1 College Readiness LINKING STUDY A Study of the Alignment of the RIT Scales of NWEA s MAP Assessments with the College Readiness Benchmarks of EXPLORE, PLAN, and ACT December 2011 (updated January 17, 2012) COPYRIGHT 2011 NORTHWEST EVALUATION ASSOCIATION All rights reserved. No part of this document may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without written permission from NWEA. MAP is a registered trademark of Northwest Evaluation Association. The ACT is a registered trademark of ACT, Inc., in the U.S.A. and other countries. EXPLORE and PLAN are registered trademarks of ACT, Inc. Disclaimer: This report is the product of research conducted by the Northwest Evaluation Association. Neither the report nor its findings are sponsored or endorsed by ACT, Inc.
2 A STUDY OF THE ALIGNMENT OF THE RIT SCALES OF NWEA S MAP ASSESSMENTS WITH THE COLLEGE READINESS BENCHMARKS OF EXPLORE, PLAN, AND ACT DECEMBER 2011 Recently, NWEA completed a study to examine the predictive relationship between the RIT scales of NWEA s MAP assessments in reading, language usage, and mathematics to the college readiness benchmarks of the EXPLORE, PLAN, and ACT achievement tests in reading,, and mathematics. The EXPLORE, PLAN, and ACT also offer tests in science achievement, but these tests were not included in the current study. The objective of this study was to identify cut scores on the MAP reading, language usage, and general mathematics tests that correspond to the published college readiness benchmarks on the EXPLORE, PLAN, and ACT assessments (ACT, 2010). A secondary objective was to create a series of probability tables that estimate the likelihood of meeting the designated college readiness benchmark, given an observed MAP score. To conduct the study, we linked together individual EXPLORE, PLAN, and ACT scale scores and NWEA MAP assessment RIT scores for a sample of students who had completed both exams in the same (or a comparable) subject. EXPLORE, PLAN, and ACT scores were provided by NWEA partnering school districts and individually linked to those students MAP assessment RIT scores from the same (or the prior) testing season. In all, the sample contained over 108,000 matched pairs of scores from 26,000 students from 140 schools in three states. All valid matched data (i.e., data with valid scores and linking IDs) from the resulting sample were included in the analyses; no attempt was made to rebalance the sample in order to simulate a state- or nationally-representative population. Visual examinations of scatter plots of the data revealed curvilinear relationships between the MAP scale scores and the EXPLORE, PLAN and ACT scale scores. Consequently, a series of curvilinear (quadratic) regression models were fitted to the data, using MAP RIT scores as the single predictor of performance on each of the college readiness tests. MAP assessments in reading and language usage were both fit to predictive models of performance on college readiness tests of and. MAP mathematics was used to predict mathematics college readiness. In all, fifteen predictive models were fitted. See the Methodology Appendix for a more detailed description of the methods used. Table Sets 1 and 2 show the estimated cut scores, or minimum equivalent RIT scores corresponding to the college readiness benchmarks on EXPLORE, PLAN, or ACT when taken in the same (spring) or prior (fall) testing seasons. Also shown are the NWEA normative percentile ranks 1 associated with these MAP 1 Percentile ranks are based on NWEA s 2011 norming study.
3 cut scores. These tables can be used to identify students who might benefit from additional assistance, or who may be at risk of failing to meet these benchmarks. The percentile ranks also provide an indicator of the difficulty of these benchmarks, relative to a nationally representative norming sample. In general, the MAP cut scores associated with the college readiness benchmarks in range from the 40 th to 60 th percentiles on the MAP reading and language usage tests, while the college readiness benchmarks in reading and mathematics are higher, ranging primarily from the 70 th to 80 th percentiles on the MAP assessments reading and mathematics tests, respectively. The tables in Table Set 3 show the estimated probability of a student meeting the designated college readiness benchmark, based on that student s RIT score taken in the same testing season. These tables provide empirical information about the likelihood of meeting or exceeding the designated college readiness benchmark, given an observed MAP RIT score. The tables in Table Set 4 show the correlation coefficients and the goodness-of-fit statistics for the regression models used to predict MAP and the corresponding college readiness tests. These statistics show the degree to which MAP scores accurately predicted the PLAN, EXPLORE, and ACT scale scores of the study sample. The reported models show a moderately high correlation between MAP RIT scores and the scores on the college readiness benchmark tests, with correlations ranging from.66 to.87, but primarily in the range of In general, values at or near 1.0 suggest a perfect predictive relationship, whereas values near 0.0 indicate no predictive relationship. Goodness-of-fit statistics indicate that substantial variation within the observed college readiness benchmark scores can be predicted by MAP RIT scores, with values ranging from 44-76% of observed variance. The tables in Table Set 5 show the accuracy of the estimated MAP cut scores in predicting whether students met or exceeded the corresponding college readiness benchmark for the study sample. In general, the estimated MAP cut scores accurately predicted whether or not students would meet the EXPLORE, PLAN, and ACT benchmarks with 75-90% accuracy. Among incorrect predictions, false negatives (students who were incorrectly predicted NOT to meet the college readiness benchmark) outnumbered false positives (students predicted to meet readiness benchmarks but who failed to do so). The estimated MAP cut scores in this report provide a basis for making useful predictions about students likely college readiness status, as measured by EXPLORE, PLAN, and ACT, when MAP is taken within the same (or nearly the same) testing season. However, MAP is not designed to measure identical content as the ACT assessments. MAP assessments are aligned to each state s curriculum standards rather than the curriculum standards of the ACT. Thus while the tests measure much content that would be similar, they do not share a common design. Knowledge of a student s MAP score permits fairly accurate predictions about a student s probable college readiness status, as measured by EXPLORE, PLAN, or ACT.
4 TABLE SET 1 MINIMUM ESTIMATED SAME-SEASON (SPRING) RIT CUT SCORES CORRESPONDING TO COLLEGE READINESS BENCHMARKS 2 MAP RIT Score as Predictor Same Season Cut Scores and Normative Percentile Ranks on MAP Corresponding to College Readiness Benchmarks Grade MAP MAP MAP MAP College Readiness Test Benchmark Cut Score Normative Percentile Rank College Readiness Test Benchmark Cut Score Normative Percentile Rank 8 EXPLORE EXPLORE PLAN PLAN ACT ACT MAP Language Usage RIT Score as Predictor Same Season Cut Scores and Normative Percentile Ranks on MAP Corresponding to College Readiness Benchmarks Grade MAP MAP MAP MAP College Readiness Test Benchmark Cut Score Normative Percentile Rank College Readiness Test Benchmark Cut Score Normative Percentile Rank 8 EXPLORE EXPLORE PLAN PLAN ACT ACT MAP Mathematics RIT Score as Predictor Same Season Cut Scores and Normative Percentile Ranks on MAP Corresponding to College Readiness Benchmarks Grade Mathematics College Readiness Test MAP Cut MAP Normative Benchmark Score Percentile Rank 8 EXPLORE Math PLAN Math ACT Math The MAP cut scores shown in these tables are the minimum estimated scores. Meeting the minimum MAP cut score corresponds to a 50% probability of achieving that benchmark. Use the probabilities in Table Set 3 to determine the appropriate target scores for a desired level of certainty.
5 TABLE SET 2 MINIMUM ESTIMATED PRIOR-SEASON (FALL) RIT CUT SCORES CORRESPONDING TO COLLEGE READINESS BENCHMARKS 3 Grade College Readiness Test 8 EXPLORE MAP RIT Score as Predictor Prior Season Cut Scores and Normative Percentile Ranks on MAP Corresponding to College Readiness Benchmarks MAP MAP MAP Cut MAP Benchmark Cut Normative College Benchmark Score Normative Score Percentile Readiness Percentile Rank Rank Test EXPLORE 10 PLAN PLAN 11 ACT ACT MAP Language Usage RIT Score as Predictor Prior Season Cut Scores and Normative Percentile Ranks on MAP Corresponding to College Readiness Benchmarks Grade MAP MAP MAP MAP College Readiness Test Benchmark Cut Score Normative Percentile Rank College Readiness Test Benchmark Cut Score Normative Percentile Rank 8 EXPLORE EXPLORE PLAN PLAN ACT ACT MAP Mathematics RIT Score as Predictor Prior Season Cut Scores and Normative Percentile Ranks on MAP Corresponding to College Readiness Benchmarks Grade Mathematics College Readiness Test Benchmark MAP Cut Score MAP Normative Percentile Rank 8 EXPLORE Math PLAN Math ACT Math The MAP cut scores shown in these tables are the minimum estimated scores. Meeting the minimum MAP cut score corresponds to a 50% probability of achieving that benchmark. Use the probabilities in Table Set 3 to determine the appropriate target scores for a desired level of certainty.
6 TABLE SET 3 PROBABILITY OF MEETING OR EXCEEDING COLLEGE READINESS BENCHMARK IN SAME SEASON (SPRING), BY STUDENT GRADE AND RIT SCORE RANGE MAP RIT Score as Predictor Benchmark Benchmark MAP EXPLORE PLAN ACT EXPLORE PLAN ACT RIT Range 8th Grade 10th Grade 11th Grade 8th Grade 10th Grade 11th Grade 145 0% 0% 0% 0% 0% 0% 150 0% 0% 0% 0% 0% 0% 155 0% 0% 0% 0% 0% 0% 160 0% 0% 0% 0% 0% 0% 165 0% 0% 0% 0% 0% 0% 170 0% 0% 0% 0% 0% 0% 175 0% 0% 0% 1% 0% 0% 180 0% 0% 0% 1% 0% 0% 185 0% 1% 0% 1% 2% 0% 190 0% 1% 0% 4% 2% 0% 195 2% 1% 0% 5% 7% 0% 200 2% 2% 0% 10% 10% 0% 205 2% 2% 1% 14% 12% 1% 210 6% 6% 3% 25% 18% 6% % 10% 6% 39% 30% 11% % 17% 10% 61% 44% 22% % 30% 16% 77% 60% 39% % 44% 32% 91% 76% 56% % 66% 54% 99% 90% 79% % 82% 80% 100% 96% 93% % 92% 93% 100% 100% 99% % 100% 96% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% *Note: This table shows the proportion of students in the study sample who, based on a MAP reading score taken during the same (season), met the associated college readiness benchmark. Example: an eighth grade student scoring 220 on a MAP reading test taken during the same season would have a 27% chance of meeting the EXPLORE college readiness benchmark in reading, and about a 61% chance of meeting the EXPLORE college readiness benchmark in.
7 MAP Language Usage RIT Score as Predictor Benchmark Benchmark MAP Language Usage EXPLORE PLAN ACT EXPLORE PLAN ACT RIT Range 8th Grade 10th Grade 11th Grade 8th Grade 10th Grade 11th Grade 130 0% 0% 0% 0% 0% 0% 135 0% 0% 0% 0% 0% 0% 140 0% 0% 0% 0% 0% 0% 145 0% 0% 0% 0% 0% 0% 150 0% 0% 0% 0% 0% 0% 155 0% 0% 0% 0% 0% 0% 160 0% 0% 0% 0% 0% 0% 165 0% 0% 0% 0% 0% 0% 170 0% 0% 0% 0% 0% 0% 175 0% 0% 0% 0% 0% 0% 180 0% 0% 0% 0% 0% 0% 185 0% 0% 0% 1% 0% 0% 190 0% 0% 0% 1% 0% 0% 195 1% 3% 0% 2% 5% 0% 200 2% 3% 0% 8% 11% 0% 205 3% 4% 0% 11% 14% 4% 210 8% 4% 4% 24% 16% 4% % 11% 6% 39% 32% 18% % 22% 12% 64% 50% 34% % 36% 24% 81% 72% 60% % 56% 38% 97% 85% 82% % 76% 77% 100% 95% 92% % 91% 84% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% % 100% 100% 100% 100% 100% *Note: This table shows the proportion of students in the study sample who, based on a MAP language usage score taken during the same (season), met the associated college readiness benchmark. Example: an eighth grade student scoring 220 on a MAP language usage test taken during the same season would have a 27% chance of meeting the EXPLORE college readiness benchmark in reading, and about a 64% chance of meeting the EXPLORE college readiness benchmark in.
8 MAP Mathematics RIT Score as Predictor Mathematics Benchmark MAP Mathematics EXPLORE PLAN ACT RIT Range 8th Grade 10th Grade 11th Grade 130 0% 0% 0% 135 0% 0% 0% 140 0% 0% 0% 145 0% 0% 0% 150 0% 0% 0% 155 0% 0% 0% 160 0% 0% 0% 165 0% 0% 0% 170 0% 0% 0% 175 0% 0% 0% 180 0% 0% 0% 185 0% 0% 0% 190 0% 0% 0% 195 0% 0% 0% 200 0% 0% 0% 205 0% 0% 0% 210 0% 0% 0% 215 1% 0% 0% 220 3% 1% 0% 225 7% 1% 0% % 3% 0% % 6% 1% % 18% 2% % 35% 17% % 55% 37% % 75% 62% % 92% 84% % 95% 99% % 100% 100% % 100% 100% % 100% 100% % 100% 100% % 100% 100% % 100% 100% % 100% 100% *Note: This table shows the proportion of students in the study sample who, based on a MAP mathematics score taken during the same (season), met the associated college readiness benchmark. Example: an eighth grade student scoring 240 on a MAP mathematics test taken during the same season would have a 53% chance of meeting the EXPLORE college readiness benchmark in mathematics.
9 TABLE SET 4 CORRELATIONS BETWEEN MAP AND COLLEGE READINESS TEST SCORES AND REGRESSION MODEL GOODNESS OF FIT STATISTICS 4 MAP Test as Predictor Grade College Readiness Test Correlations Goodness of Fit College Readiness Test Correlations Goodness of Fit 8 EXPLORE % EXPLORE % 10 PLAN % PLAN % 11 ACT % ACT % MAP Language Usage Test as Predictor Grade College Readiness Test Correlations Goodness of Fit College Readiness Test Correlations Goodness of Fit 8 EXPLORE % EXPLORE % 10 PLAN % PLAN % 11 ACT % ACT % MAP Mathematics Test as Predictor Grade College Readiness Test Correlations Goodness of Fit 8 EXPLORE Mathematics % 10 PLAN Mathematics % 11 ACT Mathematics % 4 These correlations are comparable to Pearson s r values, except that they denote the extent to which the two scales are related by a quadratic function. Correlations range from 0 to 1, where 0 indicates no correlation between college readiness test scores and MAP scores, while 1 indicates a completely correlational relationship between scores on the two tests. Goodness of fit statistics indicate the percentage of observed variance accounted for by the quadratic regression model, with 100% indicating that college readiness test scores can be predicted with full reliability, whereas 0% indicates no predictability between the two assessments.
10 TABLE 5 PERCENTAGE OF STUDENTS WHOSE PASS STATUS WAS ACCURATELY PREDICTED BY THEIR MAP PERFORMANCE USING REPORTED CUT SCORES 5 Grade College Readiness Test 8 EXPLORE 10 PLAN 11 ACT Sample Size MAP Test as Predictor Percentage of Sample whose College Readiness Status was Accurately Predicted by MAP Score Percentage Percentage Percentage College Sample Percentage Correctly of False of False Readiness Size Correctly Predicted Positives Negatives Test Predicted % 5% 14% EXPLORE % 7% 14% PLAN % 5% 11% ACT Percentage of False Positives % 10% 10% % 9% 16% % 7% 13% Percentage of False Negatives Grade College Readiness Test 8 EXPLORE 10 PLAN 11 ACT Sample Size MAP Language Usage as Predictor Percentage of Sample whose College Readiness Status was Accurately Predicted by MAP Score Percentage Percentage Percentage College Sample Percentage Correctly of False of False Readiness Size Correctly Predicted Positives Negatives Test Predicted % 5% 14% EXPLORE % 5% 17% PLAN % 4% 12% ACT Percentage of False Positives % 11% 9% % 8% 17% % 6% 14% Percentage of False Negatives Grade College Readiness Test MAP Mathematics as Predictor Percentage of Sample whose College Readiness Status was Accurately Predicted by MAP Score Sample Percentage Correctly Percentage of False Percentage of False Size Predicted Positives Negatives 8 EXPLORE Mathematics % 4% 14% 10 PLAN Mathematics % 4% 9% 11 ACT Mathematics % 1% 7% 5 Correct predictions refer to the percentage of students in the study sample whose MAP scores accurately indicated their college readiness status on the college readiness test. False positives indicate the percentage of students predicted to be college ready, but who failed to meet the college readiness benchmark. False negatives indicate the percentage incorrectly predicted to fail to meet the college readiness benchmark, but who did.
11 REFERENCES ACT Issues in College Readiness: What are ACT's College Readiness Benchmarks (IC ). Retrieved from ACT website: Northwest Evaluation Association RIT Scale Norms. Portland, OR: Northwest Evaluation Association.
12 APPENDIX 1: METHODOLOGY This linking study examines the concurrent relationship between EXPLORE/PLAN/ACT and MAP assessments with the goal of publishing benchmarks on the RIT scale that are predictive of the ACT s college readiness benchmarks (ACT, 2010). Appendix Table 1 describes the three ACT assessments with their respective college readiness targets by content area. Appendix Table 1 ACT College Readiness Cut Points EXPLORE PLAN ACT Grade 8 Grade 9 Grade 10 Grade Math Study Sample NWEA solicited all known partner districts that administer both the EXPLORE/PLAN/ACT and MAP assessments to participate in this study. While not every eligible partner participated, the final study sample was large enough (unique total student n=29,417) to proceed with the analysis. Appendix Table 2 contains the distinct sample count. Appendix Table 2 Sample Counts Test Grade Unique Unique District Unique School Unique Student State Count Count Count Count ACT Explore Plan
13 Each district s EXPLORE/PLAN/ACT test records were matched to their corresponding MAP data via a robust matching algorithm housed in NWEA s Growth Research Database. The bulk of the study used matched students who took both assessments in same term. In the cases where students took the NWEA MAP test in different terms, we employed the following prioritized matching process. Priority 1 MAP given in SAME term as EXPLORE/PLAN/ACT Priority 2 - MAP test given one term BEFORE EXPLORE/PLAN/ACT Priority 3 - MAP test given two terms BEFORE EXPLORE/PLAN/ACT Priority 4 - MAP test given one term AFTER EXPLORE/PLAN/ACT Priority 5 - Map test given two terms AFTER EXPLORE/PLAN/ACT In order to ensure comparable RIT scores, we took the MAP percentile associated with the RIT score and substituted the RIT score associated with that percentile in the term the EXPLORE/PLAN/ACT was administered. For example, a winter test score under Priority 2 with a percentile of 75 would be substituted for the corresponding spring RIT score associated with the 75 th percentile. Appendix Table 3 contains the distribution of unique students by the EXPLORE/PLAN/ACT test, MAP Grade and prioritized matching scheme. Appendix Table 3 Prioritized Matching Count (Unique Students) by ACT Test and MAP Grade EXPLORE/PLAN/ACT Test and MAP Grade ACT P1 - Exact P2-1 Term Prior Priority Matching P3-2 Terms Prior P4-1 Term After Total PLAN ,822 EXPLORE 8 13, ,915 Total 20, ,417 Analysis The goal of the analysis is to find the statistical model that best describes the scale relationship between EXPLORE/PLAN/ACT and the NWEA MAP assessments. We tested multiple models including Ordinary Least Squares Regression (Linear and Quadratic) and Hierarchical Linear Model (HLM). The best model was determined by correlation (r) and overall model fit. Akaike Information Criterion (AIC) is the measure of model fit we used. Generally speaking, the AIC examines the tradeoffs between model accuracy and complexity whereby the model with the lowest AIC value is said to be the most parsimonious
14 Separate linear (1a) and quadratic (1b) regression routines were run for each relationship model. (1a) where X= RIT (1b) where X= RIT Based on the correlations and AIC fit statistics, the quadratic regression best described the shape of the scale relationship (see Appendix Table 4).
15 Appendix Table 4 Initial Model Correlations Test Model Linear Regression Quadratic Regression r AIC r AIC ACT Language Usage to ACT Language Usage to ACT Math to Math ACT to ACT to PLAN Language Usage to PLAN Language Usage to PLAN Math to Math PLAN to PLAN to EXPLORE Language Usage to EXPLORE Language Usage to EXPLORE Math to Math EXPLORE to EXPLORE to The next step in the analytic process was to determine whether any between-school variation existed in our scale relationships by running a simple unconstrained HLM model (2): (2) is the ACT/PLAN/EXPLORE score for student i in school j; is the grand mean (students within schools) variance in intercept between schools within school variance
16 Appendix Table 4 contains the Intraclass Correlation Coefficient (ICC) for each test and model. The ICC measures the proportion of variance in the dependent variable that is accounted for by our grouping structure.
17 Appendix Table 5 Intraclass Correlation Coefficients (ICC) by Test and Model Test Model t 00 σ 2 ICC ACT Language Usage to ACT Language Usage to ACT Math to Math ACT to ACT to Plan Language Usage to Plan Language Usage to Plan Math to Math Plan to Plan to Explore Language Usage to Explore Language Usage to Explore Math to Math Explore to Explore to The ICCs offer a somewhat conflicting picture on the appropriateness of using a multilevel model in the case of this study. For instance, the EXPLORE assessments have the least amount of between-group variance (less than six percent) and the nearly the most number grouping levels (between 29 and 51 individual schools depending on the model). While no well-established ICC thresholds exist per se, it would appear the EXPLORE would not be a good candidate when compared to the ACT and PLAN ICCs. One explanation for the observed differences could be related to the specific analytic sample used. While we could have employed two separate methods (Quadratic for EXPLORE, HLM for ACT and PLAN),
18 we felt the quadratic model offered transparency and consistency while maintaining good model fit characteristics. Figures 1 through 3 illustrate the final fitted model for EXPLORE/PLAN/ACT Math to NWEA MAP Math. Each figure contains notes referencing specific sample or estimation characteristics. Please note standardized residuals greater than 2 or less than -2 were removed from the final model to eliminate potential sources of statistical noise. We should also note the MAP assessment measures student performance relative to state content standards rather than discrete college readiness standards. This difference in content alignment could possibility degrade the published regression coefficients between MAP and EXPLORE/PLAN/ACT. Figure 1 - ACT Math to NWEA Math The ACT Math scatter plot and residuals exhibit pronounced curvilinear shapes. The sample also becomes sparse toward the top end of the distribution, making those estimates less reliable.
19 Figure 2 - PLAN Math to NWEA Math The PLAN Math scatter plot and residuals display the same curvilinear pattern as the ACT but appears to have more variance along the fit line. Like the ACT, the sample also becomes sparse toward the top end of the distribution, making those estimates less reliable.
20 Figure 3 - EXPLORE Math to NWEA Math The EXPLORE Math scatter plot and residuals have a slight curvilinear profile especially when compared to the ACT and PLAN assessments. The EXPLORE assessment has a pronounced ceiling effect in reference to the NWEA MAP assessment, meaning the NWEA assessment has more stretch than EXPLORE at the eighth grade level.
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The simple linear model Regression Analysis: Basic Concepts Allin Cottrell Represents the dependent variable, y i, as a linear function of one independent variable, x i, subject to a random disturbance
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
Do Supplemental Online Recorded Lectures Help Students Learn Microeconomics?* Jennjou Chen and Tsui-Fang Lin Abstract With the increasing popularity of information technology in higher education, it has
Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing
Department of Psychology and Human Development Vanderbilt University GCM, 2010 1 Multilevel Modeling - A Brief Introduction 2 3 4 5 Introduction In this lecture, we introduce the multilevel model for change.
Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the
E x e c u t i v e S u m m a r y Improving science content and inquiry standards mastery of fourth-grade students: A study of the effectiveness of National Geographic Science Chicago Public Schools 2010
Section 3 Part 1 Relationships between two numerical variables 1 Relationship between two variables The summary statistics covered in the previous lessons are appropriate for describing a single variable.
Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma firstname.lastname@example.org The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association
The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards: Make sense of problems
THE CORRELATION COEFFICIENT 1 More Statistical Notation Correlational analysis requires scores from two variables. X stands for the scores on one variable and Y stands for the scores on the other variable.
THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i
Introductory Guide to HLM With HLM 7 Software 3 G. David Garson HLM software has been one of the leading statistical packages for hierarchical linear modeling due to the pioneering work of Stephen Raudenbush
AP Statistics 1998 Scoring Guidelines These materials are intended for non-commercial use by AP teachers for course and exam preparation; permission for any other use must be sought from the Advanced Placement
Bivariate Analysis Variable 2 LEVELS >2 LEVELS COTIUOUS Correlation Used when you measure two continuous variables. Variable 2 2 LEVELS X 2 >2 LEVELS X 2 COTIUOUS t-test X 2 X 2 AOVA (F-test) t-test AOVA
! ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE School of Mathematical Sciences New Revised COURSE: COS-MATH-252 Probability and Statistics II 1.0 Course designations and approvals:
AIMSweb & Common Core Reporting Using AIMSweb and Common Core Reporting Tools for Improved Instructional Outcomes Copyright Notice AIMSweb Instructional Reports Linked with envisionmath Common Core + focusmath
AIMSweb Default Cut Scores Explained completed a complex research project using data from 20 states to predict probabilities of success on state tests from scores on AIMSweb measures. The study used data
Office of Research and Development RN-03, May 1998 Block Schedules and Student Performance on AP Examinations BACKGROUND In the past decade, U.S. secondary schools have introduced a variety of alternative
By Hui Bian Office for Faculty Excellence 1 Email: email@example.com Phone: 328-5428 Location: 2307 Old Cafeteria Complex 2 When want to predict one variable from a combination of several variables. When want
14. Regression A. Introduction to Simple Linear Regression B. Partitioning Sums of Squares C. Standard Error of the Estimate D. Inferential Statistics for b and r E. Influential Observations F. Regression
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