In response to the ongoing debate over equity in public school expenditures, a collection of data was recently compiled in attempt to shed light upon the argument of whether individual states and geographical regions are getting what they pay for. Although some argue that finances to support public schools are spent disproportionately thereby yielding disproportionate levels of academic success among our nation’s students, others suggest money spent is statistically unrelated to student success rates. In this dataset all of variables were collected from each state, and extracted from the Digest of Educational Statistics, where the primary purpose of the Educational Statistics publication is to provide prekindergarten through graduate school information on a variety of subjects related to public and private education, primarily compiled by the National Center for Education Statistics (NCES).
Frequency Distributions of the Dependent Variables
In this study, the independent variables include each of the 50 United States including the District of Columbia. In some investigations the four geographical regions of the U.S. are compared. These regions include the West, Midwest, South, and Northeast. A breakdown of the states included in each region is given later in this report. The dependant variables in the continuous data include, but are not limited to: current expenditures per pupil in average daily attendance in public elementary and secondary schools, average pupil/teacher ratio in public elementary schools, estimated average annual salary of teachers in public education, and percent of students in elementary and secondary schools who are eligible for free or reduced-price lunch. Figure 1 shows the frequency distribution of the current expenditures per pupil in average daily attendance in public elementary and secondary schools, 2005-2006. Of the 51 states data was collected from, only one state spent less than $7,000.00 per pupil in average daily attendance and that was Utah at $5,960.00. Similarly, only one state spent more than $17,000.00 per pupil and that was the District of Columbia, spending $18,339.00 per pupil in average daily attendance in public school.
Figure 1. Expenditures per Pupil Histogram (thousands of dollars)
Results
Data analysis was compiled using numerous tabular and graphic tables available in Microsoft Office Excel, edition 2007. Figure 1. is a distribution of Expenditures per Pupil (raw scores) shown on the horizontal axis in thousands of dollars spent, with intervals of one thousand dollars along the abscissa. The ordinate indicates the frequency of occurrence by the independent variable, states, along the y axis.
Expenditure per pupil spending in the District of Columbia is an outlier, as indicated in Figure 2., a box plot of expenditures per pupil. A five-number summary of the data in Figure 2. displays the dispersion of the data, highlighting the minimum and maximum of the data, median expenditure, and the lower (Q1) and upper (Q2) quartile of the data. The expenditure per pupil for the District of Columbia at $18,339.00 falls beyond the Q2 and could be considered an outlier.
Figure 2. Expenditures per Pupil Box Plot
Distribution of Average Pupil / Teacher Ratio in Public Elementary Schools
Figures 3. and 4. display the distribution of the average pupil to teacher ratio in public elementary schools taken from the fall 2005 school year.
Figure 3. Average Pupil / Teacher Ratio in Public Elementary Schools Histogram
Figure 4. Average Pupil / Teacher Ratio in Public Elementary Schools Box Plot
Figure 4. shows the corresponding box plot for average pupil / teacher ratio in public elementary schools. Figure 4. shows the lower whisker, 10.8, is the lowest pupil to teacher ratio in the U.S. in Rhode Island. The upper whisker score, 20.8, is the highest pupil to teacher ratio, in the state of California. Utah’s pupil to teacher ratio of 22.8 to 1 is considered an outlier score.
Distribution of Estimated Annual Salary of Teachers in Public Elementary & Secondary Schools
Figures 5. and 6. illustrate the estimated annual salary of teachers in public elementary and secondary schools. The box plot below, show that there are no outliers in state’s wages among teachers.
Figure 5. Estimated Average Annual Salary of Teachers in Public Schools Box Plot, 2005-06.
Figure 6. Estimated Average Annual Salary of Teachers in Public Schools Histogram, 2005-06.
The state with the highest estimated salary is California, at an average of $61,372.00 annually. South Dakota pays its teacher’s the least in estimated annual salary at an average of $35,607.00.
Distribution of Percentage of Students Eligible for Free or Reduced-Price Lunch
Figures 7. and 8. Display the percentage of elementary and secondary students eligible for free or reduced-price lunch.
Figure 7. Percent of Students Eligible for Free or Reduced Lunch Histogram
Figure 8. Percent of Students Eligible for Free or Reduced Lunch Box Plot
The data illustrated in the histogram shows that only one state has less than a quarter of its students qualifying for free or reduced-price lunch. That state is New Hampshire, which has 17.70% of elementary and secondary students qualifying for free and reduced-price lunch. The box plot shows that there are no outliers, and that the state with the highest percentage of free and reduced lunch qualifiers is Mississippi, with nearly 68%.
Frequency Distribution of Categorical Data
Further statistical analysis was conducted to determine the frequency distribution of the aforementioned dependent variables, by the independent categorical regions. The four U.S. regions include the West, Midwest, South, and Northeast. A breakdown of the states included in each of the four regions is shown in Table 1.
| West | Midwest | South | Northeast |
| Alaska | Illinois | Alabama | Connecticut |
| Arizona | Indiana | Arkansas | Maine |
| California | Iowa | Delaware | Massachusetts |
| Colorado | Kansas | D.C. | New Hampshire |
| Hawaii | Michigan | Florida | New Jersey |
| Idaho | Minnesota | Georgia | New York |
| Montana | Missouri | Kentucky | Pennsylvania |
| New Mexico | Nebraska | Louisiana | Rhode Island |
| Nevada | North Dakota | Maryland | Vermont |
| Oregon | Ohio | Mississippi | |
| Utah | South Dakota | North Carolina | |
| Washington | Wisconsin | Oklahoma | |
| Wyoming | South Carolina | ||
| Tennessee | |||
| Texas | |||
| Virginia | |||
| West Virginia |
Table 1. U.S. States by Region
Figure 9. is a box plot displaying the frequency distribution of current expenditures per pupil in average daily attendance in public elementary and secondary schools for the 2005-2006 school year.
Figure 9. Expenditures per Pupil by Region
Again, we see that the District of Columbia indicated as the 9th state, listed in alphabetical order, spends over $18,000.00 per pupil, creating an outlier score for the South region. A closer look at the plot indicates the highest and lowest expenditures per region, as well as the upper and lower quartile for each.
Figure 10. displays the average pupil to teacher ratio for students in public elementary schools categorized by region, fall 2005.
Figure 10. Pupil / Teacher Ratio in Elementary by Region
Comparing Figure 10. with Figure 4., Utah’s pupil to teacher ratio of 22.10 / 1, is no longer indicated as an outlier when categorized with like pupil to teacher ratios for the additional 12 states in the West region. In Figure 10. our attention is drawn to the state of Virginia, number 47., in which the pupil to teacher ratio of 11.70 / 1 is considered low comparative to the South region’s other 16 states.
Estimated annual teacher salary by region, 2005-2006, is shown in Figure 11.
Figure 11. Estimated Average Teacher Salary by Region
While Figure 5. showed no outliers scores in teacher salary nationwide, our attention is again drawn to the South region in Figure 11., where it is evident that three states have an unusually high estimated, annual teacher salary, comparative to other states within the same region. They are, the District of Columbia at an average of $60,526.00, Maryland at $55,738.00, and Delaware at $55,667.00. Interestingly, Figure 9. showed that the District of Columbia had the hightest expenditure per pupil at an average of $18,339.00. Figure 11. indicates that D.C. also pays its teachers the highest annual salary, on average.
Figure 12. Percent of Students Eligible for Free / Reduced Lunch by Region
At comparing categorical data within the four regions, Figure 12. illustrates the percentage of students in elementary and secondary public schools who are eligible for free or reduced-price lunch by region, 2006-2007. Again, Figure 8. merits a second look, where it is shown that nationwide there aren’t any outlier states with either high or low free or reduced lunch eligibilities. However, a study of Figure 12. reveals that New Mexico (state 32), at nearly 61%, has a high percentage of students eligible for free or reduced lunch, compared to the remainder of the West region, which has a median percentage of eligible students under 40%. Similarly, our attention is drawn to the Northeast, where New York (state 33), also has a much higher percentage of students eligible for free or reduced-price lunch at 43.5%. Interestingly, the Northeast region also includes the state with the lowest percentage of student eligibility. New Hampshire (state 30) has an estimated 17.7% eligibility for student free or reduced price lunch.
Statistical and Practical Significance
Returning to the discussion of expendiures per pupil it can be assumed that since the distance between sucessive scale points are assumed to be equal, money spent is a scale of measurement provided in interval form. Reflecting on the controversy of amount of money spent yielding higher or lower student success rates, and considering that the research includes the use of post-facto data, a hypothesis of difference requires testing. The division of the United States into four regions necessitates the use of a one-way Analysis of Variance (ANOVA) or F Ratio statistical test.
Table 2. shows a source of variance for the dependent variable, current expenditures per pupil, per the four U.S. regions. The F ratio was calculated using the sum of the squares, or mean square. The F ratio of 9.75 helps with the goal of analysis of variance to detect the differences among MEANS. The between degrees of freedom (dfb) was calculated using the number of sample groups or regions (4) minus 1. The dfb = 3. The within degrees of freedom (wdf) was calculated using the total number of scores or states (51) minus the number of groups or regions (4). The within degrees of freedom therefore equals 47. Using the F ratio of variance between groups divided by the variance within groups, degrees of freedom = (3/48). A table of critical values of F compares the obtained value of F (9.75) with the critical value of F for the appropriate degrees of freedom. For the calculations completed, the column for 3df and the row for 47df intersect at two F values: 2.80 for an alpha level of .05 and 4.22 for an alpha level of .01. The null hypothesis is rejected when the obtained value of F is equal to, or greater than, the critical or table value of F. Therefore, using a one-way ANOVA, a significant difference was found between the expenditures per pupil, per region.
| Tests of Between-Subjects Effects | ||||||
| Dependent Variable: current expenditure per pupil in average daily attendance in public elementary and secondary schools 2005-06 | ||||||
| Source | Type III Sum of Squares | df | Mean Square | F | p | Partial Eta Squared |
| region | 120,097,648.80 | 3 | 40,032,549.60 | 9.75 | .00 | .38 |
| Error | 192,953,101.83 | 47 | 4,105,385.15 | |||
| Total | 5,752,870,321.00 | 51 | ||||
| Corrected Total | 313,050,750.63 | 50 | ||||
Table 2. Source of Variance Current Expenditures Per Pupil
However, it is important to determine where the greatest differences in expenditures per pupil, per region came from. The between-group variance is large, but perhaps it is due to one region spending significantly more than the other regions. Perhaps two or more regions do not differ significantly in their expenditures per pupil at all. Tukey’s Honestly Significantly Difference (HSD) test can be used for this post-hoc comparison of regional spending. Table 3. provides the data for the post-hoc multiple comparisons test of regional spending.
| Multiple Comparisons | ||||||
| current expenditure per pupil in average daily attendance in public elementary and secondary schools 2005-06Tukey HSD | ||||||
| (I) region | (J) region | Mean Difference (I-J) | Std. Error | P | 95% Confidence Interval | |
| Lower Bound | Upper Bound | |||||
| West | Midwest | -660.49 | 811.12 | .85 | -2820.82 | 1499.83 |
| South | -475.96 | 746.52 | .92 | -2464.23 | 1512.31 | |
| Northeast | -4356.52* | 878.61 | .00 | -6696.60 | -2016.45 | |
| Midwest | West | 660.49 | 811.12 | .85 | -1499.83 | 2820.82 |
| South | 184.53 | 763.94 | 1.00 | -1850.14 | 2219.21 | |
| Northeast | -3696.03* | 893.46 | .00 | -6075.66 | -1316.40 | |
| South | West | 475.96 | 746.52 | .92 | -1512.31 | 2464.23 |
| Midwest | -184.53 | 763.94 | .995 | -2219.21 | 1850.14 | |
| Northeast | -3880.56* | 835.25 | .000 | -6105.17 | -1655.96 | |
| Northeast | West | 4356.52* | 878.61 | .00 | 2016.45 | 6696.60 |
| Midwest | 3696.03* | 893.46 | .00 | 1316.40 | 6075.66 | |
| South | 3880.56* | 835.25 | .00 | 1655.96 | 6105.17 | |
| *. The mean difference is significant at the .05 level. | ||||||
Table 3. Multiple Comparison Test of Expenditures Between Regions
From the table, we learn that there are a number of mean differences significant at the .05 level between regional spending. Comparing the West with the Northeast there is a negative difference of $4,356.52 per pupil. There is a negative difference in the Midwest of roughly $3,700.00 per pupil compared to what is spent per pupil in the Northeast. The South falls short of Northeast spending by roughly $3,880.00 per pupil. But perhaps the most significant mean difference is in the Northeast where at the .05 confidence interval, it can be said that the Northeast is outspending all of the other regions anywhere between $3,700.00 and $4,356,00 per pupil.
It was determined in Figure 10. Virginia had a low pupil to teacher ratio. Figure 4. showed that Utah’s pupil to teacher ratio was quite high. Regionally comparative, Table 4. provides a look at how the West region has significantly higher pupil to teacher ratios: nearly 3 + students on the average compared to Midwest and Southern classrooms, and more than 5+ students in the West compared to Northeast classrooms. Similarly, compared to the Northeast, Southern classrooms have 2+ students more per teacher. Overall, the West region has the highest pupil to teacher ratio, with more students assigned per classroom teacher than any of the other U.S. regions.
With significantly higher pupil to teacher ratios in the West, and significantly higher expenditures per pupil in the Northeast, annual teacher salaries, especially between these two regions warrant an investigation. Table 5. offers a multiple comparison difference between each of the 4 U.S. regions. Starting in the Northeast where student expenditures are high, annual teacher salaries are only significantly higher than their regional counterparts in the South. However, in Western states where pupil to teacher ratios are higher than all other regions teachers are earning annually an average of more than $6,640.00 less than teachers in the Northeast. Teachers in the South also earn significantly less than their collegues in the Northeast. The practical significance of these findings is limited however, as it would have been helpful to have data on cost of living in each region and average educational level of the teachers.
| Multiple Comparisons | |||||
| average pupil/teacher ratio Fall 2005Dunnett C | |||||
| (I) region | (J) region | Mean Difference (I-J) | Std. Error | 95% Confidence Interval | |
| Lower Bound | Upper Bound | ||||
| West | Midwest | 3.00* | .94 | .19 | 5.81 |
| South | 2.94* | .86 | .40 | 5.49 | |
| Northeast | 5.07* | .94 | 2.23 | 7.92 | |
| Midwest | West | -3.00* | .94 | -5.81 | -.19 |
| South | -.06 | .58 | -1.78 | 1.67 | |
| Northeast | 2.08 | .69 | -.08 | 4.22 | |
| South | West | -2.94* | .86 | -5.49 | -.40 |
| Midwest | .06 | .58 | -1.67 | 1.78 | |
| Northeast | 2.13* | .58 | .34 | 3.92 | |
| Northeast | West | -5.07* | .94 | -7.92 | -2.23 |
| Midwest | -2.080 | .69 | -4.22 | .08 | |
| South | -2.13* | .58 | -3.92 | -.34 | |
Table 4. Multiple Comparison Test of Average Pupil / Teacher Ratio by Region
| Multiple Comparisons | ||||||
| estimated average salary 2005-2006Tukey HSD | ||||||
| (I) region | (J) region | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval | |
| Lower Bound | Upper Bound | |||||
| West | Midwest | 910.88 | 2594.81 | .99 | -6000.11 | 7821.88 |
| South | 1506.03 | 2388.15 | .92 | -4854.55 | 7866.62 | |
| Northeast | -6641.50 | 2810.72 | .10 | -14127.52 | 844.52 | |
| Midwest | West | -910.88 | 2594.81 | .99 | -7821.87 | 6000.11 |
| South | 595.15 | 2443.89 | 1.00 | -5913.89 | 7104.18 | |
| Northeast | -7552.39 | 2858.22 | .05 | -15164.94 | 60.16 | |
| South | West | -1506.03 | 2388.15 | .92 | -7866.62 | 4854.55 |
| Midwest | -595.15 | 2443.89 | 1.00 | -7104.18 | 5913.89 | |
| Northeast | -8147.54* | 2672.01 | .02 | -15264.15 | -1030.92 | |
| Northeast | West | 6641.50 | 2810.71 | .10 | -844.52 | 14127.52 |
| Midwest | 7552.39 | 2858.22 | .05 | -60.16 | 15164.94 | |
| South | 8147.54* | 2672.01 | .02 | 1030.92 | 15264.15 | |
| Table 5. Multiple Comparison Test of Estimated Average Salary by Region | ||||||
Additionally, it is necessary to take a look at the percentage of students eligible for free or reduced lunch, and how their data stacks up regionally. Figure 12. provided a regional look at socioeconomic statuses; New Mexico, in the Western region, had the largest percentage of students eligible for free or reduced lunch, while New Hampshire, in the Northeast, had the lowest. In the last multiple comparisons analysis, Table 6. presents evidence that the South has a significantly higher percentage of students eligible for free of reduced lunch than all other regions. In the Northeast, at the .05 confidence interval we see that there are significantly less students eligible for free or reduced lunch than in West and South, by as much as 19%.
| Multiple Comparisons | ||||||
| % of students eligible for free/reduced lunch 2006-07Tukey HSD | ||||||
| (I) region | (J) region | Mean Difference (I-J) | Std. Error | P | 95% Confidence Interval | |
| Lower Bound | Upper Bound | |||||
| West | Midwest | 5.14 | 3.20 | .38 | -3.38 | 13.66 |
| South | -9.57* | 2.95 | .01 | -17.43 | -1.70 | |
| Northeast | 9.79* | 3.45 | .03 | .59 | 18.99 | |
| Midwest | West | -5.14 | 3.20 | .38 | -13.66 | 3.38 |
| South | -14.71* | 2.95 | .00 | -22.58 | -6.84 | |
| Northeast | 4.65 | 3.45 | .54 | -4.55 | 13.85 | |
| South | West | 9.57* | 2.95 | .01 | 1.70 | 17.43 |
| Midwest | 14.71* | 2.95 | .00 | 6.84 | 22.58 | |
| Northeast | 19.36* | 3.23 | .00 | 10.76 | 27.96 | |
| Northeast | West | -9.79* | 3.45 | .03 | -18.99 | -.59 |
| Midwest | -4.65 | 3.45 | .54 | -13.85 | 4.55 | |
| South | -19.36* | 3.23 | .00 | -27.96 | -10.76 | |
| *. The mean difference is significant at the .05 level. | ||||||
Table 6. Multiple Comparison Test of Percentage of Students Eligible for Free / Reduced Lunch
Regional Spending and its Relationship to Academic Success
Thus far we have looked at how our nationa’s four regions compare with regard to educational spending. Data analysis has been provided for state and regional expenditures per pupil, average teacher salary, pupil to teacher ratios, and socioeconomic status of students between regions. In attempt to shed light upon the controversy of spending and its association with student success, it is essential to compare the aforementioned data with standardized test scores. The Scholastic Apptitude Test (SAT), a college admissions assessment developed by the United States College Board scores college-bound students in three areas: math, verbal, and writing. Each section of the test is worth 800 points, and the maximum total score is 2400. Depending upon the type of SAT test taken, the writing portion may or may not be included, thus a total maximum score of 1600 is also possible. The SAT is a considered fair nationwide and should not present bias based on a student’s geographical region.
Diagrams A. and B.. present average SAT scores for (A.) Math, and (B.) Verbal, 2005-2006. Scatter plots of SAT scores versus expenditures per pupil, 2005-2006, are show below. Diagram A. presents a weak negative correlation. There is some negative slope to the plot indicating that increased expenditures per pupil yield somewhat higher lower math SAT scores. This correlation is rather weak however, and shows almost as much zero correlation between the two variables.
Diagram A. Average Math SAT Scores versus Expenditures Per Pupil
Diagram B. provides more evidence of a negative correlation between expenditures per pupil and average verbal SAT scores. The negative slope is still rather weak and further analysis must be computed to determine if in fact the correlation is negative, or whether there is zero correlation between SAT scores and expenditures per pupil. The Correlation Coefficient, or Pearson r is an appropriate statistical test for determining a hypothesis of association between two measures of interval data. Pearson r can be calculated using the raw data scores in Table 7.
Diagram B. Average Verbal SAT Scores versus Expenditures Per Pupil
| Descriptive Statistics | |||
| Mean | Std. Deviation | N | |
| Expenditure/ pupil (1000$) | 10,327.78 | 2,502.20 | 51 |
| SAT score 2005-06 (verbal) | 534.94 | 37.80 | 51 |
| SAT score 2005-06 (math) | 540.59 | 37.46 | 51 |
| SAT score 2005-06 (writing) | 525.37 | 37.63 | 51 |
| verbal SAT score 2005-06 | math SAT score 2005-06 | writing SAT score 2005-06 | |||||
| Expenditure/ pupil 2005-06 | Pearson r | -0.42** | -0.39** | -0.40** | |||
| p | 0.00 | 0.00 | 0.00 | ||||
| n | 51 | 51 | 51 | ||||
| Model | R | R Square | Std. Error of the Estimate | ||||
| 1 | .39a | .16 | 34.79 | ||||
| Coefficientsa | ||||||
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||
| B | Std. Error | Beta | ||||
| 1 | (Constant) | 601.42 | 20.88 | 28.80 | .00 | |
| Expenditure/ pupil 2005-06 | -.01 | .00 | -.39 | -3.00 | .00 | |
| a. Dependent Variable: average math SAT score 2005-06Table 7. Verbal and Math SAT Scores, Expenditures Per Pupil Raw Data | ||||||
Mean math SAT scores are calculated as well as mean verbal, and the mean expenditures per pupil. Using the means the standard deviations can be determined and the data is plugged into the Pearson r equation. The value for the average math SAT score Pearson r = .39
To test for statistical correlation degrees of freedom must be obtained for the two variables. Degrees of freedom are calculated using the number of scores minus two. In the SAT math test, 51 scores were obtained, minus two, equals 49. Using a table for the critical values of r for the Pearson correlation coefficient, the value of r at the .05 confidence interval is .268 and .372 at the .01 confidence interval. The calculated value of r = .39 and is greater than the table r, thus we reject the null hypothesis, and determine there is statistical association between the two variables. The correlation between math SAT scores and expenditures per pupil is negative! The same test of statistical significance is used with verbal SAT scores, and too is found to have a negative correlation. The r ratio for verbal SAT scores = .42 where the same number of samples (51) was obtained and r values for the .05 and .01 confidence intervals yield scores of .268 and .372
It may be useful to determine if a correlation is present between SAT scores and pupil to teacher ratio. Diagrams C. and D. provide scatter plots of verbal SAT scores, 2005-2006, versus the average pupil to teacher ratio, 2006. Diagram C shows zero correlation between verbal SAT scores and pupil to teacher ratio. A glance at Diagram D provides the same evidence of zero correlation between math SAT scores and pupil to teacher ratio. Again, calculating the correlation coefficient may present evidence otherwise of either a positive or negative correlation between two of the variable data.
Diagram C. Average Verbal SAT Scores versus Average Pupil / Teacher Ratio
Diagram D. Average Math SAT Scores versus Average Pupil / Teacher Ratio
Table 8. provides raw data for math and verbal SAT scores and pupil to teacher ratios.
| Model | R | R Square | Std. Error of the Estimate | ||||||
| 1 | .03a | .00 | 38.16 | ||||||
| Coefficientsa | |||||||||
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | |||||
| B | Std. Error | Beta | |||||||
| 1 | (Constant) | 542.32 | 32.86 | 16.50 | .00 | ||||
| pupil/teacher ratio Fall 2006 | -.49 | 2.14 | -.033 | -.23 | .82 | ||||
| a. Dependent Variable: average verbal SAT score 2005-06 | |||||||||
| Model | R | R Square | Std. Error of the Estimate | |||||||
| 1 | .03a | .00 | 37.82 | |||||||
| Coefficientsa | ||||||||||
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||||||
| B | Std. Error | Beta | ||||||||
| 1 | (Constant) | 546.76 | 32.57 | 16.79 | .00 | |||||
| average pupil/teacher ratio Fall 2006 | -.41 | 2.12 | -.03 | -.19 | .85 | |||||
| a. Dependent Variable: average math SAT score 2005-06 | ||||||||||
Table 8. Verbal and Math SAT Scores, Pupil to Teacher Ratio
The number of subjects remain the same (51) – 2 = 49. Using a table for the ecritical value of r at 49 degrees of freedom yeild values of .268 at the .05 confidence interval and .372 at the .01 confidence interval. The calculated r value = .03 for both math and verbal scores and that is smaller than the table r. Therefore, we must accept the null hypothesis and assume that pupil to teacher ratio has no significant correlation on both math and verbal SAT scores.
Lastly, comparing the socioeconomic status of students with their SAT scores may be practical for those wishing to argue that finances significantly impact student success rates. Diagrams E. and F. provide scatter plots for the percentage of students eligible for free or reduced lunch, 2006-2007, versus the math and verbal SAT scores, 2005-2006. A quick look at both scatter plots indicates zero correlation between average math or verbal SAT scores and students’ socioeconomic status. However, raw data and calculating the product-moment correlation may prove otherwise. Using the data in Table 9.
Diagram E. Average Math SAT Scores versus percentage of students eligible for free / reduced lunch
the number of subjects remain the same (51) – 2 = 49. Using a table for the critical value of r at 49 degrees of freedom yield values of .268 at the .05 confidence interval and .372 at the .01 confidence interval. The calculated r value = .08 for math and .02 for verbal scores and that is smaller than the table r. Therefore, we must accept the null hypothesis and assume that socioeconomic status has no significant correlation on both math and verbal SAT scores; or does it?
Diagram F. Average Verbal SAT Scores versus percentage of students eligible for free / reduced lunch
| Model | R | R Square | Std. Error of the Estimate | ||||||
| 1 | .08a | .01 | 37.80 | ||||||
| Coefficientsa | |||||||||
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | |||||
| B | Std. Error | Beta | |||||||
| 1 | (Constant) | 552.85 | 20.90 | 26.45 | .00 | ||||
| % of students eligible for free/reduced lunch 2006-07 | -.292 | .51 | -.08 | -.58 | .57 | ||||
| a. Dependent Variable: average math SAT score 2005-06 | |||||||||
| Model | R | R Square | Std. Error of the Estimate | ||||||
| 1 | .02a | .00 | 38.19 | ||||||
| Coefficientsa | |||||||||
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | |||||
| B | Std. Error | Beta | |||||||
| 1 | (Constant) | 532.29 | 21.12 | 25.21 | .00 | ||||
| % of students eligible for free/reduced lunch 2006-07 | .09 | .51 | .02 | .17 | .87 | ||||
| a. Dependent Variable: average verbal SAT score 2005-06 | |||||||||
Table 9. Verbal and Math SAT Scores, Percentage of Students Eligible for Free or Reduced Lunch
Conclusions
Although all conclusions drawn from the analyses show a lack of positive correlation between financial spending and student success, no direct statement regarding cause and effect can be made. In other words, spending less money on student expenditures & teacher salaries and widening the ratio between pupils and teacher will not cause students to gain higher academic success. Although the data provides a possible hypothesis that more money spent in education correlates with lower levels of academic success, other hypotheses are at least possible. Perhaps a student who scores high on his SAT was encouraged to spend more time studying. Perhaps coming from a low socioeconomic background provides ambition for a child to spend more time studying. Perhaps teachers with lower salaries are motivated to be highly qualified and teach better than do teachers who are already highly paid. It is important to note that although a relationship may exist, a direct statement on cause and effect cannot be made regarding any of the preceding relationships.
