables of age, grade, and sex for the measure and remeasure Side and Across MADEDs (8 x 4 x 2 design). Univariate procedures were completed to determine which variables contribute to the overall differences.
The measured sample included both males and females whose parents had returned correctly completed forms granting permission for the child's participation. There was a total of 1,135 subjects in Grades 1 and 2. Of these, 510 were males and 625 were females. Their ages ranged from 6 years, zero months (60, young 6 = 05 months) through 9 years, 11 months (911, old 9 = 611 months). One district had subjects older than 911: In 2^{2} there was one boy 10 years old, one girl 11 years old, and one girl 12 years old. These subjects were excluded from the study by the age limitations.
No data were available on the registration cards to indicate a student's age at time of entry into school, that is, Grade 1 or kindergarten, nor were there any data to indicate that a student had been retained. There were, however, subjects in both Grades 1 and 2 whose ages were within the Old 9 age span of 9 years, 6 months (96) through 9 years, 11 months (911). The youngest subjects in first grade, first semester (Grade 1^{1}) were within the Young 6 age span of 6 years, zero months (60) through 6 years, 5 months (65). The youngest subject in Grade 2 was in the Old 6 age span, 6 years, 6 months (66) through 6 years, 11 months (611). The oldest students in Grades 1^{1} were within the Old 8 age span (86 through 811).
The subjects in one district (CFBISD) were described by the administration as being all students enrolled in mainstream classes. In addition to regular students, the mainstream classes included mildly and moderately handicapped special education students who were mainstreamed with assistance given as direct service to them or as support service to their teachers on a demand basis, slow learners (IQ between 70 and 85) who had the same assistance as the mainstreamed special education students, students in special classes for the gifted and talented (IQ of 140 or higher, plus other qualifying criteria), and students in classes for intensive language development (ILD) to acquire the English language. Other districts included all students enrolled in classes designated as Grades 1 and 2. There was no exclusion of any category of educational placement, but there was no indication that selfcontained, severely handicapped students were among the subjects.
There was a pool of 1,712 subjects enrolled in Grades 1 and 2 in the 13 schools. Of these students, 1,135 became subjects in the study. The percentages of the subjects in grade levels 1^{1} and 2^{1} were almost equal, each being between 17% and 18%. The percentages of subjects in grade levels 1^{2} and 2^{2} were also close in value, being 33.57% and 31.98% (see Table 5).
Table
5:


Subject Group 
Percentage of the Sample 

N = 1,135 
Age 









Grade Level 

1st Grade 

1st Semester 

2nd Semester 

Total 

2nd Grade 

1st Semester 

2nd Semester 

Total 

Ethnic Origin 

Anglo 

Hispanic 

Black 

Asian/Oriental 

Aleut/Native American 

There was representation of each of the five ethnic groups: Anglo, Asian/Oriental, Hispanic, Aleut/Native American, and Black. The percentage of the sample in minority, nonanglo groups was 21.98%, ranging from 0.35% (Aleut/Native American) to 10.86% (Hispanic). The incidence of representation was based on the ethnicity of the students who participated in the study and were present during the time of measurement at their schools.
Measurements were made during 7 of the 9 school months. No measurements were made in December or May. The times of measurement were scheduled by the principals.
The design of the study set the upper age limit at 9 years, 11 months. There was no lower age limit set. There was, however, no subject younger than 6 years, zero months (60) at the time of measurement. The resulting age span was from 60 through 911.
The analyses involved two types of standards: linear target distance used in nearpoint screening and plus diopter power. The diopter standards (D_{SFL} and D_{AFL}) utilized the sum of the diopter equivalent of the MADED means and the diopter power used to screen for hyperopia. The near target distances as reported by the states (10 and 12 to 18 inches) and their frequencies of use are shown in Table 6. The powers of plus lens used to screen for hyperopia and the grades at which they are used as reported by the states (+1.00 D through +2.25 D) are shown in Table 7. Not all states screen for near vision, nor do all screen for hyperopia. Near tests and the distances reported as being used for each test are shown in Table 16, Appendix Q.
Table 6:


Distance 
Test Used 
N (states) 

Corneal Light Reflection 


Near Acuity 


Cover/Uncover 


Corneal Light Reflection 


Corneal Light Reflection^{a} 


Near Acuity 


Near Point Convergence^{b} 


Muscle Balance 


Worth Dot Test 


Near Acuity 


Worth Dot Test 


Cover/Uncover^{c} 


Cover/Uncover 


Worth Dot Test 

Reading Position^{d} 
Cover/Uncover 

Reading Distance^{d} 
Cover/Uncover 


Near Phoria 

Average Reading Distance^{d} 
Cover/Uncover 


Straibsmus 

At Arm's Length 
Cover/Uncover^{c} 


Corneal Light Reflection^{a} 


Fogging Lens^{e} 

DNS 
Vision Screening Machine^{f} 

NOTES: 
^{a} Arm's length defined as 13" to 14" 
^{b} And move inward 
^{c} Arm's length defined as 14" to 16" 
^{d} Measure distance not given 
^{e} Reported by some as a near vision score 
^{f} Reported by Lebensohn (Lebensohn_1958): Telebinocular, 16 inches; Sight Screener, 14 inches; Orthorater, 13 inches 

Table
7: Power of Plus Diopter Lens Used to Screen for Hyperopia by Grade


Power of +D Lens 
Grade(s) Used 



K, 13, 48 



K12 



K1, 112, 3UP, 4UP, GNS 

>7^{b} 

GNS 



K, K2, K3, 1, 112 
VSMPNS 
GNS 
NS 
ANYTWR, NS 
NOTE: ^{a}Some states use more than one power. ^{b}Years of age.
/ = or;  = through; ANY = Any Grade; GNS = Grade Not Specified; NS = Not Specified: PNS = power not Specified; TWR = if Trouble With Reading; VSM = Vision Screening Machine
There were three sizes of chairs and two sizes of each style of desk used in the study. Table 8 presents data for the number of subjects for each desk and chair size. Descriptions of the criteria for fit of the furniture is given in Appendix M .
Table
8:


Furniture Size 
Number of Students 
per Size: 



Chair 
Measured 
Remeasured 









Total 


Side Desk 








Total 


Across Desk 








Total 


During the measure trial, fit for the bestfit chair was low for 0.53% of the subjects, high for 3.08% of the students, and appropriate for 96.39% of the children. For the bestfit side desks, the resulting fit was short for 0.97%, tall for 78.18%, and appropriate for 20.85% of the children. For the bestfit across desks, the resulting fit was short for 0.09%, tall for 83.17%, and appropriate for 16.74% of the subjects. During the remeasure trial, the percentages for best fit were: (a) chair, 0.00% low, 1.34% high, and 98.66% appropriate; (b) side desk, 0.00% short, 91.39% tall, and 8.61% appropriate; and (c) across desk, 0.00% short, 91.39 % tall, and 8.61% appropriate (see Table 31 in the Addendum). Intervening factors which might affect fit, such as body build, physique or posture, were not investigated.
Retention of Subjects for Data Analysis
From a sample pool of 1,712 students, 1,135 subjects met all criteria for inclusion in the analysis of data for this study. The criteria for retention were that the parent return a properly completed consent form, the student be present at the time of measurement, the student be under 10 years of age, and data entry be complete for the variable being analyzed. The data entry error rate was < 1%. Of the pool of 1,712 subjects, 75.18% returned consent forms by the deadline (see Table 9). Three students were excluded by the upper age limit set in the study design. In Grade 2^{2}, one boy was 10 years old, one girl was 11 years old, and one girl was 12 years old. There was no lower age limit. Data are complete for 1,135 subjects.
Data were collected on the number of students who took home parent packets for measure and remeasure phases of the study. Table 9 shows the number of students retained for data analysis in each phase.
Table
9:


Criterion 
Measure 

Remeasure 


Total N=1,172 

Total N=173 


n 
% 
n 
% 
Parent Packets 




Not returned 




Incorrect 




Consent 




Yes 




No 




Overage 




Attendance on day 




Measured 




Absent 




NOTES 
^{a} Data incomplete on 4 
^{b} Includes one retainee 
^{c} 
Followup letters and duplicate forms were sent to parents who did not return the initial packet. After followup letters were sent, 24.82% of the measure pool did not have returned packets. There was a wide variation across classrooms and teachers in the percentage of forms returned and consent granted. These ranged from 100% return and 100% consent granted to less than 25% of each. The contributing variables were not investigated, but among the variables would be teacher influence and clarity of communication to the parents. The clarity of communication could be influenced by the reading levels of the parents, as well as a limited ability to communicate in English. The pool included students in classes to learn English, whose home language was not English.
Subjects were remeasured at two schools. Of the possible remeasure pool of 194 measured subjects, 173 (89.18%) were still enrolled and became the pool of remeasured subjects. This loss of measured subjects is accentuated by the lapse of time (4 and 8 months). The adjacent semesters for Time 1 were over a long holiday at the end of the calendar year. The adjacent semesters for Time 2 were over the summer and end of a school year.
Subjects were classified within five ethnic categories: Anglo, Asian/Oriental, Hispanic, Aleut/Native American, and Black (see Table 5). The number in each category is not controlled but is a result of student enrollment, parental consent, and student presence on the day of measurement.
Subjects' Side and Across MADED individual scores (viewing distances) were determined and ranked for each style of desk. The range of individual MADEDs and the upper and lower limits of the MADEDs and the near screening target distances for the measured and remeasured trials are shown in Table 10.


Desk Type /Trial 

MADED 
(inches) 
TDNPVS 
(inches) 







Range 
Upper Limit 
Lower Limit 
Upper Limit 
Lower Limit 
Side Desk 





Measured 
11.500 
19.875 
8.375 
18 
10 
Remeasured 
7.375 
16.375 
9.000 
18 
10 
Across Desk 





Measured 
9.875 
16.500 
6.625 
18 
10 
Remeasured 
8.00 
15.250 
7.250 
18 
10 
The individual MADED scores subsequently were used to establish the Side and Across MADED means. The TDNPVS of 10 to 18 inches, in increments of 1 inch, became the set of standards used in testing for significant differences between MADED means and the standard distances (Hypothesis One). The means of the MADED at each style desk are also used to test for significant differences between the means of the measured and remeasured MADEDs (Hypothesis Three).
Diopter differences were used to test Hypothesis Two. Individual MADED scores were converted to diopter equivalents by first changing inches to metric distance (1 inch = .0254 m) and then applying the formula D = 1/metric distance. The range of individual diopter equivalents is shown in Table 11.
Table
11:


Desk type 

Diopter 
equivalents 
(N = 1,135) 
Range 
Upper 
Lower 
Side desk 
+2.27 D^{a} 
[4.70] 
[1.98] 
Across desk 
+3.55 D^{a} 
[5.94] 
[2.39] 
NOTES 

^{a} Range equals upper limit minus lower limit. 
(Reciprocity limits application of D = 1/m to a single point of viewing distance.) 
The display of the range of individual diopter equivalents shows greater variation than is apparent when only means are displayed.
In developing the diopter equivalents of the MADED means, the means were first rounded to the nearest 1/8 inch and converted to metric measurement. This number was then converted to diopter equivalents by utilizing the formula D = 1/metric distance. The set of standards used in the test of significant differences for Hypothesis Two were unique for each cell. Each set was created by summing a D_{S} or D_{A} and the incremental powers (+0.25 D), in turn, across the range of plus fogging lenses (D_{FL}) reported by the states as being used to screen for hyperopia (D_{SFL} = D_{S} + D_{FL}; D_{AFL} = D_{A} + D_{FL}). The reported +D fogging lens ranged from 1.00 D through 2.50 D. The range of diopter equivalents and the range of the MADED scores cannot be shown on the same table giving upper and lower limits because reciprocity results in the upper limit of the MADEDs converting to the lower limits of the diopter equivalents, and the lower limit of the MADEDs converting to the upper limit of the diopter equivalents.
Presentation of the mean scores of the MADED at each style of desk for the different age spans (6month, 1year, 2year, 3year, and 4year) are shown in Table 12. The presentation includes the means of the MADED, standard deviations, and number of subjects for the described cells, and may be used as a norm table. The remainder of the norms are presented in Table 22, Table 23, Table 24, Table 25, Table 26, and Table 27, in Appendix Q.
Table
12:


Age Span 

Side Desk 


AcrossDesk 


n 
mean 
SD 
N 
Mean 
SD 




Sixmonth 


Young 6^{a} 






Old 6^{b} 






Young 7^{a} 






Old 7^{b} 






Young 8^{a} 






Old 8^{b} 






Young 9^{a} 






Old 9^{bc} 










Oneyear 


































Twoyear 




















Threeyear 




















Fouryear 









NOTES 
^{a} Year plus zero to 5 months 
^{b} Year plus 6 to 11 months 
^{c} Fewer than 10 subjects per cell 
All hypotheses were subjected to statistical analyses. Hypotheses One and Two were tested utilizing an independentsamples student's tTest (twotailed, p < .05). Hypothesis Three was tested utilizing a pairedsamples student's tTest (twotailed, p < .05). Table 13 illustrates the analysis of data for each student's tTest.
Table
13:


Hypothesis/Number of Tests Run 
Expected % 
Actual % 
Independent Samples (twotailed, p < .05): 


H 


H 


Paired Samples (twotailed, p < .05): 


H 


The basis for decisions regarding rejection or failure to reject Hypotheses One, Two, and Three is the relationship of the expected proportion of the tests that are significant and the actual proportion of the tests that are significant.
Hypothesis One states:
There is a significant difference between the mean of the MADED for each cell as described and each standard distance used as target distance for nearpoint vision screening (TDNPVS).
The actual proportion of student's tTests that were significant (twotailed, Independent Samples, p < .05) is 92.169%, which is greater than the expected 89% significant proportion. Therefore, Hypothesis One is supported.
Hypothesis Two states:
There is a significant difference between the mean MADED diopters (the mean of the MADED for each cell as described when converted to plus diopters of accomodation [D_{S}, D_{A}]) and the summed diopters (D_{SFL}, D_{AFL}) of the given plus diopters fogging lens and MADED diopters for a given cell.
The actual proportion of student's tTests that were significant (twotailed, independent samples, p < .05) is 95.080%, which is greater than the expected 89% proportion. Therefore, Hypothesis Two is supported.
Hypothesis Three states:
There is a significant difference between the remeasure/measure means of the MADED across time for the children in Time 1, Grades 1^{1} and 2^{1} and Time 2, Grade 1^{2} .
The actual proportion of student's ttests that are significant (twotailed, paired samples, p < .05) is 98.368%, which is greater than the expected 89% proportion. Therefore, Hypothesis Three is supported.
Results of tests of significance in the MANOVA procedures must be statistically significant before there is cause to examine univariate results. The univariate results determine the variables which contribute the most to overall differences (NoruÆis_1985).
Two analyses of variance (ANOVAs) were performed for effects of age, grade, and sex (8 x 4 x 2 design) for the Side and Across MADED means using MANOVA procedures (SPSSX). The first analysis includes the repeated measure factor, retesting on both the Side and Across MADEDs, thus being a true multivariate analysis of variance. The second analysis deletes the measurement factor and examines the difference between the Side and Across MADED measures, thus being a univariate analysis of variance (see Table14).
Table
14:


Source of 
Wilkes 
Approximate 
Hypothesis 
Error 
Significance of 
Age Group 





Grade 





Sex 





Age Group x Grade 





Age Group x Sex 





Grade x Sex 





Age Group x Grade x Sex 





Measure 





Age Group x Measure 





Grade x Measure 





Sex x Measure 





Age Group x Grade x Measure 





Age Group x Sex x Measure 





Grade x Sex x Measure 





Age Group x Grade x Sex x Measure 





The difference between the Side and Across MADEDs is computed as D_{A}  D_{S}. All of the resulting mean differences are of negative value. This indicates that the Side MADED is larger in value than is the Across MADED (see Table 15).
Table
15:


Age Group / Grade 
Mean 
SD 
n 
Young 6 



Grade 1^{1} 



Grade 1^{2} 



Old 6 



Grade 1^{1} 



Grade 1^{2} 



Grade 2^{1} 



Young 7 



Grade 1^{1} 



Grade 1^{2} 



Grade 2^{1} 



Grade 2^{2} 



Old 7 



Grade 1^{1} 



Grade 1^{2} 



Grade 2^{1} 



Grade 2^{2} 



Young 8 



Grade 1^{1} 



Grade 1^{2} 



Grade 2^{1} 



Grade 2^{2} 



Old 8 



Grade 1^{1} 



Grade 1^{2} 



Grade 2^{1} 



Grade 2^{2} 



Young 9 



Grade 1^{1} 



Grade 1^{2} 



Grade 2^{1} 



Old 9 



Grade 1^{1} 



Grade 1^{2} 



Grade 2^{1} 



Total Sample 



NOTES 
Cells with n = 1 were not tested. 
*Means which differ significantly. 
**Means which differ from other means of smaller value but do not differ from each other. 
The second analysis of variance shows a significant Fratio only on the threeway interaction among age, grade, and desk style (Side or Across). This effect was investigated further by univariate tests. The grades means are found to differ significantly for the following age groups: Old 6 (6 years, 6 months through 6 years, 11 months) through Young 9 (9 years, zero months through 9 years, 5 months). The interaction significance is due to the mean difference between Side and Across MADEDs not being consistent between grades when viewed across age groups. Therefore, Hypothesis Three is accepted.
Analysis of the data reveals that there are significant differences between the means of the Side and Across MADEDs and the target distances used for nearpoint vision screening (TDNPVS). Thus, Hypothesis One is not rejected. A mean may be shorter than some of the TDNPVS, or equal to or longer than others. There are significant differences between the diopter equivalents of the means of the MADED for each style of desk and the D_{SFL} and D_{AFL} (sum of each MADED diopter equivalent and each power of +D fogging lens used to screen for hyperopia). Thus, Hypothesis Two is not rejected. There are significant differences between the remeasure and measure means of the MADED involving the threeway interaction of age, grade, and style of desk. The means difference between the Side and Across MADEDs is not consistent between grades when viewed across the different age spans. Therefore Hypothesis Three is not rejected.