SPSS/Excel Project: Eligibility and its Relationship to ...
SPSS/Excel Project: Eligibility and its Relationship to Average SAT Scores for Reading, Writing and Math
By Heidi Riehl
EDU 6976 Interpreting & Applying Educational Research II, Prof. Mvududu
March 14, 2010
Part One
Introduction
The data in this analysis was collected by Deborah Lynn Guber in response to a controversy over equity in public school expenditures. She titled her compiled data, Getting What You Pay For: The Debate Over Equity in Public School Expenditures. She used nine variables and had a total of fifty observations. The variables were pulled from the Digest of Education Statistics and tables from the National Center for Education Statistics. This analysis specifically evaluates Reading (the average verbal SAT score, 2005-2006), Math (the average math SAT score, 2005-2006), Writing (the average writing SAT score, 2005-2006), and Eligibility (the percentage of graduates taking the SAT, 2006-2007).
Histograms
Below is a histogram for each of the variables listed above. All the tables contain data for the 51 states and all display a positive distribution with a skew to the right, with a majority of the scores and percentages falling in the lower portion of the distribution.
Table 1 shows the average scores for the verbal SAT for the year 2005-2006. The table has a lowest score of 470 and a highest score of 620 with an interval width of ten. The distribution of data is not normal, but instead is skewed to the right which indicates a positive skew (.31). The table shows the highest frequency of verbal scores lies within the 490 – 500 interval. The second highest grouping fell within the 510 – 520 range. Both are lower than the mean 534.94 and median 523.00. There is a large cluster of scores between 550 and 610.
Table 2 shows the average scores for the math SAT for the year 2005-2006. The table has a lowest score of 460 and a highest score of 630 with an interval width of twenty. The distribution of data is again not normal, but instead skewed to the right which indicates a positive skew (.47). The table shows the highest frequency of math scores fell within the 500 – 520 interval. To be expected the high frequency of scores are lower than the mean 540.59 and median 529.00. Most of the scores clustered between 520 and 620.
Table 3 shows the average scores for the writing SAT for the year 2005-2006. This table has a lowest score of 470 and a highest score of 610 with an interval width of ten. The distribution of data is non-normal. It is skewed to the right which indicates a positive skew (.30). The table shows the highest frequency of math scores fell within the 480 – 490 interval. These frequencies of scores are lower than the mean 525.37 and median 511.00. Table 3 also presents a bimodal distribution. The second highest frequencies fell between 500 – 510 and 560 – 570.
Table 4 shows the percentages of students eligible in each state for the SAT in the year 2006-2007. This table has a lowest percentage of 0 and a highest percentage of 110 with an interval width of ten. The distribution of data is non-normal. It is skewed to the right which indicates a positive skew (.25). The table shows the states that had a percentage between 0 and 10 was the highest frequency. Eighteen states had 10% or less of students eligible to take the SAT. This frequency of percentages is lower than the mean 39.33 and median 32.00. Table 4 shows significantly lower frequencies in the rest of the intervals. One state even showed 100% eligibility, which is quite a contrast to the high frequency. This table also shows a wide distribution.
Box plots
Using the data from the 51 states for the same variables, box plots were created.
Average verbal SAT scores, 2005-2006
Table 5 shows the median to be 523, a low score of 482, and a high score of 610. The box plot reveals that 50% of the scores fell between 498 and 569. As the median is not equidistant from the lower and upper hinge, the distribution is skewed. Within the 50% of scores, most are found between the median and the 75th percentile. The lower and upper whisker points are not far from the box indicating the distribution is not wide. Outliers usually lay three to four standard deviations away from the mean. The table indicates no outliers are present.
Average math SAT score, 2005-2006
Table 6 shows the median to be 529, a low score of 472, and a high score of 617. The box plot reveals that 50% of the scores fell between 509.5 and 568.5. As the median is not equidistant from the lower and upper hinge, the distribution is skewed. Within the 50% of scores, most are found between the median and the 75th percentile. The lower and upper whisker points are not far from the box indicating the distribution is not wide. Again, the table indicates no outliers are present.
Average writing SAT score, 2005-2006
Table 7 shows the median to be 511, a low score of 472, and a high score of 591. The box plot reveals that 50% of the scores fell between 490.5 and 564. As the median is not equidistant from the lower and upper hinge, the distribution is skewed. Within the 50% of scores, most are found between the median and the 75th percentile. The lower and upper whisker points are not far from the box indicating the distribution is not wide. The table indicates no outliers are present.
Percentage of graduates taking the SAT, 2006-2007
Table 8 shows the median to be 32, a low score of 3, and a high score of 100. The box plot reveals that 50% of the scores fell between 8 and 68.5. As the median is not equidistant from the lower and upper hinge, the distribution is skewed. Within the 50% of scores, most are found between the median and the 75th percentile. The box sits closest to the low score indicating a positive skew. The table indicates no outliers are present.
Part Two
Introduction
The following graphs compare data on variables from four regions, West, Midwest, South, and Northeast. The West contains 13 states, the Midwest contains 12 states, the South contains 17 states and the Northeast contains 9 states. The variables being looked at are expenditure per pupil, pupil to teacher ratio, percentage of eligible students taking the SAT in 2006-2007, and performance on the Reading portion of the SAT in 2005-2006.
Expenditure per pupil
[pic]
Table 9 shows box plots for the four regions mentioned above in regards to the variable expenditure per pupil. The Northeast spends the most money per pupil, while the other three regions spend less. The West indicates one of the states within the group spends the least of all fifty-one. The West also appears to have the widest distribution while the Midwest has a smaller distribution. The West’s median looks equidistant from the hinges implying a normal distribution. The other regions have a skewed distribution. The South contains an outlier.
| |
|Descriptive Statistics |
|Dependent Variable: current expenditure per pupil in average |
|daily attendance in public elem and sec schools 2005-06 |
| region |Mean |Std. Deviation |N |
|West |9244.92 |2024.64 |13 |
|Midwest |9905.42 |814.05 |12 |
|South |9720.88 |2626.95 |17 |
|Northeast |13601.44 |1804.85 |9 |
|Total |10327.78 |2502.20 |51 |
|Levene's Test of Equality of Error Variancesa |
|Dependent Variable: current expenditure per pupil in average |
|daily attendance in public elem and sec schools 2005-06 |
|F |df1 |df2 |P |
|1.45 |3 |47 |.24 |
|Tests of Between-Subjects Effects |
|Dependent Variable: current expenditure per pupil in average daily attendance in public elem and sec schools 2005-06 |
|Source |
|current expenditure per pupil in average daily attendance in public elem and sec schools 2005-06 |
|Tukey HSD |
|(I) region |
Ratio of pupils to teacher
[pic]
Table 10 shows box plots for the four regions in regards to the variable pupil to teacher ratio. The West shows a higher teacher to pupil ratio, with the upper whisk set at 22. Again the West has the widest spread distribution. The other three regions have smaller distributions. The West indicates one of the states within the group spends the least of all fifty-one, while the Midwest has a smaller distribution. All four regions have medians that are not equidistant from the hinges implying a skewed distribution. The West and the South are closest to a normal distribution. The other two regions have a skewed distribution. Again, the South contains an outlier.
|Descriptive Statistics |
|Dependent Variable: average pupil/teacher ratio Fall |
|2005 |
|region |Mean |Std. Deviation |N |
|West |17.81 |2.90 |13 |
|Midwest |14.81 |1.71 |12 |
|South |14.86 |1.28 |17 |
|Northeast |12.73 |1.46 |9 |
|Total |15.23 |2.54 |51 |
|Levene's Test of Equality of Error |
|Variancesa |
|Dependent Variable: average pupil/teacher |
|ratio Fall 2005 |
|F |df1 |df2 |P |
|4.92 |3 |47 |.01 |
|Tests of Between-Subjects Effects |
|Dependent Variable: average pupil/teacher ratio Fall 2005 |
|Source |
According to the data above in the descriptive statistics, the Northeast’s mean amount of pupils to teacher is small, whereas, the West has the largest. The West has the largest standard deviation (variances by chance), while the Midwest has the smallest. The Levene test shows a P-value of .01. This is less than .05, so we cannot assume homogeneity. Looking at the Tests of Between-Subjects Effects, we can reject the null hypothesis based on (F(3,46)=13.08, p ................
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