Table Of Content

Statistics guide for student and researchers With SPSS illustrations Abdiasis Abdallah Jama 1 ©2020 ALL RIGHTS RESERVED. 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, or otherwise, without the prior written permission of the author. Published in Somalia. 2 This book is dedicated to my late father Abdallah Jama Jibril 3 Preface The purpose of this book is to teach students statistical techniques they need in order to write successful graduation research dissertation and also to prepare them demanding job opportunities. All job opportunities will need statistics to arrive at an effective research conclusion and to predict growth and progress. This study guide is also intended for researchers who want to update their existing knowledge on statistics as well as having understanding gap in inferential statistics to draw conclusion about population study. The book is designed to be in study guide fashion whereby too much theory is not addressed but rather practical understanding of concepts connected with relevant examples is emphasized. Having said that the guide is not intended to cover all aspects of statistics rather it gives both students and researchers enough statistical tools they need to solve everyday research problems faced in all disciplines. 4 Contents 1. Preface .................................................................................................................................. 4 2. Architecture of the study guide ............................................................................................. 8 3. Introduction to descriptive statistics .................................................................................. 9 Levels of Measurement ................................................................................................................ 11 Frequency distribution of ungrouped data .................................................................................. 11 Frequency distribution of grouped data ....................................................................................... 22 Boxplot for groups variances ........................................................................................................ 23 Review questions .......................................................................................................................... 25 4. Probability basics ............................................................................................................... 27 Introduction .................................................................................................................................. 28 Probability of events ..................................................................................................................... 29 Conditional probability ................................................................................................................. 33 Review questions .......................................................................................................................... 35 5. Introduction to probability distributions ........................................................................ 36 Introduction to random variable .................................................................................................. 37 Cumulative distribution function .................................................................................................. 38 Expectation and standard deviation of discrete random variable ............................................... 39 Continuous random variable ........................................................................................................ 40 Review questions .......................................................................................................................... 42 6. Common discrete probability distributions .................................................................... 43 Binomial distribution .................................................................................................................... 44 Poison distribution ........................................................................................................................ 46 Review questions .......................................................................................................................... 48 7. The normal distribution .................................................................................................... 49 Introduction .................................................................................................................................. 50 Standard normal probabilities ...................................................................................................... 52 Normal approximation to Binomial distribution. ......................................................................... 56 Review questions .......................................................................................................................... 60 8. Sampling distributions ...................................................................................................... 61 Sampling methods ........................................................................................................................ 62 Sample Statistics ........................................................................................................................... 64 5 Preface Sampling distribution statistic calculation .................................................................................... 65 Central limit theorem ................................................................................................................... 69 Interval estimation of population parameter ............................................................................... 70 Confidence interval for a population mean .................................................................................. 73 Confidence interval for population standard deviation ............................................................... 76 Confidence interval for population proportion ............................................................................ 78 Review questions .......................................................................................................................... 80 9. Hypothesis test of single sample ....................................................................................... 82 Introduction .................................................................................................................................. 83 Hypothesis test for population mean ........................................................................................... 85 Hypothesis test for population standard deviation ...................................................................... 91 Review questions .......................................................................................................................... 93 10. Goodness of fit test for normality ..................................................................................... 94 Chi – square goodness of fit test for normality ............................................................................ 95 Kolmogorov – Smirnov (KS) goodness of fit test ........................................................................ 108 Review questions ........................................................................................................................ 113 11. Independent and dependent samples hypothesis test ................................................... 114 Dependent (paired) samples test ............................................................................................... 116 Independent samples t – test to compare means ...................................................................... 120 Chi-square test for nominal variables independence ................................................................. 124 Review questions ........................................................................................................................ 130 12. Linear regression and correlation .................................................................................. 131 Linear regression equation ......................................................................................................... 133 Goodness of fit for the regression equation............................................................................... 139 Confidence interval for regression equation slope .................................................................... 141 Multiple linear regression ........................................................................................................... 143 Correlation coefficient r .............................................................................................................. 147 Review questions ........................................................................................................................ 151 13. One – way Analysis of variance (one – way ANOVA) .................................................. 152 Randomized experimental design .............................................................................................. 153 One-way ANOVA test for three samples means equality ........................................................... 154 Fisher LSD multiple comparisons ................................................................................................ 162 Repeated measures one-way ANOVA ........................................................................................ 165 6 Preface Review questions ........................................................................................................................ 168 14. Non-parametric tests ......................................................................................................... 170 Kruskal – Wallis test .................................................................................................................... 171 Mann-Whitney U test .................................................................................................................. 175 Wilcoxon signed rank test ........................................................................................................... 178 Spearman rank correlation coefficient ....................................................................................... 182 Friedman test .............................................................................................................................. 184 Review questions ........................................................................................................................ 185 15. Appendix A: questionnaire design for collecting sample data .......................................... 186 16. Appendix B: SPSS data entry .............................................................................................. 187 Multiple response questions ...................................................................................................... 188 Likert scale .................................................................................................................................. 191 17. Appendix C: Guide to selecting appropriate statistical test .............................................. 192 18. Appendix D: Statistical tables ............................................................................................ 194 Standard normal left tail probabilities P (Z ≤ -z) ..................................................................... 194 Chi – square 𝜒2 distribution table right tailed ....................................................................... 196 Student’s t – distribution left tailed ........................................................................................ 200 F-distribution probabilities right tailed ................................................................................... 201 7 Architecture of the study guide Architecture of the study guide 8 Introduction to descriptive statistics Chapter one Introduction to descriptive statistics After completing this section, you should be able to  Understand the meaning of statistics and different data levels  Explain the importance of studying statistics  Understand how to analysis sample data using descriptive statistics  Appreciate how to calculate mean, variance and standard deviation of ungrouped and grouped data  Practice descriptive statistics analysis using SPSS tool 9 Introduction to descriptive statistics Statistics is the art of collecting, summarizing, analyzing, and interpreting data. Data for statistical analysis may include financial records of an organization, population census, development of new products, and the like. Statistics has found significant position in our daily life. Newspapers, job recruiters, managerial decisions, lottery winning, election forecasting, weather, production effectiveness all use statistical technique known as probability. Data collection and analysis are required in the following examples.  Businesses send questionnaire to customers to determine level of service satisfaction.  Test score of students are statistically analyzed to improve quality of education.  To test effectiveness of new product, companies subject their new products to sample of customers. This helps the manager to decide if the new system is better than the older one. Why write this book?  Modern statistical data collection and analysis are carried out in computer programs which can process data much faster and provide accurate results. The focus of this book is to walk you through statistics principles with SPSS illustrations.  To give readers comprehensive but simple text that does not flood too much mathematics and theories but rather emphasize the most important concepts and tools that you need in your day to day statistical work. In the study of statistics it is useful to define terms like data, variable, descriptive, inference, sample, and population and so on. The beginning chapters will mainly focus on descriptive statistics which provides information about central tendency and variation of a set of data. Frequency tables summarize the raw data, and then mean and standard deviation are calculated to account for the center of the data and its spread around the mean respectively. This analysis will depend on the scale of measurement used. To better visualize the data, graphs are plotted. For continuous data we use histograms while bar charts display discrete data. Data is the information collected by conducting survey or experiment. Examples of data include the income salary of employees, medical records of students, and economic growth of a country. 10