In Table 2, the following statistics are presented, by grade level, for words correct on the Year 1 CBM oral passage reading measure and for correct replacements on the Year 2 CBM maze measure: (a) average slopes and standard deviations, (b) percentages of individual student regressions for which the quadratic term significantly contributed to the modeling of student progress, (c) information about the distribution of the slopes across students, and (d) percentages of students with negative slopes. Additionally, in footnotes to these tables, information is presented about results of ANOVAs, testing for the effect of grade level on slope. We discuss these data with respect to three major questions: How well does a linear relationship model student progress within 1 academic year?; How well does the normal distribution characterize the distribution of slopes?; and What is the weekly rate of student progress and to what extent does it vary as a function of grade level?
How well does a linear relationship model student reading progress within 1 academic year? Preliminary analyses assessed the extent to which a linear relationship adequately modeled student progress within one academic year in reading. As the regression between each student's scores and calendar days was computed, a quadratic component was included to determine whether it contributed to the modeling of student progress. Results revealed that, for the CBM oral reading measure and for the CBM maze reading measure, respectively, 0-21% and 19-31% of the relationships had significant quadratic terms. For almost all of these cases, a slightly negatively accelerating pattern of progress was revealed within one academic year. With this pattern, student performance continues to improve over the academic year; however, the amount of that improvement gradually decreases.
For the CBM oral passage reading measure, a linear relationship contributed significantly to the description of student progress for 100%,100%,100%, 86%, 81%, and 24% of the individuals at Grades 16, respectively. For the CBM maze reading measure, a linear relationship satisfactorily contributed to the modeling of progress for 95%, 93%, 80%, 84%, and 70% of the students at Grades 2-6, respectively.
How well does the normal distribution characterize the distribution of slopes? A second set of analyses was conducted to examine the extent to which the distribution of slopes conformed to the normal distribution. As shown in Table 2, distributions of the CBM oral reading slopes appeared normal (i.e., kurtosis and skewness fell within 2 standard errors) for Grades 1,4,5, and 6; the CBM maze slopes were normally distributed for Grades 1, 2, and 6. At Grades 2 and 3 for oral reading and at Grades 3, 4, and 5 for maze, however, kurtosis and skewness exceeded 2 standard errors. At these grades, the distributions were leopkurtic (i.e., more peaked than a normal distribution) and positively skewed with a few extreme positive slopes. The exception was at Grade 4 on the maze measure, where the distribution was negatively skewed, with one extreme negative slope.
What is the weekly rate of student progress and, to what extent, does it vary with grade level? The effect of grade level on CBM reading slopes differed for the two types of measures. For oral passage reading, the ANOVA revealed statistically significant differences in slope as a