Table 3.

The Impact of Observed Versus Normalized Scores on Skewness, Kurtosis, Grade-to-Grade Correlation, and School Percentile Rank on a “Value Added” Metric.

		Skewness				Kurtosis
Grade pair	Number of students	2010		2011		2010		2011		Correlation(2010, 2011)		Number of schools	$r_{{\overline{e}}_j^{\mathrm{norm}},{\overline{e}}_j^{\mathrm{obs}}}$	Absolute difference in school percentile rank
		Obs.	Norm.	Obs.	Norm.	Obs.	Norm.	Obs.	Norm.	Obs.	Norm.			Median	90th percentile
3-4	181,847	1.17	−0.22	−0.17	−0.01	4.94	2.64	4.02	2.95	0.64	0.75	2177	0.956	4.41	13.62
4-5	185,131	0.45	−0.06	−0.58	−0.01	4.88	2.85	6.04	2.94	0.78	0.81	2129	0.982	2.60	7.70
5-6	181,912	0.04	−0.06	−0.32	−0.02	5.13	2.85	5.59	2.91	0.75	0.79	1465	0.994	1.47	4.22
6-7	183,514	−0.40	−0.03	−0.46	−0.01	6.64	2.86	6.82	2.93	0.78	0.82	1250	0.989	1.95	5.56
7-8	184,698	−0.29	−0.02	−1.62	0.00	7.08	2.91	11.86	2.92	0.76	0.83	1233	0.962	3.51	9.74

Note. Skewness and kurtosis of observed (Obs.) and normalized (Norm.) scores are shown. Normalization does not result in skewness = 0 or kurtosis = 3 due to the discreteness of the score distributions. The Correlation (2010, 2011) values show the grade-to-grade correlation for observed and normalized scores. The $r_{{\overline{e}}_j^{\mathrm{norm}},{\overline{e}}_j^{\mathrm{obs}}}$ correlation is that between the school “value added” on the observed scale and the school “value added” on the normalized scale.