Cohorts for statistical analysis
For the purpose of this analysis, the math SOL test scores of Camelot Elementary School 3rd and 5th grade students were used.  The cohorts were students tested in the 3rd grade for the 2002-2007 and 5th grade for the 2002-2007 end of the year mathematics SOL tests for the fall of 2001 school year through the spring of 2007 school year (6 years).  These students included in the analysis also attended Camelot Elementary School for three consecutive years in grades 3, 4, and 5.  The raw data for these students was  found in Table I.  The number of students in each sample were as follows:

Two sample T for 2002-2004 3rd Grade vs 2005-2007 3rd Grade Math SOL Scores

Two Sample T-Test and Confidence Interval
Two sample T for 2002-2004 3rd Grade  vs 2005-2007 3rd Grade Scores

                     N       Mean       StDev    SE Mean
2002-2004  113     455.5      72.8       6.8
2005-2007    91     493.1      88.9       9.3

95% CI for mu 2002-2004 - mu 2005-2007: (-60.4, -14.8)
T-Test mu 2002-2004 = mu 2005-2007 (vs not =): T = -3.25 P = 0.0014 DF = 172

Two sample T for 2002-2004 5th Grade vs 2005-2007 5th Grade Math SOL Scores

Two Sample T-Test and Confidence Interval
Two sample T for 2002-2004 5th Grade  vs 2005-2007 5th Grade Scores

                    N       Mean      St Dev    SE Mean
2002-2004  120     416.1      43.4       4.0
2005-2007    91     493.1      88.9       9.3 

95% CI for mu 2002-2004 - mu 2005-2007: (-97.0, -56.9)
T-Test mu 2002-2004 = mu 2005-2007 (vs not =): T = -7.60 P = 0.0000 DF = 122

There were 71 students that took this exam. The average score for the 3rd grade test was 472.93 and 459.87 for the 5th grade test. The highest score made on the 3rd grade test was 595 and 600 on the 5th grade test.

The regression equation is y = 75.2 + 0.811 x

Predictor        Coef       StDev          T        P
Constant        75.23       25.44       2.96    0.004
x             0.81144     0.05338      15.20    0.000

S = 39.54       R-Sq = 77.0%     R-Sq(adj) = 76.7%

Analysis of Variance

Source            DF          SS          MS         F        P
Regression         1       361290      361290    231.09    0.000

Residual Error    69      107874         1563
Total                  70      469164

Correlation (Pearson)
Correlation of 2002 3rd grade.  Scaled Score and 2004 5th grade. Scaled Score = 0.878, P-Value = 0.000

Two Sample T-Test and Confidence Interval

Two sample T for 2002 3rd Gr SOL Scores vs 2004 5th Gr SOL Scores

           N      Mean     StDev   SE Mean
2002 3rd  71     468.4      88.5        11
2004 5th  71     455.3      81.9       9.7

95% CI for mu 2002 3rd - mu 2004 5th: ( -15,  41.4)
T-Test mu 2002 3rd = mu 2004 5th (vs not =): T = 0.91  P = 0.36  DF = 139

There were 81 students that took this exam. The average score for the 3rd grade test was 482.86 and 463.90 for the 5th grade test. The highest score made on the 3rd grade test was 600 and 600 on the 5th grade test.

The regression equation is y = 165 + 0.619 x

Predictor        Coef       StDev          T        P
Constant       164.80       38.86       4.24    0.000
x             0.61943     0.07966       7.78    0.000

S = 49.87       R-Sq = 43.4%     R-Sq(adj) = 42.6%

Analysis of Variance

Source            DF          SS          MS         F        P
Regression         1      150363      150363     60.47    0.000
Residual Error    79      196450        2487
Total             80      346813

Correlations (Pearson)

Correlation of 2003 3rd.Scaled Score and 2005 5th.Scaled Score = 0.658, P-Value = 0.000

Two Sample T-Test and Confidence Interval

Two sample T for 2003 3rd Gr SOL Scores vs 2005 5th Gr SOL Scores

           N      Mean     StDev   SE Mean
2003 3rd  81     482.9      70.0       7.8
2005 5th  81     463.9      65.8       7.3

95% CI for mu 2003 3rd - mu 2005 5th: ( -2.1,  40.0)
T-Test mu 2003 3rd = mu 2005 5th (vs not =): T = 1.78  P = 0.078  DF = 159

There were 55 students that took this exam. The average score for the 3rd grade test was 499.85 and 515.00 for the 5th grade test. The highest score made on the 3rd grade test was 600 and 600 on the 5th grade test.

The regression equation is y = 180 + 0.657 x

Predictor        Coef       StDev          T        P
Constant       179.83       74.25       2.42    0.019
x              0.6568      0.1467       4.48    0.000

S = 71.76       R-Sq = 27.8%     R-Sq(adj) = 26.4%

Analysis of Variance

Source            DF          SS          MS         F        P
Regression         1      103184      103184     20.04    0.000
Residual Error    52      267775        5150
Total             53      370959

Correlations (Pearson)
Correlation of 2004 3rd.Scaled Score and 2006 5th.Scaled Score = 0.527, P-Value = 0.000

Two Sample T-Test and Confidence Interval

Two sample T for 2004 3rd Gr SOL Scores vs 2006 5th GR SOL Scores

           N      Mean     StDev   SE Mean
2004 3rd  55     499.9      67.9       9.2
2006 5th  55     509.3      83.7        11

95% CI for mu 2004 3rd - mu 2006 5th: ( -38.4,  20)
T-Test mu 2004 3rd = mu 2006 5th (vs not =): T = -0.65  P = 0.52  DF = 101

There were 67 students that took this exam. The average score for the 3rd grade test was 515.96 and 511.33 for the 5th grade test. The highest score made on the 3rd grade test was 600 and 600 on the 5th grade test.

The regression equation is y = 101 + 0.795 x

Predictor        Coef       StDev          T        P
Constant       101.32       47.80       2.12    0.038
x             0.79467     0.09191       8.65    0.000

S = 49.53       R-Sq = 53.5%     R-Sq(adj) = 52.8%

Analysis of Variance

Source            DF          SS          MS         F        P
Regression         1      183428      183428     74.76    0.000
Residual Error    65      159477        2453
Total             66      342905

Correlations (Pearson)
Correlation of 2005 3rd.Scaled Score and 2007 5th grade Scaled Score = 0.731, P-Value = 0.000

Two Sample T-Test and Confidence Interval

Two sample T for 2005 3rd Gr SOL Scores vs 2007 5th Gr SOL Scores

           N      Mean     StDev   SE Mean
2005 3rd  67     516.0      66.3       8.1
2007 5th  67     511.3      72.1       8.8

95% CI for mu 2005 3rd - mu 2007 5th: ( -19.0,  28.3)
T-Test mu 2005 3rd = mu 2007 5th (vs not =): T = 0.39  P = 0.70  DF = 131