Understanding Educational Statistics Using Microsoft Excel and SPSS UNDERSTANDING EDUCATIONAL STATISTICS USING MICROSOFT EXCEL1 AND SPSS1 UNDERSTANDING EDUCATIONAL STATISTICS USING MICROSOFT EXCEL1AND[.]
UNDERSTANDING EDUCATIONAL STATISTICS USING MICROSOFT EXCEL1 AND SPSS1 UNDERSTANDING EDUCATIONAL STATISTICS USING MICROSOFT EXCEL1AND SPSS1 MARTIN LEE ABBOTT Department of Sociology Seattle Pacific University Seattle, Washington Copyright # 2011 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic formats For more information about Wiley products, visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data: ISBN: 978-0-470-88945-9 Printed in Singapore 10 To those who seek a deeper understanding of the world as it appears and of what lies beyond CONTENTS Preface xix Acknowledgments xxi Introduction Approach of the Book, Project Labs, Real-World Data, Research Design, “Practical Significance”—Implications of Findings, Coverage of Statistical Procedures, Getting Acquainted with Microsoft Excel1 Data Management, Rows and Columns, Data Sheets, The Excel1 Menus, Home, Insert Tab, Page Layout, Formulas, 10 Data, 11 Review and View Menus, 16 vii viii CONTENTS Using Statistics in Excel1 17 Using Statistical Functions, 17 Entering Formulas Directly, 17 Data Analysis Procedures, 20 Missing Values and “0” Values in Excel1 Analyses, 20 Using Excel1 with Real Data, 20 School-Level Achievement Database, 20 TAGLIT Data, 21 The STAR Classroom Observation ProtocolTM Data, 22 SPSS1 Basics 23 Using SPSS1, 23 General Features, 24 Management Functions, 26 Reading and Importing Data, 26 Sort, 26 Additional Management Functions, 30 Split File, 30 Transform/Compute (Creating Indices), 32 Merge, 34 Analysis Functions, 39 Descriptive Statistics—Central Tendency Research Applications—Spuriousness, 41 Descriptive and Inferential Statistics, 44 The Nature of Data—Scales of Measurement, 44 Nominal Data, 45 Ordinal Data, 46 Interval Data, 48 Ratio Data, 50 Choosing the Correct Statistical Procedure for the Nature of Research Data, 50 Descriptive Statistics—Central Tendency, 51 Mean, 52 Median, 52 Mode, 54 Using Excel1 and SPSS1 to Understand Central Tendency, 56 Excel1, 56 SPSS1, 58 Distributions, 61 Describing the Normal Distribution, 62 Central Tendency, 63 Skewness, 63 41 514 TABLE A Z-Score Table (Values Shown Are Percentages) z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 0.000 3.983 7.926 11.791 15.542 19.146 22.575 25.804 28.814 31.594 34.134 36.433 38.493 40.320 41.924 43.319 44.520 45.543 46.407 47.128 47.725 48.214 48.610 48.928 49.180 49.379 49.534 49.653 49.744 49.813 49.865 50.000 46.017 42.074 38.209 34.458 30.854 27.425 24.196 21.186 18.406 15.866 13.567 11.507 9.680 8.076 6.681 5.480 4.457 3.593 2.872 2.275 1.786 1.390 1.072 0.820 0.621 0.466 0.347 0.256 0.187 0.135 0.01 0.399 49.601 4.380 45.620 8.317 41.683 12.172 37.828 15.910 34.090 19.497 30.503 22.907 27.093 26.115 23.885 29.103 20.897 31.859 18.141 34.375 15.625 36.650 13.350 38.686 11.314 40.490 9.510 42.073 7.927 43.448 6.552 44.630 5.370 45.637 4.363 46.485 3.515 47.193 2.807 47.778 2.222 48.257 1.743 48.645 1.355 48.956 1.044 49.202 0.798 49.396 0.604 49.547 0.453 49.664 0.336 49.752 0.248 49.819 0.181 49.869 0.131 0.02 0.798 4.776 8.706 12.552 16.276 19.847 23.237 26.424 29.389 32.121 34.614 36.864 38.877 40.658 42.220 43.574 44.738 45.728 46.562 47.257 47.831 48.300 48.679 48.983 49.224 49.413 49.560 49.674 49.760 49.825 49.874 49.202 45.224 41.294 37.448 33.724 30.153 26.763 23.576 20.611 17.879 15.386 13.136 11.123 9.342 7.780 6.426 5.262 4.272 3.438 2.743 2.169 1.700 1.321 1.017 0.776 0.587 0.440 0.326 0.240 0.175 0.126 0.03 1.197 48.803 5.172 44.828 9.095 40.905 12.930 37.070 16.640 33.360 20.194 29.806 23.565 26.435 26.730 23.270 29.673 20.327 32.381 17.619 34.850 15.151 37.076 12.924 39.065 10.935 40.824 9.176 42.364 7.636 43.699 6.301 44.845 5.155 45.818 4.182 46.638 3.363 47.320 2.680 47.882 2.118 48.341 1.659 48.713 1.287 49.010 0.990 49.245 0.755 49.430 0.570 49.573 0.427 49.683 0.317 49.767 0.233 49.831 0.169 49.878 0.122 0.04 1.595 48.405 5.567 44.433 9.483 40.517 13.307 36.693 17.003 32.997 20.540 29.460 23.891 26.109 27.035 22.965 29.955 20.045 32.639 17.361 35.083 14.917 37.286 12.714 39.251 10.749 40.988 9.012 42.507 7.493 43.822 6.178 44.950 5.050 45.907 4.093 46.712 3.288 47.381 2.619 47.932 2.068 48.382 1.618 48.745 1.255 49.036 0.964 49.266 0.734 49.446 0.554 49.585 0.415 49.693 0.307 49.774 0.226 49.836 0.164 49.882 0.118 0.05 1.994 48.006 5.962 44.038 9.871 40.129 13.683 36.317 17.364 32.636 20.884 29.116 24.215 25.785 27.337 22.663 30.234 19.766 32.894 17.106 35.314 14.686 37.493 12.507 39.435 10.565 41.149 8.851 42.647 7.353 43.943 6.057 45.053 4.947 45.994 4.006 46.784 3.216 47.441 2.559 47.982 2.018 48.422 1.578 48.778 1.222 49.061 0.939 49.286 0.714 49.461 0.539 49.598 0.402 49.702 0.298 49.781 0.219 49.841 0.159 49.886 0.114 0.06 2.392 47.608 6.356 43.644 10.257 39.743 14.058 35.942 17.724 32.276 21.226 28.774 24.537 25.463 27.637 22.363 30.511 19.489 33.147 16.853 35.543 14.457 37.698 12.302 39.617 10.383 41.309 8.692 42.786 7.215 44.062 5.938 45.154 4.846 46.080 3.920 46.856 3.144 47.500 2.500 48.030 1.970 48.461 1.539 48.809 1.191 49.086 0.914 49.305 0.695 49.477 0.523 49.609 0.391 49.711 0.289 49.788 0.212 49.846 0.154 49.889 0.111 0.07 2.790 47.210 6.749 43.251 10.642 39.358 14.431 35.569 18.082 31.918 21.566 28.434 24.857 25.143 27.935 22.065 30.785 19.215 33.398 16.602 35.769 14.231 37.900 12.100 39.796 10.204 41.466 8.534 42.922 7.078 44.179 5.821 45.254 4.746 46.164 3.836 46.926 3.074 47.558 2.442 48.077 1.923 48.500 1.500 48.840 1.160 49.111 0.889 49.324 0.676 49.492 0.508 49.621 0.379 49.720 0.280 49.795 0.205 49.851 0.149 49.893 0.107 0.08 3.188 46.812 7.142 42.858 11.026 38.974 14.803 35.197 18.439 31.561 21.904 28.096 25.175 24.825 28.230 21.770 31.057 18.943 33.646 16.354 35.993 14.007 38.100 11.900 39.973 10.027 41.621 8.379 43.056 6.944 44.295 5.705 45.352 4.648 46.246 3.754 46.995 3.005 47.615 2.385 48.124 1.876 48.537 1.463 48.870 1.130 49.134 0.866 49.343 0.657 49.506 0.494 49.632 0.368 49.728 0.272 49.801 0.199 49.856 0.144 49.897 0.104 0.09 3.586 46.414 7.535 42.465 11.409 38.591 15.173 34.827 18.793 31.207 22.240 27.760 25.490 24.510 28.524 21.476 31.327 18.673 33.891 16.109 36.214 13.786 38.298 11.702 40.147 9.853 41.774 8.226 43.189 6.811 44.408 5.592 45.449 4.551 46.327 3.673 47.062 2.938 47.670 2.330 48.169 1.831 48.574 1.426 48.899 1.101 49.158 0.842 49.361 0.639 49.520 0.480 49.643 0.357 49.736 0.264 49.807 0.193 49.861 0.139 49.900 0.100 Source: Pearson, Karl, F.R.S Tables for Statisticians and Biometricians, Part I, 3rd ed., University College, London: Biometric Laboratory, Cambridge University Press, 1930 Used with permission 515 APPENDIX: STATISTICAL TABLES TABLE B Exclusion Values for the T Distribution One-Tailed Two-Tailed 0.4 0.8 0.25 0.5 0.1 0.2 0.05 0.1 0.025 0.05 0.01 0.02 0.005 0.01 Degrees of Freedom 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 0.325 0.289 0.277 0.271 0.267 0.265 0.263 0.262 0.261 0.260 0.260 0.259 0.259 0.258 0.258 0.258 0.257 0.257 0.257 0.257 0.257 0.256 0.256 0.256 0.256 0.256 0.256 0.256 0.256 0.256 0.255 0.254 0.254 0.253 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.677 0.674 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.303 1.296 1.289 1.282 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.671 1.658 1.645 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.021 2.000 1.980 1.960 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.358 2.326 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.660 2.617 2.576 0.0025 0.005 127.320 14.089 7.453 5.598 4.773 4.317 4.029 3.833 3.690 3.581 3.497 3.428 3.372 3.326 3.286 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.104 3.091 3.078 3.067 3.057 3.047 3.038 3.030 2.971 2.915 2.860 2.807 Source: Pearson, E S., and Hartley, H O Biometrika Tables for Statisticians, Volume I., 2nd ed Cambridge, UK: University Press, 1962 Used with permission 516 APPENDIX: STATISTICAL TABLES TABLE C Critical (Exclusion) Values for the Distribution of F Exclusion Level df in the Denominator 10 11 12 13 14 15 16 17 18 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 df in the Numerator (Between) 161 4052 18.51 98.49 10.13 34.12 7.71 21.20 6.61 16.26 5.99 13.74 5.59 12.25 5.32 11.26 5.12 10.56 4.96 10.04 4.84 9.65 4.75 9.33 4.67 9.07 4.60 8.86 4.54 8.68 4.49 8.53 4.45 8.40 4.41 8.28 200 4999 19.00 99.00 9.55 30.82 6.94 18.00 5.79 13.27 5.14 10.92 4.74 9.55 4.46 8.65 4.26 8.02 4.10 7.56 3.98 7.20 3.88 6.93 3.80 6.70 3.74 6.51 3.68 6.36 3.63 6.23 3.59 6.11 3.55 6.01 216 5403 19.16 99.17 9.28 29.46 6.59 16.69 5.41 12.06 4.76 9.78 4.35 8.45 4.07 7.59 3.86 6.99 3.71 6.55 3.59 6.22 3.49 5.95 3.41 5.74 3.34 5.56 3.29 5.42 3.24 5.29 3.20 5.18 3.16 5.09 225 5625 19.25 99.25 9.12 28.71 6.39 15.98 5.19 11.39 4.53 9.15 4.12 7.85 3.84 7.01 3.63 6.42 3.48 5.99 3.36 5.67 3.26 5.41 3.18 5.20 3.11 5.03 3.06 4.89 3.01 4.77 2.96 4.67 2.93 4.58 230 5764 19.30 99.30 9.01 28.24 6.26 15.52 5.05 10.97 4.39 8.75 3.97 7.46 3.69 6.63 3.48 6.06 3.33 5.64 3.20 5.32 3.11 5.06 3.02 4.86 2.96 4.69 2.90 4.56 2.85 4.44 2.81 4.34 2.77 4.25 234 5859 19.33 99.33 8.94 27.91 6.16 15.21 4.95 10.67 4.28 8.47 3.87 7.19 3.58 6.37 3.37 5.80 3.22 5.39 3.09 5.07 3.00 4.82 2.92 4.62 2.85 4.46 2.79 4.32 2.74 4.20 2.70 4.10 3.66 4.01 237 5928 19.36 99.36 8.88 27.67 6.09 14.98 4.88 10.45 4.21 8.26 3.79 7.00 3.50 6.19 3.29 5.62 3.14 5.21 3.01 4.88 2.92 4.65 2.84 4.44 2.77 4.28 2.70 4.14 2.66 4.03 2.62 3.93 2.58 3.85 10 11 12 239 5981 19.37 99.37 8.84 27.49 6.04 14.80 4.82 10.29 4.15 8.10 3.73 6.84 3.44 6.03 3.23 5.47 3.07 5.06 2.95 4.74 2.85 4.50 2.77 4.30 2.70 4.14 2.64 4.00 2.59 3.89 2.55 3.79 2.51 3.71 241 6022 19.38 99.39 8.81 27.34 6.00 14.66 4.78 10.15 4.10 7.98 3.68 6.71 3.39 5.91 3.18 5.35 3.02 4.95 2.90 4.63 2.80 4.39 2.72 4.19 2.65 4.03 2.59 3.89 2.54 3.78 2.50 3.68 2.46 3.60 242 6056 19.39 99.40 8.78 27.23 5.96 14.54 4.74 10.05 4.06 7.87 3.63 6.62 3.34 5.82 3.13 5.26 2.97 4.85 2.86 4.54 2.76 4.30 2.67 4.10 2.60 3.94 2.55 3.80 2.49 3.69 2.45 3.59 2.41 3.51 243 6082 19.40 99.41 8.76 27.13 5.93 14.45 4.70 9.96 4.03 7.79 3.60 6.54 3.31 5.74 3.10 5.18 2.94 4.78 2.82 4.46 2.72 4.22 2.63 4.02 2.56 3.86 2.51 3.73 2.45 3.61 2.41 3.52 2.37 3.44 244 6106 19.41 99.42 8.74 27.05 5.91 14.37 4.68 9.89 4.00 7.72 3.57 6.47 3.28 5.67 3.07 5.11 2.91 4.71 2.79 4.40 2.69 4.16 2.60 3.96 2.53 3.80 2.48 3.67 2.42 3.55 2.38 3.45 2.34 3.37 517 APPENDIX: STATISTICAL TABLES TABLE 14.C (Continued) Exclusion Level 19 20 21 22 23 24 25 df in the Denominator 26 27 28 29 30 32 34 36 38 40 42 44 46 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 df in the Numerator (Between) 4.38 8.18 4.35 8.10 4.32 8.02 4.30 7.94 4.28 7.88 4.26 7.82 4.24 7.77 4.22 7.72 4.21 7.68 4.20 7.64 4.18 7.60 4.17 7.56 4.15 7.50 4.13 7.44 4.11 7.39 4.10 7.35 4.08 7.31 4.07 7.27 4.06 7.24 4.05 7.21 3.52 5.93 3.49 5.85 3.47 5.78 3.44 5.72 3.42 5.66 3.40 5.61 3.38 5.57 3.37 5.53 3.35 5.49 3.34 5.45 3.33 5.42 3.32 5.39 3.30 5.34 3.28 5.29 3.26 5.25 3.25 5.21 3.23 5.18 3.22 5.15 3.21 5.12 3.20 5.10 3.13 5.01 3.10 4.94 3.07 4.87 3.05 4.82 3.03 4.76 3.01 4.72 2.99 4.68 2.98 4.64 2.96 4.60 2.95 4.57 2.93 4.54 2.92 4.51 2.90 4.46 2.88 4.42 2.86 4.38 2.85 4.34 2.84 4.31 2.83 4.29 2.82 4.26 2.81 4.24 2.90 4.50 2.87 4.43 2.84 4.37 2.82 4.31 2.80 4.26 2.78 4.22 2.76 4.18 2.74 4.14 2.73 4.11 2.71 4.07 2.70 4.04 2.69 4.02 2.67 3.97 2.65 3.93 2.63 3.89 2.62 3.86 2.61 3.83 2.59 3.80 2.58 3.78 2.57 3.76 2.74 4.17 2.71 4.10 2.68 4.04 2.66 3.99 2.64 3.94 2.62 3.90 2.60 3.86 2.59 3.82 2.57 3.79 2.56 3.76 2.54 3.73 2.53 3.70 2.51 3.66 2.49 3.61 2.48 3.58 2.46 3.54 2.45 3.51 2.44 3.49 2.43 3.46 2.42 3.44 2.63 3.94 2.60 3.87 2.57 3.81 2.55 3.76 2.53 3.71 2.51 3.67 2.49 3.63 2.47 3.59 2.46 3.56 2.44 3.53 2.43 3.50 2.42 3.47 2.40 3.42 2.38 3.38 2.36 3.35 2.35 3.32 2.34 3.29 2.32 3.26 2.31 3.24 2.30 3.22 2.55 3.77 2.52 3.71 2.49 3.65 2.47 3.59 2.45 3.54 2.43 3.50 2.41 3.46 2.39 3.42 2.37 3.39 2.36 3.36 2.35 3.33 2.34 3.30 2.32 3.25 2.30 3.21 2.28 3.18 2.26 3.15 2.25 3.12 2.24 3.10 2.23 3.07 2.22 3.05 2.48 3.63 2.45 3.56 2.42 3.51 2.40 3.45 2.38 3.41 2.36 3.36 2.34 3.32 2.32 3.29 2.30 3.26 2.29 3.23 2.28 3.20 2.27 3.17 2.25 3.12 2.23 3.08 2.21 3.04 2.19 3.02 2.18 2.99 2.17 2.96 2.16 2.94 2.14 2.92 10 2.43 3.52 2.40 3.45 2.37 3.40 2.35 3.35 2.32 3.30 2.30 3.25 2.28 3.21 2.27 3.17 2.25 3.14 2.24 3.11 2.22 3.08 2.21 3.06 2.19 3.01 2.17 2.97 2.15 2.94 2.14 2.91 2.12 2.88 2.11 2.86 2.10 2.84 2.09 2.82 2.38 3.43 2.35 3.37 2.32 3.31 2.30 3.26 2.28 3.21 2.26 3.17 2.24 3.13 2.22 3.09 2.20 3.06 2.19 3.03 2.18 3.00 2.16 2.98 2.14 2.94 2.12 2.89 2.10 2.86 2.09 2.82 2.07 2.80 2.06 2.77 2.05 2.75 2.04 2.73 11 2.34 3.36 2.31 3.30 2.28 3.24 2.26 3.18 2.24 3.14 2.22 3.09 2.20 3.05 2.18 3.02 2.16 2.98 2.15 2.95 2.14 2.92 2.12 2.90 2.10 2.86 2.08 2.82 2.06 2.78 2.05 2.75 2.04 2.73 2.02 2.70 2.01 2.68 2.00 2.66 12 2.31 3.30 2.28 3.23 2.25 3.17 2.23 3.12 2.20 3.07 2.18 3.03 2.16 2.99 2.15 2.96 2.13 2.93 2.12 2.90 2.10 2.87 2.09 2.84 2.07 2.80 2.05 2.76 2.03 2.72 2.02 2.69 2.00 2.66 1.99 2.64 1.98 2.62 1.97 2.60 (continued) 518 APPENDIX: STATISTICAL TABLES TABLE 14.C (Continued) Exclusion Level 48 50 55 60 df in the Denominator 65 70 80 100 125 150 200 400 1000 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.05 0.01 df in the Numerator (Between) 4.04 7.19 4.03 7.17 4.02 7.12 4.00 7.08 3.99 7.04 3.98 7.01 3.96 6.96 3.94 6.90 3.92 6.84 3.91 6.81 3.89 6.76 3.86 6.7 3.85 6.66 3.84 6.63 3.19 5.08 3.18 5.06 3.17 5.01 3.15 4.98 3.14 4.95 3.13 4.92 3.11 4.88 3.09 4.82 3.07 4.78 3.06 4.75 3.04 4.71 3.02 4.66 3.00 4.62 2.99 4.60 2.80 4.22 2.79 4.20 2.78 4.16 2.76 4.13 2.75 4.10 2.74 4.08 2.72 4.04 2.70 3.98 2.68 3.94 2.67 3.91 2.65 3.88 2.62 3.83 2.61 3.80 2.60 3.78 2.56 3.74 2.56 3.72 2.54 3.68 2.52 3.65 2.51 3.62 2.50 3.60 2.48 3.56 2.46 3.51 2.44 3.47 2.43 3.44 2.41 3.41 2.39 3.36 2.38 3.34 2.37 3.32 2.41 3.42 2.40 3.41 2.38 3.37 2.37 3.34 2.36 3.31 2.35 3.29 2.33 3.25 2.30 3.20 2.29 3.17 2.27 3.14 2.26 3.11 2.23 3.06 2.22 3.04 2.21 3.02 2.30 3.20 2.29 3.18 2.27 3.15 2.25 3.12 2.24 3.09 2.23 3.07 2.21 3.04 2.19 2.99 2.17 2.95 2.16 2.92 2.14 2.90 2.12 2.85 2.10 2.82 2.09 2.80 2.21 3.04 2.20 3.02 2.18 2.98 2.17 2.95 2.15 2.93 2.14 2.91 2.12 2.87 2.10 2.82 2.08 2.79 2.07 2.76 2.05 2.73 2.03 2.69 2.02 2.66 2.01 2.64 2.40 2.90 2.13 2.88 2.11 2.85 2.10 2.82 2.08 2.79 2.07 2.77 2.05 2.74 2.03 2.69 2.01 2.65 2.00 2.62 1.98 2.60 1.96 2.55 1.95 2.53 1.94 2.51 10 2.08 2.80 2.07 2.78 2.05 2.75 2.04 2.72 2.02 2.70 2.01 2.67 1.99 2.64 1.97 2.59 1.95 2.56 1.94 2.53 1.92 2.50 1.90 2.46 1.89 2.43 1.88 2.41 2.03 2.71 2.02 2.70 2.00 2.66 1.99 2.63 1.98 2.61 1.97 2.59 1.95 2.55 1.92 2.51 1.90 2.47 1.89 2.44 1.87 2.41 1.85 2.37 1.84 2.34 1.83 2.32 11 1.99 2.64 1.98 2.62 1.97 2.59 1.95 2.56 1.94 2.54 1.93 2.51 1.91 2.48 1.88 2.43 1.86 2.40 1.85 2.37 1.83 2.34 1.81 2.29 1.80 2.26 1.79 2.24 12 1.96 2.58 1.95 2.56 1.93 2.53 1.92 2.50 1.90 2.47 1.89 2.45 1.88 2.41 1.85 2.36 1.83 2.33 1.82 2.30 1.80 2.28 1.78 2.23 1.76 2.20 1.75 2.18 Source: Snedecor, G W., and Cochran, W G Statistical Methods Ames, IA: Iowa State University Press, 1980 Used with permission 519 APPENDIX: STATISTICAL TABLES TABLE D k ¼ Num of Groups MSwdf 10 11 12 13 14 15 16 17 18 19 20 24 30 40 60 120 Tukey’s Range Test (Upper 5% Points) 18.00 6.09 4.50 3.93 3.64 3.46 3.34 3.26 3.20 3.15 3.11 3.08 3.06 3.03 3.01 3.00 2.98 2.97 2.96 2.95 2.92 2.89 2.86 2.83 2.80 2.77 27.00 8.30 5.91 5.04 4.60 4.34 4.16 4.04 3.95 3.88 3.82 3.77 3.73 3.70 3.67 3.65 3.63 3.61 3.59 3.58 3.53 3.49 3.44 3.40 3.36 3.31 32.80 9.80 6.82 5.76 5.22 4.90 4.68 4.53 4.42 4.33 4.26 4.20 4.15 4.11 4.08 4.05 4.02 4.00 3.98 3.96 3.90 3.84 3.79 3.74 3.69 3.63 37.10 10.90 7.50 6.29 5.67 5.31 5.06 4.89 4.76 4.65 4.57 4.51 4.45 4.41 4.37 4.33 4.30 4.28 4.25 4.23 4.17 4.10 4.04 3.98 3.92 3.86 40.40 11.70 8.04 6.71 6.03 5.63 5.36 5.17 5.02 4.91 4.82 4.75 4.69 4.64 4.60 4.56 4.52 4.49 4.47 4.45 4.37 4.30 4.23 4.16 4.10 4.03 43.10 12.40 8.48 7.05 6.33 5.89 5.61 5.40 5.24 5.12 5.03 4.95 4.88 4.83 4.78 4.74 4.71 4.67 4.65 4.62 4.54 4.46 4.39 4.31 4.24 4.17 45.40 13.00 8.85 7.35 6.58 6.12 5.82 5.60 5.43 5.30 5.20 5.12 5.05 4.99 4.94 4.90 4.86 4.82 4.79 4.77 4.68 4.60 4.52 4.44 4.36 4.29 47.40 13.50 9.18 7.60 6.80 6.32 6.00 5.77 5.60 5.46 5.35 5.27 5.19 5.13 5.08 5.03 4.99 4.96 4.92 4.90 4.81 4.72 4.63 4.55 4.48 4.39 10 49.10 14.00 9.46 7.83 6.99 6.49 6.16 5.92 5.74 5.60 5.49 5.40 5.32 5.25 5.20 5.15 5.11 5.07 5.04 5.01 4.92 4.83 4.74 4.65 4.56 4.47 Source: Pearson, E S., and Hartley, H O Biometrika Tables for Statisticians, Volume I, 2nd ed Cambridge, UK: University Press, 1962 Used with permission 520 TABLE E APPENDIX: STATISTICAL TABLES Critical (Exclusion) Values for Pearson’s Correlation Coefficient, r One-Tailed Two-Tailed 0.05 0.1 0.025 0.05 0.01 0.02 0.005 0.01 0.0025 0.005 0.0005 0.001 Degrees of Freedom 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 60 70 80 90 100 0.988 0.9000 0.805 0.729 0.669 0.621 0.582 0.549 0.521 0.497 0.476 0.457 0.441 0.426 0.412 0.400 0.389 0.378 0.369 0.360 0.323 0.296 0.275 0.257 0.243 0.231 0.211 0.195 0.183 0.173 0.164 0.9969 0.950 0.878 0.811 0.754 0.707 0.666 0.632 0.602 0.576 0.553 0.532 0.514 0.497 0.482 0.468 0.456 0.444 0.433 0.423 0.381 0.349 0.325 0.304 0.288 0.273 0.250 0.232 0.217 0.205 0.195 0.9995 0.9800 0.9343 0.882 0.833 0.789 0.750 0.715 0.685 0.658 0.634 0.612 0.592 0.574 0.558 0.543 0.529 0.516 0.503 0.492 0.445 0.409 0.381 0.358 0.338 0.322 0.295 0.274 0.257 0.242 0.230 0.999877 0.99000 0.9587 0.9172 0.875 0.834 0.798 0.765 0.735 0.708 0.684 0.661 0.641 0.623 0.606 0.590 0.575 0.561 0.549 0.537 0.487 0.449 0.418 0.393 0.372 0.354 0.325 0.302 0.283 0.267 0.254 0.9999692 0.99500 0.9740 0.9417 0.9056 0.870 0.836 0.805 0.776 0.750 0.726 0.703 0.683 0.664 0.647 0.631 0.616 0.602 0.589 0.576 0.524 0.484 0.452 0.425 0.403 0.384 0.352 0.327 0.307 0.290 0.276 0.99999877 0.99900 0.99114 0.9741 0.9509 0.9249 0.898 0.872 0.847 0.823 0.801 0.780 0.760 0.742 0.725 0.708 0.693 0.679 0.665 0.652 0.597 0.554 0.519 0.490 0.465 0.443 0.408 0.380 0.357 0.338 0.321 Source: Pearson, E S., and Hartley, H O Biometrika Tables for Statisticians, Volume I, 2nd ed Cambridge, UK: University Press, 1962 Used with permission 521 APPENDIX: STATISTICAL TABLES TABLE F Critical Values of the Chi Square Distribution p Value Degrees of Freedom (k) 0.1 0.05 0.02 0.01 0.001 10 11 12 13 14 15 16 17 18 19 20 2.706 4.605 6.251 7.779 9.236 10.645 12.017 13.362 14.684 15.987 17.275 18.549 19.812 21.064 22.307 23.542 24.769 25.989 27.204 28.412 3.841 5.991 7.815 9.488 11.070 12.592 14.067 15.507 16.919 18.307 19.675 21.026 22.362 23.685 24.996 26.296 27.587 28.869 30.144 31.410 5.412 7.824 9.837 11.668 13.388 15.033 16.622 18.168 19.679 21.161 22.618 24.054 25.472 26.873 28.259 29.633 30.995 32.346 33.687 35.020 6.635 9.210 11.345 13.277 15.086 16.812 18.475 20.090 21.666 23.209 24.725 26.217 27.688 29.141 30.578 32.000 33.409 34.805 36.191 37.566 10.827 13.815 16.266 18.467 20.515 22.457 24.322 26.125 27.877 29.588 31.264 32.909 34.528 36.123 37.697 39.252 40.790 42.312 43.820 45.315 Source: Pearson, E S., and Hartley, H O Biometrika Tables for Statisticians, Volume I, (2nd ed.) Cambridge, UK: University Press, 1962 Used with permission INDEX Aggregate scores, 21 Alpha error See Type I error Analysis of variance (ANOVA), 257–336 calculation of, 262–69 components of variance, 260–61 F-test, 262 factorial (2XANOVA), 307–336 interaction effect, See Interaction main effects, 310–11 one way, 257–305 simple effects, See Simple effects two-way within-subjects, 308 within-subjects, 307–8, 329, 499–508 ANCOVA, 309, 327 Assumptions of ANOVA, 276–77 bivariate regression, 408–9 chi square test of independence, 462 correlation, 360–62 independent-samples T-test, 229–36 multiple linear regression, 434–36 Average deviation, 89–91 Beta, 407–8, 419 Beta error See Type II error Bimodal distribution, See Distribution, bimodal Bivariate regression, See Regression Case study, 157, 169 Central limit theorem, 157–58, 169 Central tendency, See Descriptive statistics, central tendency Chi square, 453–83 contingency tables, 453–54, 483 effect size, See Effect size expected frequencies, 456, 462–64 frequencies versus proportions, 460 goodness of fit, 455–461, 483 repeated measures, 470–72, 483 special 2X2, 466–67 test of independence, 456–57, 461–72, 483 Coefficient of determination, 354, 374 Cohen’s d, 192, 228, See also Effect size Confidence interval, defined, 197, 204 for independent t test, 227–28 for population mean, 197–99 Understanding Educational Statistics Using Microsoft Excel1 and SPSS1 By Martin Lee Abbott # 2011 John Wiley & Sons, Inc Published 2011 by John Wiley & Sons, Inc 523 524 Confidence interval (Continued ) for regression, 396–97, 419 value of, 199 Contingency coefficient, 460, 483 Contingency tables, See Chi square, contingency tables Continuous variable, 240 Control group, 150, 169 Convenience sample, 169 Correlation, 337–69, See also Pearson’s r versus causation, 357 contingency coefficient, See Contingency coefficient Cramer’s V, See Cramer’s V eta square, See Eta square nature of, 338–39 partial eta square, See Partial eta square phi, See Phi problems, 356–58 Spearman’s rho, See Nonparametric statistics z score method, 349–51 Cramer’s V, 469–470, 483 Crosstabs See Chi Square, contingency tables Cumulative proportions, 105, 108, 115–119, See also Percentile deriving sample scores, 130–31 transforming to z scores, 128–29 Curvilinear relationship, 358, 409–12, 433 Deciles, 83, 96 Degrees of freedom in ANOVA, 266 in chi square, 464–66 in correlation, 353 defined, 185–86, 204 in independent T test, 221, 224 in single sample T test, 185–87 Dependent variables, 169 Descriptive statistics, 41–99 central tendency, 51, 54–60, 63, 71–75 contrasted to inferential statistics, 44 graphical methods, 66–71 research applications, 41–44 scales of measurement, 44–50, 74 standard deviation, 87–97 variability, 81–99 Diagnostics, 292, 412 INDEX Dichotomized variable, 339, 375 Distribution, 61–62 bimodal, 54, 71 data, 61–62, 73 frequency, 66, 73 of means, 160 nature of, 61 normal, See Normal distribution sampling, 178, 156–61 Distribution-free tests, See Nonparametric statistics Dunnett test, 273 Effect size, 4–5, 168–69, 193 ANOVA, factorial, 318–19 ANOVA, one way, 269–71 Chi square goodness of fit, 460 Chi square 2x2 tables, 467 Chi square test of independence, 469 correlation, 354–56 defined, 191, 205 multiple linear regression, 430 regression, 391–92, 414 T test, dependent, 494 T test, independent samples, 228 T test, single mean, 191–93 within-subjects ANOVA, 507 Z test, 168 Error regression, See standard error, of estimate sampling, 157 Estimate biased and unbiased, 181, 204 interval, See Confidence interval point, See Point estimate Eta Square (2), 270 EXCEL1, xix–xx, 1, 3, 5–21 ANOVA, 285–87 bivariate regression, 401–404 central tendency, 56–58 chi square, 472–78 correlation, 366–67 cumulative proportions, 115–120 data analysis procedures, 20 data management, 7–9 dependent t-test, 496–98 entering formulas directly, 17–19 F-test two sample for variances, 230 independent t test, 236–38 525 INDEX menus, 9–16 missing cases and zeros, 20 parameter estimation, 181–82 percentiles, 84–87 real-world data with, 20–22 scattergram, 345–47 single sample T test, 203–4 standard deviation, 92–94, 180 transforming scores, 132–34 use of statistical functions, 17 use of statistics, 17 z scores, 115–120 Exclusion values, 160–61, 185–88, 224–25 Expected frequency, see Chi square, expected frequencies Experiment, See Research design, experiment Extreme score, 358, 375 F distribution, 230–33, 269 F ratio, 267–68, 317–18 F test, 296 analysis of variance, see Analysis of variance (ANOVA) two sample for variances, 230 Factor analysis, 205 Familywise error, 259, 296 Frequency distribution, 66 Frequency polygon, 121 Friedman test, 509 Grade equivalent score, 132, 144 Graphs, See Histograms Greenhouse-Geisser test, 506–7, 509 Group designs between, 246 within, 247 Heteroscedasticity, 358, 375 Histograms, 67–71, See also Scattergram Homogeneity of variance assumption of, 277 Homoscedasticity, 358, 375 HSD, See Post Hoc analyses Hypothesis, 149 alternative, 167 null, 167 Hypothesis test, 167–68 Inferential statistics, 147, 156 contrasted to descriptive statistics, 44 defined, 73, 143 populations and samples, 162 Interaction, 309 ANOVA, 310–11 charting, 311 disordinal, 311, 328 effect, 328 ordinal, 311, 328 Interquartile range, 83, 96 Interval data, 48–50, 73 Interval estimate, See Confidence interval Kruskal-Wallis test, See Nonparametric statistics Kurtosis, 65, 73 Levels of measurement, See Scales of measurement Levene’s test, 233–35, 280, 296 Line of best fit, See Regression, line Linear relationship, 342, 375 Main effects, See Analysis of variance (ANOVA) MANCOVA, 309, 328 Mann-Whitney U test, See Nonparametric statistics MANOVA, 309, 328 Matched groups, 212 Mauchley’s test of sphericity, 505, 506, See also Sphericity McNemar test See Chi square, repeated measures Mean, 52, 73 Mean squares, 265 Measurement, see Scales of measurement Median, 52–53, 73 Mixed designs, 246 Mode, 54, 73 Multicollinearity, 431, 443, 445 Multiple comparisons, 258, 272 Multiple correlation, 417–19 Multiple linear regression, 419, 429–52 coefficients, 430–31, 442 elements of, 429–31 entry schemes, 432, 439 hierarchical, 439–42, 445 526 Multiple linear regression (Continued ) multilevel analysis, 433 squared part correlation, 443–44 stepwise, 439 Multivariate, 309, 328 Nominal data, 45, 73 Nonparametric statistics, 243 dependent t-test See T-test, dependent-samples Kruskal-Wallis test, 293, 296 Mann-Whitney U test, 243–46 Spearman’s rho (rank order correlation), 369–374 within-subjects ANOVA, See Analysis of variance, within-subjects Normal curve equivalent (NCE) scores, 83, 96, 131 Normal distribution, 62, 101–126 nature of, 101–103 normal curve, 101–102, 131 raw score distributions, 114 standard, 102 and z score, See Z score, distribution Null hypothesis, See Hypothesis, null Observed frequency, 458 Omnibus results ANOVA, 317–18 bivariate regression, 414 within subjects ANOVA, 506–7 One-tailed test, See Two-tailed and one-tailed tests Ordinal data, 46–47, 73 Outlier, See Extreme score Parameter defined, 162, 170 estimation, 178–82, 187 Parametric statistics, 243 Partial correlation, 418–20 Partial eta square (2), 318, 328 Pearson’s r, 340–41 Percentile, 82–83, See also Cumulative proportions calculating, 108 defined, 82, 96 identification, 84–87 scores, 83–84 INDEX Phi, 467, 483 Point estimate, 197, 205 Pooled variance, See Variance, pooled Population mean, 162 and samples, 162 standard deviation, 92, 96, 162, 178–80 Post facto research, See Research design, post facto Post hoc analyses, 271–76, 296 Tukey’s HSD test, 273–76 varieties of, 272–3 within subjects ANOVA, 507–8 Power, 193, 196–97, 205, 496 Practical significance, See Effect size Predictor variable, see Regression, predictor variables Pretest sensitivity, 213 Probability, 134–44 determinism versus probability, 135 elements of, 136 empirical probability, 136–37 exact probability, 141–43 inside and outside areas, 139–41 normal curve, 136–37 relationship to z score, 137 sampling, 170 Program Evaluation Prism, The, 20, 41–42, 309, 340, 358, 408, 412, 419, 429, 443 Proportional reduction in error (PRE), 339, 375 Quartiles, 83, 96 Quasi-experimental design, See Research design r2, see Coefficient of determination Random sample, defined, 171 stratified random sampling, 171 Randomization, 170 Range, 82, 96 Rank order correlation, See Nonparametric statistics Ranked data, 369–71 Ranks, tied, 371–73 Ratio data, 50, 73 INDEX Real-world data, 3, 20–22 Regression, bivariate, 383–428 coefficients, 394, 407–8 explaining variance, 397–401 interpretation of, 390–91 line, 383–88, 419–20 nature of, 384–85 predictor variables, 170, 383–4, 397–401 slope, 386, 389 y intercept, 386, 420 z score formula, 392–93 Rejecting null hypothesis, 168 Repeated measures, 489–509 chi square, See Chi square, repeated measures dependent t-test, 491–99 within-subjects ANOVA, 499–508 Research design, 3–4, 148 experiment, 150, 170, 177, 210–11, 499–501 hypothesis, 149 nature of, 154 post facto, 153, 170, 178, 214–15, 339–40, 455, 501 quasi-experimental, 151–52, 170 sampling, 155, See also Sample(s) and Sampling distribution theory, 149 variables, See Variable Restricted range, 357–58, 375 Sample(s), convenience, 155, 169 defined, 170 dependent, 211, 246, 509 equal and unequal, 229 error, 157, 171 independent, 211, 246 matched, 212, 246 mean, 163–66 population, 162 random, 171 scores, 130–31 snowball sampling, 171 standard deviation, 97 values, 143–44 527 Sampling distribution, 157–61, 171, See also Distribution, sampling of differences, 217–18 Scales of measurement, 44, 74 choosing the correct statistical procedure, 50 interval data, 48 nominal data, 45 ordinal data, 46 ratio data, 50 Scattergram, 342–48, 375 in multiple linear regression, 431 in regression, 399–400, 416 Scheffe test, 273 School-level achievement data, 20 Significance, See Statistical significance Simple effects in ANOVA, 312, 325–27, 329 Skewness, 63–65, 74 Slope, See Regression, line Social research, 148 Sphericity, 501–502, 505–6, 509 Spearman’s rho, See Nonparametric statistics SPSS1, xix–xx, 1, 5, 23–39 ANOVA, 287–92 analysis functions, 39 bivariate regression, 404–8 central tendency, 58–60 chi square, 478–83 correlation, 367–69 curvilinear relationships, 409–12 dependent t-test, 495–96 ‘‘explore’’ feature, 233–34 factorial ANOVA, 321–27 general features, 24–26 independent-samples t test, 236, 239–43 management functions, 26–39 multiple linear regression, 438–45 parameter estimation, 181–82 percentiles, 84, 86–87 scattergram, 347–48 single sample T test, 200–203 standard deviation, 92–96, 180 syntax, 323–25, 329 transforming scores, 132–34 within-subjects ANOVA, 501–508 z score, 119–20 Spuriousness, 41–44, 74 528 INDEX Standard deviation, 87–97 calculation of, 88–91 defined, 87, 97 in descriptive statistics, 87–99 sample and population, 92 Standard error of difference, 218–20 of estimate, 394–96, 420 estimated, of difference, 218–20 estimated, of the mean, 183 of the mean, 162–63, 171 Standard normal distribution, 121 Standard normal score, See z score Stanine, 131–32, 144 Statistical significance, 160–61, 168, 171, 202, 241, 289, 295 Statistics, 171 Sum of squares, 91–92, 262–65, 351–52 T distribution, 187–88 T score, 132, 144 T test dependent-samples, 212, 491–99 independent-samples, 209–46 single sample, 175–204 versus Z test, 175–76 Theory, 149, 171 Ties in ranks, See Ranks, tied Treatment group, 171 Tukey’s HSD test, See Post hoc analyses Two-tailed and one-tailed tests, 193–96, 205 Type I error (alpha), 189–90, 205 Type II error (beta), 190–91, 193, 205 Univariate, 309, 329 Variable, 152, 171 dependent, 153 independent, 152–53, 170 manipulated independent, 170 nonmanipulated independent, 170 transformation, 436, 445 Variance, 87–99 between, 261, 296 calculation of, 88–92 components of, 260–61 defined, 87, 97 in descriptive statistics, 81–99 pooled, 218–20 total, 261, 266, 296 within, 260, 296 Washington School Research Center, Wilcoxen test, 509 Wilks’ lambda, 507, 509 Winning the Math Wars, 2, 43 Yates correction for continuity in chi square, 468–69, 483 z score, 103–125 and bivariate regression, 392 calculating, 105–8, 111–14 and correlation, 349 creating rules for locating, 108–110 and cumulative proportions, 105, 115 defined, 121 deriving sample scores from cumulative percentages, 130–31 distribution, 102–111, 127, 176 inflection point, 103 table of values, 104–5 transforming cumulative proportions to z scores, 128–29 transforming to a raw score, 128–29 Z test, 166–69, 171 elements, 169 hypothesis test, See Hypothesis test versus T test, 175–76