3. CENTRAL TENDENCY MEASURES AND OTHER CLASSICAL ITEM ANALYSES OF THE 2011 MOD-MSA: MATHEMATICS
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1 3. CENTRAL TENDENCY MEASURES AND OTHER CLASSICAL ITEM ANALYSES OF THE 2011 MOD-MSA: MATHEMATICS This section provides central tendency statistics and results of classical statistical item analyses for students in Grades 3 through 8. All analyses provided in this report are based on the equating sample, which consisted of the full population after the application of the exclusion criteria for equating purposes. Unless otherwise stated, the analyses in this report will be assumed to be based on the equating sample Measures of Central Tendency The classical measures of central tendency, variability, and score precision of raw scores are presented in Table by grade for each strand as well as the total operational test. The tables include the following: Number of items by strands and the total test Maximum score attainable (sample size) Mean (average raw score) SD (standard deviation) SE (standard error of the mean) Standard Error of the Mean The standard error of the mean (SE) is an estimate of the magnitude of sampling error associated in the estimation of the population mean. It is defined as follows: ˆ SE n, where SE = standard error of the mean ˆ = standard deviation of the sample n = number of responses in the sample Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 30
2 Table Central Tendency Statistics of the Operational Test by Subscales and Grades Grade Modality () # s Max Points N Count RS Mean SD SE 4 3 Algebra Geometry and Measurement Statistics and Probability Number and Computation Process Total Test Algebra Geometry and Measurement Statistics and Probability Number and Computation Process Total Test Algebra Geometry and Measurement Statistics and Probability Number and Computation Process Total Test Algebra Geometry and Measurement Statistics and Probability Number and Computation Process Total Test Algebra Geometry and Measurement Statistics and Probability Number and Computation Process Total Test Algebra Geometry and Measurement Statistics and Probability Number and Computation Process Total Test Level Descriptive Statistics This section presents the raw score summary statistics for all items in the Mod-MSA: Mathematics spring 2011 within the framework of classical test theory (CTT). The p-value for Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 31
3 each item is defined as the proportion of students that answer an item correctly for the multiple choice items. A high p-value means that an item is easy; a low p-value means that an item is difficult. The point biserial correlation for each item is an index of the association between the item score and the total test score. It shows the proficiency of the item to discriminate between low proficiency and high proficiency students. An item with a high point biserial correlation discriminates more effectively between the low and the high proficiency students than a low point biserial correlation. The item-level statistics for the operational and the embedded field test items for the 2011 Mod- MSA: Mathematics based on the equating sample are presented in Table to Table The following item information and statistics are presented for each item: number based on their sequential appearance in the form. UIN number strand number N-count (number of students) options P-value for multiple choice items (percentage of examinees that answered the item correctly) Point biserial (index of discrimination between high and low scoring students) distractor analyses are provided in Appendix B. These analyses include UIN number strand number mean standard deviation Percentage of distribution by distractors Percent of omits Distractor-to-total correlation Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 32
4 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 3 UIN Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 33
5 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 3 (Cont.) UIN Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 34
6 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 3 (Cont.) UIN N- Count Note: = Algebra, 246=Geometry, 251=Measurement, 257=Statistics, 262= Probability, 268=Numbers and Computation, and 273 & 274= Process Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 35
7 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 4 UIN Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 36
8 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 4 (Cont.) UIN Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 37
9 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 4 (Cont.) UIN Note: = Algebra, 246=Geometry, 251=Measurement, 257=Statistics, 262= Probability, 268=Numbers and Computation, and 273 & 274= Process Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 38
10 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 5 UIN Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 39
11 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 5 (Cont.) UIN Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 40
12 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 5 (Cont.) UIN Note: = Algebra, 246=Geometry, 251=Measurement, 257=Statistics, 262= Probability, 268=Numbers and Computation, and 273 & 274= Process Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 41
13 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 6 UIN N- Count Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 42
14 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 6 (Cont.) UIN Note: = Algebra, 246=Geometry, 251=Measurement, 257=Statistics, 262= Probability, 268=Numbers and Computation, and 373b & 374= Process Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 43
15 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 7 Seq. UIN Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 44
16 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 7 (Cont.) Seq. UIN Note: 1 #28 was not scored = Algebra, 246=Geometry, 251=Measurement, 257=Statistics, 262= Probability, 268=Numbers and Computation, and 273 & 274= Process Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 45
17 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 8 UIN Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 46
18 Table The 2011 Mod-MSA: Mathematics Classical Statistics: Grade 8 (Cont.) UIN Note: = Algebra, 246=Geometry, 251=Measurement, 257=Statistics, 262= Probability, 268=Numbers and Computation, and 273 & 274= Process Technical Report 2011 Maryland Mod-MSA: Mathematics Pearson 47
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National 5 Mathematics Notes with Examples Calculating a percentage To calculate a percentage of an amount we divide the percentage by 100 and multiply by the amount. To calculate one number as a percentage