Quantitative Methods PDF Course Pack

Institute of Computing Bachelor of Science in Information Systems A Course Pack on MS221/IS223 Quantitative Methods MARK VAN M. BULADACO, MIT Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods...

Institute of Computing Bachelor of Science in Information Systems A Course Pack on MS221/IS223 Quantitative Methods MARK VAN M. BULADACO, MIT Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods PREFACE VISION A premiere Higher Institution in Agri-Fisheries and Socio-cultural Development in the ASEAN Region Davao del Norte State College envisions being one of the pillars of higher education system by becoming a premier higher institution that provides agri-fisheries and socio- cultural development in the ASEAN region. To attain this, the College strives to become a University with recognized center of development and excellence; to be a beacon of knowledge; to lead innovation on uplifting lives of every Filipino family; and to be a strong advocate of nature preservation especially the agriculture and aquatic resources of the country and beyond. MISSION DNSC strives to produce competent human resource, generate and utilize knowledge and technology, uphold good governance and quality management system for sustainable resources and resilient communities. The College strives to achieve greater goals into becoming a University that upholds high standards in education, research, extension and production. Particularly, the College commits to: 1. deliver in the areas of instruction, research, extension and production, and good governance; 2. influence development through research, extension and production in collaboration with stakeholders; and 3. uphold good governance and quality management system through optimum participation, accountability, transparency and adherence to the rule of law. i Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods CORE VALUES We commit to pursue our vision, accomplish our mission and achieve our goals through our core values of: Excellence Integrity Innovation Stewardship Love of God and Country ABOUT THIS COURSE PACK This course pack is intended as the main module and reference for the course Quantitative Methods in the BS in Information Technology and BS in Information Systems program of Davao del Norte State College aims to provide students with the mathematical fundamentals required for successful quantitative analysis of problems in the field of business computing. This course introduces the mathematical prerequisites for understanding statistics and quantitative methods which include sampling, t-test, ANOVA, Chi-Square Test, Pearson R, Spearman rho and simple linear regression using a statistical software. This course explains the different quantitative research design to be used for writing a full research paper. This also includes topics on research methods and how to write a research paper. Also, part of the requirements of this course is to produce a full research paper implementing correlation design or linear regression. Credit units: 3 units (Lecture) Course Outcomes: CO1 Use appropriate statistical tools and software for solving statistical problems relevant to quantitative methods. CO2 Write a full research paper on ICT variables implementing correlation design. ii Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods Learning Objectives: These are the course learning objectives during the conduct of studying this course pack. Understand concepts of quantitative methods and its types of research designs Demonstrate ability to analyze and solve problems utilizing descriptive and inferential statistics Solve statistics problems correlating two variables using Pearson R, Spearman Rho and simple linear regression Demonstrate ability to do statistical analysis and reporting using a statistical software Write a full research paper on ICT variables implementing correlation design Disclaimer: Some images included (without citation) in this course pack were downloaded from an image hosting website with free to reuse and modify license. Images with noncommercial use labels but are free were properly cited. Some images were also original and made by the author. iii Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods TABLE OF CONTENTS Preface VM, Core Values i About the course pack ii Course Outcomes and Learning Objectives ii Table of Contents iv Module 1: Understanding Quantitative Methods 1 Lesson 1: Introducing Quantitative Methods 2 Lesson 2: Quantitative Research Designs 8 Lesson 3: Stages of Research 14 Module 2: Descriptive Statistics and Inferential Statistics 23 Lesson 1: Review on Descriptive Statistics and Sampling 24 Techniques Lesson 2: Hypothesis Testing (T-Test and ANOVA) 47 Module 3: Correlation and Regression Analysis 62 Lesson 1: Correlation Analysis using Pearson R and 63 Spearman Rho Lesson 2: Regression Analysis using Simple Linear 73 Regression Module 4: Using a Statistical Software 92 Lesson 1: Introducing statistical software and its 93 Environment Lesson 2: Using statistical software in Descriptive and 103 Inferential Analysis Module 5: Writing a Quantitative Research paper 125 Lesson 1: Writing the Introduction 126 Lesson 2: Writing the Methodology 142 Lesson 3: Writing the Results, Conclusions and Recommendations 153 iv Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods MODULE 1: UNDERSTANDING QUANTITATIVE METHODS OVERVIEW This module will introduce the definition and concepts of scientific inquiry and quantitative methods for the students to understand and appreciate its impact on research writing. Quantitative research uses objective measurement to gather numeric data that are used to answer questions or test predetermined hypotheses. This module also includes discussion and comparison of the different quantitative research designs and how it is applied to research writing. Stages of research are also discussed and presented with examples. Research variables are also introduced. MODULE OBJECTIVES At the end of this module, the student is expected to be able to: Understand the concepts of quantitative methods. Compare and contrast the different quantitative research designs. Relate the characteristic of the scientific approach presented in everyday life. LESSONS IN THIS MODULE Lesson 1: Introducing Quantitative Methods Lesson 2: Quantitative Research Designs 1 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods INTRODUCING QUANTITATIVE METHODS LESSON 1 LEARNING OUTCOMES At the end of this lesson, the student is expected to be able to: Understand concepts of the nature of scientific inquiry and quantitative methods. Relate the characteristic of a scientific approach to everyday life and research writing. TIME FRAME Week 1 INTRODUCTION Welcome to Lesson 1 of Module 1: Understanding quantitative methods! Here, you are going to learn concepts of the nature of scientific inquiry and introduce the definition and concepts of quantitative methods for the students to understand and appreciate its impact on research writing. Quantitative research uses objective measurement to gather numeric data that are used to answer questions or test predetermined hypotheses. So, let us learn what Quantitative Methods and their impact on research writing? Furthermore, why understanding scientific inquiry significant in research? Let us find the answers in this lesson. ACTIVITY: Quote Analysis Read the quote in the right and answer the questions in the analysis questions. ANALYSIS 1. Give your own reflection of the quote above. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 2. Relate the quote to research writing. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 2 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods ABSTRACTION Sources of Knowledge Before we further pursue the role of scientific inquiry in education, let us review some of how human beings throughout history have sought knowledge. The significant sources of knowledge can be categorized under five headings: (1) experience, (2) authority, (3) deductive reasoning, (4) inductive reasoning, and (5) the scientific approach. Table 1.1.1 Sources of Knowledge Sources Discussion Experience Experience is a familiar and well-used source of knowledge. After trying several routes from home to work, you learn which way takes the least time or is the freest of traffic or is the most scenic. With personal experience, you can find the answers to many of the questions you face. Authority For things difficult or impossible to know by personal experience, people frequently turn to authority; that is, they seek knowledge from someone who has had experience with the problem or has some other source of expertise. People accept as truth the word of recognized authorities. We go to a physician with health questions or to a stockbroker with questions about investments. A student can look up the accepted pronunciation of a word in a dictionary. Deductive A thinking process in which one proceeds from general to specific Reasoning knowledge through logical argument. Ancient Greek philosophers made perhaps the first significant contribution to the development of a systematic approach for gaining experience. Aristotle and his followers introduced the use of deductive reasoning, which can be described as a thinking process in which one proceeds from general to specific knowledge through logical argument. An argument consists of several statements standing concerning one another. The final statement is the conclusion, and the rest, called premises, offer supporting evidence. 3 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods Deductive reasoning can answer the question, "How likely is it that a student could pass a 20-item multiple-choice test with five options per item by chance alone?" Inductive The conclusions of deductive reasoning are correct only if the premises Reasoning on which they are based are correct. But how are you to know if the beliefs are true? In the Middle Ages, people often substituted dogma for true premises, so they reached invalid conclusions. It was Francis Bacon (1561–1626) who first called for a new approach to knowing. He held that thinkers should not enslave themselves by accepting premises handed down by an authority as absolute truth. He believed that an investigator should establish general conclusions based on facts gathered through direct observation. In Bacon's system, the investigator made observations on events in a class (or category) and then, based on the observed events, made inferences about the whole level. This approach, known as inductive reasoning, is the reverse of the deductive method. Observations are made on events in a class (or category) and then, based on the observed events, made inferences about the whole level. Example: "The coin I pulled from the bag is a penny.... Therefore, all the coins in the bag are pennies." Scientific Exclusive use of induction often resulted in the accumulation of Approach isolated knowledge and information that made little contribution to the advancement of knowledge. Furthermore, people found that many problems could not be solved by induction alone. In the 19th century, scholars began to integrate the most critical aspects of the inductive and deductive methods into a new technique, namely the inductive– deductive method, or the scientific approach. Examples of Deductive, Inductive and Scientific Approach Deductive and Inductive Reasoning Deductive: Every mammal has lungs. All rabbits are mammals. Therefore, every rabbit has lungs. Inductive: Every rabbit that has ever been observed has lungs. Therefore, every rabbit has lungs. 4 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods Note that in deductive reasoning, you must know the premises before you can conclude. Still, in inductive reasoning, you conclude by observing examples and generalizing from the samples to the whole class or category. To be sure of an inductive conclusion, the investigator must observe all models. The statement is known as perfect induction under the Baconian system; it requires that the investigator examine every example of a phenomenon. Scientific Approach In the 19th century, scholars began to integrate the most critical aspects of the inductive and deductive methods into a new technique, namely the inductive–deductive method, or the scientific approach. This approach differs from inductive reasoning in that it uses hypotheses. A hypothesis is a statement describing relationships among variables that are tentatively assumed to be true. For example, a researcher interested in increasing student on-task behavior might hypothesize that positive teacher feedback increases on-task behavior. All hypotheses indicate specific phenomena to be observed (the variables), in this case, positive teacher feedback and on-task behavior. After studying reinforcement theory, a teacher hypothesizes that using a tutorial computer program will lead to superior achievement in arithmetic. She devises a study in which the tutorial is used with two sixth-grade classes, whereas conventional materials are used with two other sixth-grade classes. Research Approaches Research designs are categorized into two approaches: Quantitative approach and Qualitative approach. Quantitative research uses objective measurement to gather numeric data that are used to answer questions or test predetermined hypotheses. It generally requires a well-controlled setting. Qualitative research, in contrast, focuses on understanding social phenomena from the perspective of the human participants in natural environments. It does not begin with formal hypotheses, but it may result in hypotheses as the study unfolds. Table 1.1.2 Comparing Quantitative Research and Qualitative Research Quantitative Research Qualitative Research Aims to characterize trends and Involves processes, feelings, and patterns motives; the why is and the how's (data are in-depth and holistic) Usually starts with neither theory nor Usually concerned with generating a hypothesis about the relationship hypothesis from data rather than testing between two or more variables. a hypothesis 5 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods Uses structured research instruments Uses either unstructured or semi- like questionnaires or schedules structured instruments Use large sample sizes that are Uses small sample sizes chosen representative of the population purposely Research of this kind can be replicated Validity should be high Used for greater understanding of It is used to gain a greater understanding group similarities in terms of feelings, motives, and experiences. Uses structured processes Uses more flexible processes Methods include census, survey, Methods include the field of research, experiments, and secondary analysis. case study, secondary analysis. Statistical analysis of numeric data Narrative description and interpretation What are the quantitative methods and research? According to Babbie, quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques. Quantitative research focuses on gathering numerical data and generalizing it across groups of people and explain a phenomenon. Quantitative research is defined as a systematic investigation of phenomena by gathering quantifiable data and performing statistical, mathematical, or computational techniques. Quantitative research collects information from existing and potential customers using sampling methods and sending out online surveys, online polls, questionnaires, etc., the results of which can be depicted in the form of numerical. After careful understanding of these numbers to predict the future of a product or service and make changes accordingly. An example of quantitative research is the survey conducted to understand the amount of time a doctor takes to tend to a patient when the patient walks into the hospital. A patient satisfaction survey template can be administered to ask questions like how much time did a doctor takes to see a patient, how often does a patient walks into a hospital, and other such questions. 6 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods APPLICATION Analyze the statement below and determine if it is deductive reasoning, inductive reasoning, or a scientific approach. _______________1. After extensive observation of reactions, Lavoisier concluded that combustion is a process in which a burning substance combines with oxygen. His work was the death blow to the old phlogiston theory of burning. _______________2. Dalton, after much reflection, concluded that matter must consist of small particles called atoms. His early assumptions became the basis for the atomic theory. _______________3. Later, scientists took Dalton's assumptions, made deductions from them, and proceeded to gather data that confirmed these assumptions. They found support for the atomic theory. _______________4. Knowing that radioactive substances constantly give off particles of energy without apparently reducing their mass, Einstein developed the formula E = mc2 for converting matter into energy. _______________5. Accepting Einstein’s theory, Fermi carried on experimentation that resulted in splitting the atom. Congratulations! You finished lesson 1 of module 1. Should there be some parts of the lesson which you need clarification, we will have a virtual meeting interaction. You may now proceed to lesson 2 that will discuss and introduce Quantitative Research Designs. 7 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods QUANTITATIVE RESEARCH DESIGNS LESSON 2 LEARNING OUTCOMES At the end of this lesson, the student is expected to be able to: Compare and contrast the different quantitative research designs. TIME FRAME Week 2 INTRODUCTION Welcome to Lesson 2 of Module 1: Quantitative Research Designs! In this lesson, you will discover the different research designs on conducting quantitative research. How they differ from each other? When will we use a research design on a given problem? You will also learn how to determine the appropriate quantitative research design for a given research problem by comparing each approach. ACTIVITY: Picture Analysis Analyze the picture in the right and answer the questions in the analysis questions. ANALYSIS 1. What does the picture tell you about? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 2. How does it relate with research writing? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 8 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods ABSTRACTION Quantitative Approach Designs Quantitative research may further be classified as either experimental or non-experimental. Experimental research involves a study of the effect of the systematic manipulation of one variable(s) on another variable. The manipulated variable is called the experimental treatment or the independent variable. The observed and measured variable is called the dependent variable. To have a "true" experiment, researchers must use a random process such as a coin toss to assign available subjects to the experimental treatments. For example, assume a university researcher wanted to investigate the effect of providing online feedback to students immediately following course examinations. Using two sections of economics taught by the same professor, the researcher using a random procedure would select one section to receive immediate online feedback about their performance on test questions; the other section would receive feedback during their next class session (independent variables). The researcher would compare the two sections' exam scores and their final grades in the course (dependent variables). If test scores and final grades were higher than could be accounted for by chance in the section receiving online feedback, the researcher could tentatively conclude that there is evidence the online feedback (treatment or independent variable) contributed to more significant learning than the in-class feedback. Table 1.2.1. Experimental Research Designs Experimental Research Description Design True Experimental A design is considered a true experiment if the following Design criteria are present: the researcher manipulates the experimental variables, i.e., the researcher has control over the independent variables, as well as the treatment and the subjects, there must be one experimental and one comparison or control group: and subjects are randomly assigned either to the control group or experimental group. A control group is a group that does not receive the treatment. Quasi-Experimental It is a design in which there is no control group, or the subjects Design are not randomly assigned to groups. 9 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods Pre-Experimental Design This experimental design is considered very weak, as the researcher has little control over the research. True Experimental Design can be categorized into three variations based on its implementation: Pretest-posttest controlled group design, Posttest only controlled group design, Solomon four-group design, and pretest-posttest design. a. Pretest-posttest controlled group design i. Subjects are randomly assigned groups ii. A pretest is given to both groups. iii. The experimental group receives the treatment while the control group does not iv. A posttest is given to both The procedure is summarized as follows: R→O1→X→O2 (experimental group) R→O1→O2 (control group) Where: R stands for random selection O1 stands for pretest O2 stands for posttest X stands for intervention b. Posttest only controlled group design i. Subjects are randomly assigned to groups ii. The experimental group receives the treatment while the control group does not receive the treatment. iii. A posttest is given to both groups. The procedure is summarized as follows: R→X→O2 (experimental group) R→O2 (controlled group) Where: R stands for random selection O2 stands for posttest X stands for intervention c. Solomon four-group design. It is considered as the most prestigious experimental design. It minimizes internal and external validity i. Subjects are randomly assigned to one of four groups. ii. Two of the groups (experimental group 1 and control group 1) are pretested. iii. The other two groups (experimental group 2 and control group 2) receive routine or no treatment. iv. A posttest is given to all four groups: 10 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods The procedure is summarized as follows: R→O1→X→O2 (experimental group) R→O1→O2 (control group) R→ X→O2 (experimental group) R → O2 (control group) d. One group pretest-posttest design. It provides a comparative description of a group of subjects before and after the experimental treatment. The procedure is summarized below: O1→X→O2 In a quasi-experimental design, the experimenter must use already assembled groups such as classes. This design has two types: non- equivalent controlled group design and time-series design. a. Non-equivalent controlled group design. This design is like the pretest-posttest control group design except that there is no random assignment of subjects to the experimental and control groups. The procedure is summarized as follows: O1→ X→ O2 (experimental group) O1→O2 (control group) b. Time-series design. The researcher periodically observes or measures the subjects. O1→O2→O3→X→O4→O5→O6 Where: O1, O2, O3 stand for pretest (multiple observations) O4, O5, O6 stand for Posttest (multiple observations) Pre-experimental design is considered very weak, as the researcher has little control over the research. The design is also called a One-shot case study. A single group is exposed to an experimental treatment and observed after the treatment The procedure is summarized as follows: X→O In non-experimental quantitative research, the researcher identifies variables and may look for relationships among them but does not manipulate the variables. Significant forms of non- experimental research are relationship studies, including ex post facto and correlational research and survey research. Non-experimental research designs include Ex post facto research, Correlational Research, and Survey (Descriptive) Research. 11 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods Table 1.2.2 Non-Experimental Research Designs Experimenta Description Examples l Research Design Ex Post Facto Ex Post Facto research design is like an For example, to answer the experiment, except the researcher does not question, "What is the effect manipulate the independent variable, which has of part-time work on school already occurred in the natural course of events. achievement of high school The researcher simply compares groups students?" differing on the pre-existing independent variable to determine any relationship to the dependent variable. Correlational Correlational research gathers data from Example: ask about the Research individuals on two or more variables and then relationship between the seeks to determine if the variables are related quality of writing samples (correlated). Correlation means the extent to produced by incoming which the two variables vary directly (positive college freshmen and their correlation) or inversely (negative correlation). academic performance during The degree of relationship is expressed as a the freshman year. Also, one numeric index called the coefficient of might investigate the correlation. relationship between Correlational research might ask about the performance on a language relationship between the quality of writing aptitude test and success in a samples produced by incoming college high school foreign language freshmen and their academic performance course. during the freshman year. Also, one might investigate the relationship between performance on a language aptitude test and success in a high school foreign language course. Survey Survey research design uses instruments such An educational researcher (Descriptive as questionnaires and interviews to gather might ask a group of parents Research) information from groups of individuals. about what kind of sex Design Surveys permit the researcher to summarize the education program; if any, characteristics of different groups or to measure they believe schools should 12 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods their attitudes and opinions toward some issues. provide for middle school Researchers in education and the social sciences students. A survey of teachers use surveys widely. could reveal their perceptions of giftedness in schoolchildren. APPLICATION Based on the titles below, classify each of the following studies according to the research methodology most likely used: ______________________1. It is an experimental design that assesses the effect of having been pretested on the magnitude of the treatment effect. Participants are randomly divided into four groups, and each group experiences a different combination of experimental manipulations: the first group (A) receives the pretest, the treatment, and the Posttest; the second group (B) receives only the treatment and Posttest; the third group (C) receives the pretest, no treatment, and a posttest; and the fourth group (D) receives only a posttest. ______________________2. A research design described the performance level of first-year students in reading comprehension skills and performance in Mathematics. It explained the significant difference between private and public high school students' overall performance in the two learning areas. It further investigated how related all the elements of reading skills to students' performance in Mathematics are. ______________________3. The study examined the ICT capability of CHMSC faculty members about selected variables. The study intended to provide a clearer representation of CHMSC faculty members skill and capabilities in using technology-based delivery system for instruction. ______________________4. Using a research design, researchers examined the effectiveness of the Get Ready to Learn (GRTL) classroom yoga program among children with autism spectrum disorders (ASD). The intervention group received the manualized yoga program daily for 16 weeks, and the control group engaged in their standard morning routine. Researchers assessed challenging behaviors with standardized measures and behavior coding before and after the intervention. They completed a between-groups analysis of variance to assess differences in gain scores on the dependent variables. Congratulations! You finished lesson 2 of module 1. Should there be some parts of the lesson which you need clarification, we will have a virtual meeting interaction. You may now proceed to lesson 3 that will introduce stages of research and kinds of research variables. 13 Mark Van M. Buladaco, MIT, PhilNITS (JITSE) FE Quantitative Methods STAGES OF RESEARCH LESSON 3 LEARNING OUTCOMES At the end of this lesson, the student is expected to be able to: Explain the stages of research and how it is essential to keep track of the processes. Distinguish among types of variables: categorical versus continuous and independent versus dependent. TIME FRAME Week 2 INTRODUCTION Good day students! This lesson will discuss the steps for a researcher to conduct and execute research writing. It explains the stages of research and its processes. This lesson will also discuss how important for a researcher to be on the right track for each step. In this lesson, you will distinguish the different types of variables: categorical versus continuous and independent versus dependent. ACTIVITY: Flowchart Algorithm: Problem solving in Step 1: Input M1,M2,M3,M4 computing can be designed Step 2: GRADE = (M1+M2+M3+M4)/4 by an algorithm and a Step 3: if (GRADE