Identifying and Quantifying “Stress Factors”
in Schools and their Impact on Student Achievement

For the purposes of this investigation “stress” was operationally defined as “a demographic factor or factors that negatively impacted student achievement”.  Once more, these factors were identified as being largely beyond the school’s control.  The stress factors are directly related to the population of students a school serves.  The stress factors identified and used in this study include: 1) Student Attendance Rate, 2) Suspension Rate, 3) Percentage of students classified as English Language Learners (ELL), 4) Socio-Economic-Status (SES) based on free and reduced lunch counts, 5) Percentage of minority students, 6) Student Mobility Rate, and 7) Percentage of students in Exceptional Education.  While there are likely a number of additional stress factors that might impact student achievement we are restricted to those factors for which we have reliable data.  The dependent measure of student achievement was the 2005 (Arizona Instrument to Measure Standards (AIMS).  The percentage of students meeting or exceeding the State Standards on the AIMS was used as the measure of a schools academic performance. 

Tables 1a through 1d show the correlations between the stress factors and measures of academic achievement broken out by subject area and grade level.  As can be seen in the tables, the highest correlations were between SES and percentage of students passing the AIMS.  The positive correlations between SES and AIMS indicate that as SES increases the percentage of students passing the AIMS also tends to increase.  Likewise, the negative correlations between mobility rate and AIMS indicate that as mobility rate increases the percentage of student passing the AIMS tends to decrease.

While the correlations between stress factors and measures of academic achievement might on the surface indicate that all the chosen stress factors have a substantial impact on student achievement it is likely that a number of the chosen stress factors also correlate with one another and therefore do not contribute unique information.  As a first step in determining the relationship between the stress factors, correlations were calculated between all the stress factors, shown in Table 2.  As can be seen in Table 2 there tended to be high correlations between SES, percentage of minority students, and percentage of ELL students.  This finding suggests that minority status alone has little direct impact on achievement.  It appears more likely that minority status is an indirect measure of SES and ELL status given the higher percentage of minority students in the lower SES group and the much larger percentage of minority students who are learning English as a second language compared to non-minority students. This interpretation will be further supported by the results of the Multiple Regression found in Table 3.

Table 3 shows the result of a Multiple Regression using stress factors to predict the percentage of students passing the AIMS.  The Multiple Regression combines all the unique variance or information from all the predictor variables (stress factors) to form a single correlation called a “Multiple Correlation” denoted using a capitol “R”.  As can be seen in Table 3 the multiple R was .82 with an R² value of .68.  R-squared indicates the amount of variance in the dependent measure (AIMS) that can be accounted for by the predictor variables (stress factors).  The obtained R² value of .68 means that 68% of the variability in academic achievement as measured by the AIMS can be explained by the stress factors that were included in this model.  A multiple correlation of 1.0 would result in the ability to make perfect predictions.  The column in Table 3 labeled “B” are the regression weights, they are used in a linear equation by multiplying them by their corresponding variable then summed to calculate a single value called a predicted score.  The B-weights are on the same scale as their corresponding variable and therefore are not directly comparable.  The column labeled “Beta” on the other hand are standardized to the same scale and are directly comparable.  Looking at the beta weights it can be seen that the best single predictor of AIMS performance is SES followed by Mobility.

The derived regression equation is used to predict the percentage of students passing the AIMS for each school in the district.  The predicted value for each school serves as an indicator of stress.  The predicted value is finally rescaled to form a T-score having a mean of 50 and a standard deviation of 10 (Stress Index).  Since the T-score is based on all the schools in the district each school’s Stress Index is relative to other schools within the district.  Referring to the normal curve it is know that a school receiving a Stress Index one standard deviation above the mean (60) would have a stress level greater than approximately 84% of all the schools in the district.

A very useful byproduct of running a multiple regression can be obtained by subtracting the predicted value from the actual obtained value.  In this case we subtracted the predicted percentage of students passing the AIMS from the actual percentage of students passing the AIMS.  The resulting value following subtraction is called a residual (obtained – expected = residual).  By subtracting the predicted value from the obtained value we remove all variance associated with the predictors, in this case the demographic variables we have included in our model.  The resulting residual can be either a positive or a negative value.  A negative value can be interpreted as a school scoring lower than expected, while a positive value can be interpreted as a school scoring higher than expected.  In this case a positive residual would indicate that the percentage of students passing the AIMS is higher than expected given the demographic composition of the school.  The reverse (negative) residual would suggest the opposite interpretation.

As a final check, correlations were run between the Stress Index and the dependent measures (AIMS passing rate), and the residual.  As can be seen in Table 4, the amount of stress in a school is highly predictive of a schools academic performance.  The very small correlation between the residual and the Stress Index indicates that the effects of the stress factors have been removed from the residual.  The advantage of removing the effects of stress is that it allows schools to be directly compared as if all schools serve the same demographic population of students.  When the residuals are the basis of comparison among schools they are often referred to as School’s Effectiveness Index (SEI).

Table 1a

Elementary Schools N

Table 1b

Middle Schools N

Table 1c

High Schools N

Table 1d

All Schools N

Table 2

Table 3

R = .82       R˛ = .68     

Table 4

N=116

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