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A Methodology for Analyzing the Association Between Student Performance and Indoor Air Quality

Posted on: Tuesday, 23 March 2004, 06:00 CST

ABSTRACT

Past research that has evaluated the association between student performance and some change variable (building renovation, room temperature, curriculum, teacher involvement, etc.) has focused on student-level data and has not adequately accounted for regression artifacts (regression to the mean). The methodology presented in this paper provides guidance for the analysis of school-level student performance results through the use of the Smirnov test (randomness), Lilleifors test (normality), Daniel's test (cohort trends), and chisquared test (renovated to non-renovated differences). Recommendations are provided for setting up future research to avoid problems and obtain better results.

INTRODUCTION

For over 40 years sehool districts have investigated the link between the indoor environment and student performance. The primary focus of this research has been on evaluating how students perform at different tasks under varying comfort conditions. Some of the key studies include:

* McNaIl and Nevins (1967) accomplished some of the first documented research on the impact that comfort had on student performance when they tested the hypothesis that "thermal environmental control in or near the comfort zone facilitates academic achievement of junior High School students" in 1959. The results indicated strong non-statistically significant trends in academic achievement favoring the air-conditioned school. However, statistically, the research could not determine if it was the air- conditioning or other variables such as student motivation, previous preparation of students, teacher variables, or socioeconomic backgrounds that resulted in improved performance in the air- conditioned school.

* Schoer and Shaffran (1973) summarized three experiments on comfort and student performance. The basic approach for all of the experiments was to bring two matched groups of students from the Saydel School District north of Des Moines, Iowa, to a laboratory facility. The laboratory facility had two identical classrooms where the temperature and humidity could be independently controlled. The coursework and tests were identical for the two classrooms, with one classroom airconditioned and the other just ventilated. The primary result of these experiments was that complex tasks were affected more than simple learning.

* As a marker for the quality of the indoor environment, Myhrvold et al. (1996) compared the concentration of carbon dioxide to student performance over a three-year period in eight Norwegian schools. The conclusion reached through this study was that higher carbon dioxide levels, indicative of poorer indoor air quality, resulted in reduced performance. However, the relationship was not statistically significant.

* Green (1974) evaluated the indoor environment by examining the key absenteeism rate in schools as a function of the humidity in six schools in both Saskatoon, Saskatchewan, and the City of Halifax, Nova Scotia, during the winter of 1960-1961. The study concluded, "Increasing the relative humidity of occupied spaces from 20% to 50% rh reduces illnesses where the occupants are in close contact and are particularly susceptible to upper respiratory infections."

* A study completed for the Alliance to Save Energy by the Heschong Mahone Group ( 1999) compared the test results from 21,000 students as a function of the level of daylighting in 2,000 elementary school classrooms in three school districts (Los Angeles, California; Seattle, Washington; and Fort Collins, Colorado). The results showed that "students with the most daylighting in their classrooms progressed 20% faster on math tests and 26% on reading tests in one year than those with the least." Further, "students in classrooms with the most daylighting were found to have 7% to 18% higher scores than those in rooms with the least."

In addition to studies linking the indoor environment to student performance, other research has focused on looking at the influence of organizational and curriculum structure, family involvement, type of test, socioeconomic status, resource deployment, and teacher efficacy. The following is a summary of these studies.

* Wise (2000) evaluated the effect that organizational structure had on student performance by comparing test scores from the Indiana Department of Education database for those students that attended middle school (Grades 6-8) to those that attended junior-senior high school (Grades 7-12). The results of this research showed that "on average junior-senior high students perform better on math tests than do students in middle school."

* Ebrahim (2000) evaluated the impact that using integrated math, science, and technology programs had on student performance. This was accomplished by comparing the number of times it took students to pass the Ohio standardized proficiency tests and the passing scores for students in the integrated program (58) with those in the non-integrated program (221). The results indicated that those students that had two or more courses in the integrated program scored significantly higher ([alpha] = 0.05) on the science subsection of the standardized proficiency test than students who did not have any integration.

* Stuhlman (2000) evaluated the student performance changes after an intervention in the curriculum due to poor performance on standardized tests had been accomplished. This analysis evaluated over a four-year period the improvement in performance in an average of eight school districts with intervention compared to the district average increase. The results indicated that the performance of students improved over the short term but then decreased over the long term.

* Thompson (2000) "explored the history of a unique elementary school and how parent involvement evolved as a part of the school's culture." The findings indicated that when "parents, teachers, and administration have a very high perception of the school, this has a positive impact on student performance."

* Cakan (2000) investigated the interaction of cognitive style and the assessment style of tests. The cognitive style (field dependent or field independent) was determined through interviews using the group embedded figures test (students are asked to identify a specified simple figure that is embedded in a more complex figure). Overall, the results indicated that compared to multiple-choice format, the performance-based assessment of a second language is less affected by cognitive style, ethnicity, gender, and socioeconomic status.

* Fricker (2000) examined the test medium in two informational system courses. The types of media were paper, electronic, and telephone media. The results indicated that for the lower-level grade, there was no difference in performance based on the medium. However, for the higher-level grade, there was a significant relationship ([alpha] = 0.05) between the medium and achievement.

* In analyzing the effectiveness of North Carolina's accountability model. Knight (2000) showed the importance of socioeconomic status in the analysis of performance data. In her research, the ethnicity of the school was highly correlated with the improvement in performance of the students after the accountability model was implemented. She also showed that "higher family income students performed better on achievement tests."

* Freeman (2000) showed that the amount of money allocated to a school is positively correlated to the performance of its students. This was determined by comparing the resource allocation in four schools (one low, two average, and one high performing) in Tennes see.

* Magers (2000) showed that "metropolitan schools appropriated a significantly higher amount than suburban, town, and rural corporations in the area of instruction." Also, metropolitan schools' appropriations for support and business services were significantly higher than rural schools. Relative to student performance, support service allocations were the best predictor for metropolitan schools and instruction appropriations for town school corporations.

* In evaluating the effect of resource allocation on student outcomes Shive's (2000) central finding was "that lower levels of faculty education and faculty experience consistently predicted lower student outcomes." This study included three years of data for approximately 2,500 schools in Florida, composed of 69 school districts.

* Sonnen (2000) in a study of resource allocation and student performance in 150 Texas elementary schools near the Texas-Mexico border showed that student performance increased with increasing teacher salary.

During the review of this past research in preparation for evaluating the association between renovation status and student performance in the Houston Independent School District, it became evident that few of the methodologies used for analyzing data attempted to verify the data sets for randomness and normality, and none evaluated the results for regression artifacts (regression to the mean). Therefore, during the completion of the recent research, a methodology was developed specifically focusing on the analysis of student performance data relative to building or system renovation. The methodology was applied to renovation of the central cooling systems and lighting in approximate\ly 30% of the schools in the Houston Independent School District.

This paper presents the methodology developed, limitations of the methodology, guidelines for future research, and conclusions from the methodology. It is not the intent of this paper to provide a detailed discussion of the statistical methods or alternatives available. Information on the details from applying the methodology to the Houston Independent School District renovations is provided in other publications (Dorgan 2003,2001).

METHODOLOGY

The basic methodology (Dorgan 2001 ) presented in this section is for evaluating the change in school-level student performance relative to a change incidence. The change incidence for which this methodology was developed, tested, and refined was the replacement of the central cooling systems and the classroom lighting.

The methodology compares the pre- and post-renovation performance of students for a renovated set of schools against a nonrenovatcd set of schools. Typical performance indicators include standardized test passing rates, student attendance rates, student promotion rates, and student disciplinary actions. The methodology assumes that historical data are available for the analysis, which was the case for the Houston schools.

It should be noted that one of the bases for developing this methodology was to eliminate improvements in the measured factors, based strictly upon improvement related to other influences. This was the case for the Houston schools, as all schools improved in most of the measured benchmark parameters over the eight-year data set. This is the most important aspect of many previous studies that has been ignored, in that they are not strictly evaluating the intervention contribution independent of other factors. It is very difficult to achieve this when there are not equivalent schools in the same district, city, or county.

Based on the previous research completed on indoor environment and student performance and on the various confounding factors, the basic information that should be collected includes:

* School data includes the school name, address, district, grades served/type, and the number of administrative staff (counselors, assistant principals, other professional staff, educational aides, and auxiliary staff) assigned to the school.

* Student demographics-includes enrollment, gender, ethnicity, mobility, students by program, free/reduced cost lunch, at-risk students, limited English program students, and attendance rate.

* Teacher demographics-includes number, gender, ethnicity, attendance rate, average experience, years of experience, teachers by program, and advanced degrees.

* Student performance-includes percent promoted to the next grade, the number of disciplinary actions taken, and the percentage of those passing standardized tests. If possible, actual passing scores for the tests should be used, though the number and percent passing can be used.

These variables are required to identify and account for confounding factors (sociocconomic, ethnicity, location, age, etc.) to avoid reporting of a nonexistent statistical relationship. Additional variables detailing the socioeconomic distribution of the school's neighborhood could also be included. However, this information is considered difficult to obtain for historical studies. For this study it was assumed the student and teacher demographics would identify key confounders and differences.

For the performance information to be comparable over any length of time, the standardized test used should be developed and graded such that the results from year-to-year and from grade-to-grade can be directly compared (TEA 2000). For example, the 4th grade reading test results for year one can be directly compared to the 4th grade reading test results for year two. In addition, with this approach, it should also be possible to compare the 4th grade year one reading test results with the 5th grade year two reading test results to estimate the progression of the student or group from year-to-year.

Due to the unknown quality and depth of historic data sets, a stepped analysis methodology was developed, where the analysis only progresses when it is determined that the type and level of data warrant more complex analysis techniques based on reliability and accuracy criteria. More complex statistical methods could be employed when a step fails in this methodology to further analyze the data, such as transformations and nonparametric alternatives that were not the intent of the research.

The six primary steps used for analyzing the data are: ( 1 ) data input, (2) evaluation of pre-renovation data sets, (3) examination of descriptive statistics, (4) initial analysis of associations, (5) advanced analysis of associations, and (6) final modeling.

Data Input

For the first step, the historical data are entered into an industry standard statistical analysis computer tool (SAS 2000). The validity and accuracy of the data are then verified through two tasks. The first task entails summing of percentages for those variables that should equal 100% (e.g., gender, ethnicity, school funding, etc.). Where the summed values do not equal 100%, then the original data set is reviewed. If the original data set is in error (published values did not add to 100% due to founding or data entry error), then the largest percentage number is modified to obtain 100%. However, if the original data set is in disagreement by greater than 4%, then the difference is proportionally distributed among the variables (e.g., male/female).

The second task is the independent random entry verification of 20% of the data (every 5th entry). Any errors found are rectified. If the rate of entry errors is less than 0.1%, then the data set is assumed to be accurate (Wise 200O).1 If the rate of entry errors is greater than 0.1 %, then another 20% is verified. If the error rate is still greater than 0.1%, then the entire data set is verified.

Evaluation of Pre-Renovation Data Sets

Prior to analyzing any data, it was important to remove all nonrenovated school types that did not have a renovated counterpart. This was accomplished to eliminate extraneous data that could skew the results due to unique school requirements from makeup of the grades (Conover 1999).

The Smirnov test should be completed using the pre-renovation data forthe entire district (all grades), forthe low grades (3, 4, 5, and 6) and for the high grades (7, 8, and 10) for each of the standardized test results (math, reading, and writing). The low and high grades are analyzed separately to account for the potential differences in the teaching and learning styles. (Prior to analyzing any data, it was important to remove all nonrenovated school types that did not have a renovated counterpart. This was accomplished to eliminate extraneous data that could skew the results due to unique school requirements from makeup of the grades [Schoer and Shaffran 1973].)

The advantage of the Smirnov test is that it is "consistent against all types of differences that may exist between the two distribution functions;" whereas, other tests, such as the median test, the Mann-Whitney test, or the parametric t test, "are sensitive to differences between the two means or medians, but they may not detect differences of other types, such as differences in variances (Conover 1999)."

"Acceptance of the null hypothesis does not mean that the parent population is normal, but it does mean that the normal distribution does not seem to be an unreasonable approximation to the true unknown distribution; therefore, either nonparametric methods or parametric statistical procedures that assume a normal parent distribution may be appropriate for further testing with these data (Draper and Smith 1981)."

The Lilleifors test is completed for those data sets that are shown to be the same using the Smirnov test.

If the Lilleifors test shows that one of the data sets (renovated or nonrenovated) is a good approximation of a normal distribution and the other docs not, then the 0.99 quantile is calculated. Since it has already been shown with the Smirnov test that the renovated and nonrenovated data sets are from the same function, it is a reasonable assumption that using the less stringent 0.99 quantile is acceptable.

If the Lilleifors test shows a non-normal distribution, the subsequent chi-square test can be accomplished to better understand relationship. However, the correlation and regression tests used in this research project and the methodology developed would not be valid. There are multiple other nonparametric tests available that could be used for additional analysis and interpretation. The options and discussion of these are beyond the scope of this paper.

Examination of Descriptive Statistics

The third step is to calculate the descriptive statistics (mean and standard deviation) to provide a basic understanding of the data sets with the purpose of identifying potential confounding factors and associations that could skew subsequent analyses. The calculations are accomplished for the data sets found to be randomly assigned and normally distributed. The descriptive statistics are calculated for the performance variables, with the following data sets analyzed:

* Pre-renovation

* Post-renovation

* Combined grades (e.g., Grades 7, 8, and 10)

* Reading, writing, and math tests passing percentages

* Number of students passing (passing rate times number of students per grade)

As part of the descriptive statistics analysis, the pre- to post- renovation data sets are evaluated to identify if the regression to the mean phenomenon is occurring (Trochim 1999). This phenomenon is where someone with a high score on one test has a high probability of scoring lower on the next test and where someone with a low score on one test has a high probability of scoring higher on the next test.

The general result of Equation 10 is \that data sets that are highly correlated have a low regression to the mean relationship, and those data sets that are not correlated have a high regression to the mean. Since "there is no statistical analysis that can remove or eliminate regression artifacts" (regression to the mean), the regression to the mean analysis is used to identify potential explanations of the statistical analysis results (Winer 1971). Therefore, for those data sets that have a high regression to the mean, the results need to be evaluated and used carefully to avoid incorrect conclusions.

Initial Analysis of Associations

Variables that represent similar confounders are identified and discussed (e.g., ethnicity and special programs). The variables that are included are those with a significant (p-value < 0.05) Pearson correlation coefficient of between 0.7 and 1.0 according to the following (Rea and Parker 1997):

* 0.9 to 1.0 very high correlation

* 0.7 to 0.9 high correlation

* 0.5 to 0.7 moderate correlation

* 0.3 to 0.5 low correlation

* O to 0.3 little if any correlation

To better understand the relationship between performance of the renovated and nonrenovated schools, population data (percent passing) is transformed to the actual number of students or teachers to enable the calculation of the chi-squared value (see Equation 12 and Table 1 ). This transformation is accomplished by multiplying the percentage values by the number of students or teachers per grade.

TABLE 1

Chi-Squared Calculation Inputs

An important limitation to recognize of the chi-squared analysis is that it only indicates if there is a relationship, not which direction the relationship is in. Therefore, the results of the chi- squared analysis must be combined with the correlations determined during previous and subsequent analyses to actually comprehend.

As many chi-square calculations as possible should be completed to better understand the relationship between renovation and the performance indicators. In addition to the individual performance indicators, the chi-square should be calculated for subsets of data (different school types) and for combining the performance indicators over grades.

Similar to the chi-squared analysis, the Daniels trend test statistic does not provide which data set has the larger increase.

Advanced Analysis of Associations

To progress from the initial to the advanced analysis of association requires that the chi-square and mean difference analyses indicate a promising association that may be hidden or exaggerated by confounders (Pearson correlation coefficient analysis). If this is the case, then the next step is to use a general least squares linear regression modeling approach to test the association between school renovation and performance relative to potential confounding variables. This is done to better quantify the relationship by determining its direction and accounting for confounding variables, such as demographics (Yandell 1997).

The linear regression model is used to regress the change in test results against the renovation status and on all previously identified potential confounding variables, according to Pearson correlation coefficient.

Final Modeling

To progress beyond linear regression requires that the linear regression show a result, but it is not conclusive either due to inconsistent results between the performance indicators or the indication of a relationship that is not statistically significant.

A potential limitation of school data is that differences in operations of schools and school types have an effect on the variability of performance indicators. This variability needs to be accounted for in the final analysis to verify the relationships found are not caused by other factors. Therefore, to better evaluate the true relationship of change in performance relative to renovation status requires a statistical model that goes beyond the fixed (renovation) effects to include the random effects encountered in typical school testing applications.

A general linear mixed-effects modeling approach is used for this purpose as the final model to test the association between school renovation and test scores (Littcll ct al. 1996). The mixed-effects model is chosen for its simplicity and ability to account for the random effects in the results. This model is implemented as follows (Sen and Srivastava 1990).

The data table is set up so that school, school year, and grade level (3-8, 10) jointly and uniquely define each row of data. To distinguish the data from the pre-renovation years (1993-1995) with the post-renovation years (1996-1999), a binary indicator variable called "era" is formed (O = pre-renovation. 1= post-renovation). A second binary indicator variable ("renovation") is formed to distinguish data collected from schools that had a renovation (= 1 ) with those that did not (=0). .

"Baseline" mixed-effects models regress test scores (TAAS math, reading, and writing) on school (random effect), and grade, era, renovation, and era*renovation interaction (fixed effects). With the proper coding of the era and renovation variables, the estimated coefficient of the era*renovation interaction is an estimate of the excess increase in test scores from the pre- to post-renovation eras associated with having a renovation. This is the main association of interest in the analysis. Significance tests (t-tests) and 95% confidence intervals for the interaction term are calculated.

After fitting the baseline models, additional interactions with important covariatcs (e.g., year, grade) are tested for significance. A conservative alpha-level of 0.01 is used to define statistical significance for the interaction terms because multiple tests are performed on variables that are not testing the central a- priori hypotheses. Potential confounding by covariatcs (e.g., variables representing school demographic profile) is assessed by (separate) addition of each covariate to the "baseline" models. Covariates whose addition to the "baseline" models resulted in a 10% or greater change (from "baseline") in the estimated coefficient of the era*renovation interaction are considered confounders.

Confoundcrs with substantial missing data are removed from consideration. However, as a check, the missing data confoundcrs are compared with other confounders to verify they are correlated with an included confbundcr.

Final models are built by addition of all potential confoundcrs to baseline models. Regression diagnostics are then performed on the models to assess substantial deviations from model assumptions. The regression diagnostics include:

* Evidence of non-normality of the residuals. This is accomplished by plotting the histogram of the residuals and visually inspecting for normality (Sen and Srivastava 1990).

* Evidence of non-constant variance. This is accomplished by plotting the residuals versus the predicted values and important predictor variables. If a fan-like pattern with greater variability for larger predicted valucs results, then there is nonconstant variance (Campbell and Kenny 1999).

LIMITATIONS OF METHODOLOGY

As the methodology presented focuses upon the use of historic data that are limited by what was collected, there are several limitations of the methodology:

* Confidence Level: The confidence level used (95%) was based on what has been traditionally used in past research and was chosen due to the limited data set and not to eliminate the identification of potential relationships with too strict oflevel (e.g.. 97% or 99%).

* No Relationships: The identification of no relationships does not mean that none exist. This methodology is intended to provide an easy means to quickly identify the effect of interventions on performance. Depending upon the actual data set, additional nonparametric techniques may be required.

* School Level: The published data readily available from most school districts and states is for the school level. Obtaining student-level data is often very costly and requires additional parental approval. Therefore, the methodology is limited to this type of data set and is intended to be structured for such analysis.

* Step-Wise Approach: Using the step-wise analysis approach can eliminate datasets that could be analyzed using transformations and nonparametric methods.

Future Research Guidelines

Based on the results of applying the methodology to the Houston Independent School District renovations, future research can apply the methodology presented in this paper to focus on clearly documenting the link between indoor air quality and student performance. To accomplish this, the following is suggested:

* Identify and elicit support of school districts with the ideal study characteristics -These school districts need to be willing to accomplish defined improvements to subsets of their facilities, or already have accomplished an improvement in systems or operations on only a portion of their schools.

* Define scope of interest-The scope of the study relative to the type and number of schools to be analyzed needs to be defined. It may be beneficial to focus on just elementary or high schools to ensure comparison of performance change is between similar schools. The scope of interest needs to also contain the performance variable to be measured. This should include absenteeism, promotion, and test results.

* Define improvement to evaluate-The improvement to be accomplished on a subset of schools needs to be identified and documented and a hypothesis created as to the effect on student and teacher performance. For example:

* Maintenance. The maintenance program for a subset of the schools could be improved or contracted out to determine if having improved maintenance has an impact on the performance. The hypothesis is that the improved maintenance will improve the indoor environmental quality by having consistent conditions in the space that meet the comfort requirements. In\door environmental quality markers such as temperature, humidity, and outdoor airflow need to be measured before and after the change in maintenance to ensure the link between the maintenance and performance could be evaluated.

* Comfort. Similar to, and as a subset of the maintenance study, comfort could be improved in a subset of schools through improved control or determining the optimal setting. The actual characteristic to study would have to be determined. Is it the difference in maintaining consistent comfort levels in a space versus lack of consistency, or is it the comparison of two different comfort levels? The focus of the research and outcomes may be different. The basic hypothesis is that improving the stability or level of comfort in a school increases performance. Comfort is influenced by multiple factors ranging from management to physical, social, and mental.

* Lighting. It would be beneficial to accomplish research on daylighting and other lighting systems by comparing a subset of renovated schools to nonrenovated schools. The hypothesis would be that the use of daylighting improves student and teacher performance.

* Ergonomics. The physical comfort of sitting all day in a classroom can have significant impacts on the ability to learn. If a student is uncomfortable, he/she will be less likely to concentrate on what the teacher is saying. Therefore, the same study methodology could be used in comparing two different styles of chairs and desks. The hypothesis would be that the more ergonomically designed furniture would improve performance.

Each of these improvements should be implemented one at a time to simplify the analysis and minimize the confounding of variables. At some point it may be beneficial to combine several factors to determine if the effects on performance are additive.

* Define length of study-The length of the study is important in that a short study period is not conducive to fully documenting the change. Since most standardized tests are only given once a year, it is recommended that at least two years of pre- and post-renovation data be available for analysis. This often makes retrospective (historic) studies much more economical. If other performance measures, such as surveys or intermediate tests, are used, then the length of the study can be reduced.

* Define methodology-Using the methodology defined in this current research; developing the specific methodology for collecting and analyzing the data must be accomplished. This methodology must focus on minimizing confounding factors and any action that would adversely impact the study subjects. Key concerns with implementing the methodology are (Campbell and Kenny 1999):

* Randomization of renovated school selection-This is required to minimize the regression to the mean effect, to use any of the parametric analysis techniques (linear regression and mixed-effects models), and to obtain proof of causality.

* Balance of having one nonrenovated school for each renovated school is ideal. Skewed distribution of renovated schools by school types can cause problems with the data analysis and limit the results, as was shown in this research. The level of balancing can extend from the school down to the classroom depending on the data available for comparison.

* Proper application of the techniques used in the methodology should be verified. Blind application of the statistical tools will likely result in poor or misinterpreted results.

* Complete analysis-Use the methodology developed to complete the analysis of the collected data. As part of the analysis, evaluate the methodology used and make recommended changes to the methodology for future research.

Ideally, concurrent studies across several school districts would be completed to provide for a stronger power study, to provide decision-makers with the facts and supporting information needed to properly construct and maintain our nation's schools.

CONCLUSIONS

This methodology, using historical data for analyzing the impact of improving indoor environmental systems, is intended to enable future researchers to evaluate the effect that changing the environment has on student and teacher performance. In addition, the discussion of setting up the research and of key issues to account for in the data analysis is intended to provide a cohesive approach applicable to a wide range of performance-based studies.

ACKNOWLEDGMENTS

I would like to acknowledge those who have made this paper possible. First and foremost was the support and guidance of my doctoral committee at the University of Wisconsin-Madison, composed of John Mitchell, Matty Kanarek, Ramon Aldag, Michael Smith, Henry Anderson, and Marc Anderson.

In addition, the grant from the American Society of Heating, Refrigerating and Air-Conditioning Engineers and the data supplied by the Houston Independent School District were critical to being able to complete this research.

1 Verification procedure based on statistical random sampling philosophy.

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Chad Dorgan, Ph.D., P.E.

Member ASHRAE

Chad Dorgan is director of Facilities Science & Technology, Farnsworth Group, Inc., Corona, Calif.

Copyright American Society of Heating, Refrigeration and Air Conditioning Engineers, Inc. 2003

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