Basic Concepts in Statistics.pdf

Engineering Data Analysis Basic Concepts in Statistics Department of Mathematics and Statistics College of Science 1/29 What is Statistics? Statistics I is the science of collecting, organizing, summarizing, and analyzing info...

Engineering Data Analysis Basic Concepts in Statistics Department of Mathematics and Statistics College of Science 1/29 What is Statistics? Statistics I is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or to answer questions. I is not an exact Science. It is usually considered a distinct mathematical science rather than a branch of mathematics. I is about providing a measure of confidence in any conclusions. 2/29 Understand the Process of Statistics 1. Identify the research objective I determine the question you want to be answered I question must be detailed to identify the group to be studied 3/29 Population and Sample Definition The total collection of all the elements that we are interested in is called a population. A subgroup of the population that will be studied in detail is called a sample. 4/29 Exercises: A research objective is presented. For each research objective, identify the population and sample in the study. 1. The PUP administration wanted to determine whether the institution was ready for a face-to-face learning environment. To find out if the institution has enough space and resources for the students, they conducted a survey. They asked 200 randomly chosen College of Science students if they had a space for a face-to-face setting and if the room had the necessary equipment to run a class. 5/29 Exercises: A research objective is presented. For each research objective, identify the population and sample in the study. 1. The PUP administration wanted to determine whether the institution was ready for a face-to-face learning environment. To find out if the institution has enough space and resources for the students, they conducted a survey. They asked 200 randomly chosen College of Science students if they had a space for a face-to-face setting and if the room had the necessary equipment to run a class. 2. The PUP open university wanted to cater to working students effectively. They conducted a survey among 150 randomly selected working students who are currently enrolled in PUP’s open university. They were asked for suggestions on how the students wanted the class to be conducted so that they could cope with their lessons while working. 5/29 Understand the Process of Statistics 1. Identify the research objective I determine the question you want to be answered I question must be detailed to identify the group to be studied 2. Collect the information needed to answer the questions 6/29 Data Collection Data collection is the process of gathering and measuring information on variables of interest, in an established systematic fashion that enables one to answer stated research questions, test hypotheses, and evaluate outcomes. 7/29 Data Collection Data collection is the process of gathering and measuring information on variables of interest, in an established systematic fashion that enables one to answer stated research questions, test hypotheses, and evaluate outcomes. Importance of Data Collection I Data empowers you to make informed decisions. I Data helps you identify problems. I Data allows you to develop accurate theories. I Data will backup your arguments. I Data helps you get your hands-on funding. I Data increases your return on assets. I Data improves quality of life. 7/29 Consequences from Improperly Collected Data I Inability to answer research questions accurately I Inability to repeat and validate the study I Distorted findings resulting in wasted resources I Misleading other researchers to pursue fruitless avenues of investigation I Compromising decisions for public policy I Causing harm to human participants and animal subjects 8/29 Steps in Data Gathering 1. Set the objectives for collecting data. 2. Determine the data needed based on the set objectives. 3. Determine the method to be used in data gathering and define the comprehensive data collection points. 4. Design data gathering forms to be used. 5. Collect data. 9/29 Sources of Data 1. Primary sources provide a first-hand account of an event or time period and are considered to be authoritative. They represent original thinking, reports on discoveries or events, or they can share new information. Often these sources are created at the time the events occurred but they can also include sources that are created later. 2. Secondary sources offer an analysis, interpretation or a restatement of primary sources and are considered to be persuasive. They often involve generalisation, synthesis, interpretation, commentary or evaluation in an attempt to convince the reader of the creator’s argument. 10/29 Methods of Collecting Primary Data The primary data can be collected by the following five methods: 1. Direct personal interviews. The researcher has direct contact with the interviewee. The researcher gathers information by asking questions to the interviewee. 2. Indirect/Questionnaire Method. This methods of data collection involve sourcing and accessing existing data that were originally collected for the purpose of the study. 3. Focus group is a group interview of approximately six to twelve people who share similar characteristics or common interests. A facilitator guides the group based on a predetermined set of topics. 4. Experiment is a method of collecting data where there is direct human intervention on the conditions that may affect the values of the variable of interest. 5. Observation is a method of collecting data on the phenomenon of interest by recording the observations made about the phenomenon as it actually happens. 11/29 Methods of Collecting Secondary Data The secondary data can be collected by the following five methods: 1. Published report on newspaper and periodicals 2. Financial Data reported in annual reports 3. Records maintained by the institution 4. Internal reports of the government departments 5. Information from official publications 12/29 Methods of Collecting Secondary Data The secondary data can be collected by the following five methods: 1. Published report on newspaper and periodicals 2. Financial Data reported in annual reports 3. Records maintained by the institution 4. Internal reports of the government departments 5. Information from official publications TAKE NOTE! I Always investigate the validity and reliability of the data by examining the collection method employed by your source. I Do not use inappropriate data for your research. 12/29 Understand the Process of Statistics 1. Identify the research objective. I determine the question you want to be answered I question must be detailed to identify the group to be studied 2. Collect the information needed to answer the questions. 3. Organize and summarize the information. I the process of descriptive statistics I Descriptive statistics describe the information collected through numerical measurements, charts, graphs, and tables. The main purpose of descriptive statistics is to provide an overview of the information collected. 13/29 Understand the Process of Statistics 1. Identify the research objective. I determine the question you want to be answered I question must be detailed to identify the group to be studied 2. Collect the information needed to answer the questions. 3. Organize and summarize the information. I the process of descriptive statistics I Descriptive statistics describe the information collected through numerical measurements, charts, graphs, and tables. The main purpose of descriptive statistics is to provide an overview of the information collected. 4. Draw conclusion from the information. I the information collected from the sample is generalized to the population (inferential statistics) I Inferential statistics uses methods that take results obtained from a sample, extend them to the population, and measure the reliability of the result. 13/29 Exercises: For the following statements, decide whether it belongs to the field of descriptive statistics or inferential statistics. 1. Out of 200 students surveyed, 50% of them were not able to cope in an online class setting. 2. It is estimated that 50% of students in the Philippines were not able to cope in an online class setting. 3. A badminton player wants to know his average score for the past 10 games. 4. A car manufacturer wishes to estimate the average lifetime of batteries by testing a sample of 50 batteries. 5. Janine wants to determine the variability of her six exam scores in Algebra. 14/29 Distinction between Qualitative and Quantitative Variables Variables are the characteristics that differentiate every individual within the population/sample. 15/29 Distinction between Qualitative and Quantitative Variables Variables are the characteristics that differentiate every individual within the population/sample. Variables can be classified into two groups: 1. Qualitative variables 2. Quantitative variables 15/29 Distinction between Qualitative and Quantitative Variables Variables are the characteristics that differentiate every individual within the population/sample. Variables can be classified into two groups: 1. Qualitative variables are variables that yield categorical responses. It is a word or a code that represents a class or category. 16/29 Distinction between Qualitative and Quantitative Variables Variables are the characteristics that differentiate every individual within the population/sample. Variables can be classified into two groups: 1. Qualitative variables are variables that yield categorical responses. It is a word or a code that represents a class or category. 2. Quantitative variables take on numerical values representing an amount or quantity. 16/29 Exercises: Determine whether the following variables are qualitative or quantitative. 1. Hair Color 2. Temperature 3. No. of Hamburger sold 4. No. of children 5. Zip Code 17/29 Distinction between Discrete and Continuous Variables Quantitative variables may be further classified into: 1. Discrete variable 2. Continuous variable 18/29 Distinction between Discrete and Continuous Variables Quantitative variables may be further classified into: 1. Discrete variable is a quantitative variable that has either a finite number of possible values or a countable number of possible values. The term countable means that the values result from counting, such as 0, 1, 2, 3, and so on. 19/29 Distinction between Discrete and Continuous Variables Quantitative variables may be further classified into: 1. Discrete variable is a quantitative variable that has either a finite number of possible values or a countable number of possible values. The term countable means that the values result from counting, such as 0, 1, 2, 3, and so on. 2. A continuous variable is a quantitative variable that has an infinite number of possible values that are not countable. 19/29 Exercises: Determine whether the following quantitative variables are discrete or continuous. 1. The number of heads obtained after flipping a coin five times 2. The number of cars that arrive at a McDonald’s drive-through between 12:00 P.M and 1:00 P.M. 3. The distance of a 2005 Toyota Prius can travel in city conditions with a full tank of gas 4. Number of words correctly spelled 5. Time of a runner to finish one lap 20/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. 21/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. source: https://conjointly.com/kb/levels-of-measurement/ 21/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. source: https://conjointly.com/kb/levels-of-measurement/ 22/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. source: https://conjointly.com/kb/levels-of-measurement/ 23/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. source: https://conjointly.com/kb/levels-of-measurement/ 24/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. 25/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. 1. Nominal Level Identify, name, classify, or categorize objects or events. 26/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. 1. Nominal Level Identify, name, classify, or categorize objects or events. Examples: Method of payment (cash, check, debit card, credit card), Type of school (public vs. private), Eye Color (Blue, Green, Brown) 26/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. 1. Nominal Level Identify, name, classify, or categorize objects or events. Examples: Method of payment (cash, check, debit card, credit card), Type of school (public vs. private), Eye Color (Blue, Green, Brown) 2. Ordinal Level Like nominal scales, identify, name, classify, or categorize, objects or events but have an additional property of a logical or natural order to the categories or values. 26/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. 1. Nominal Level Identify, name, classify, or categorize objects or events. Examples: Method of payment (cash, check, debit card, credit card), Type of school (public vs. private), Eye Color (Blue, Green, Brown) 2. Ordinal Level Like nominal scales, identify, name, classify, or categorize, objects or events but have an additional property of a logical or natural order to the categories or values. Examples: Rank of a Military officer, Social Economic Class (First, Middle, Lower) 26/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. 3. Interval Level Identify, have ordered values, and have the additional property of equal distances or intervals between scales. 27/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. 3. Interval Level Identify, have ordered values, and have the additional property of equal distances or intervals between scales. Example: Temperature on Fahrenheit/Celsius Thermometer, Trait anxiety (e.g., high anxious vs. low anxious), IQ (e.g., high IQ vs. average IQ vs. low IQ) 27/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. 3. Interval Level Identify, have ordered values, and have the additional property of equal distances or intervals between scales. Example: Temperature on Fahrenheit/Celsius Thermometer, Trait anxiety (e.g., high anxious vs. low anxious), IQ (e.g., high IQ vs. average IQ vs. low IQ) 4. Ratio Level Identify, order, represent equal distances between scores values, and have an absolute zero point. 27/29 Levels of Measurement The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. 3. Interval Level Identify, have ordered values, and have the additional property of equal distances or intervals between scales. Example: Temperature on Fahrenheit/Celsius Thermometer, Trait anxiety (e.g., high anxious vs. low anxious), IQ (e.g., high IQ vs. average IQ vs. low IQ) 4. Ratio Level Identify, order, represent equal distances between scores values, and have an absolute zero point. Example: Height, Weight, Number of words correctly spelled 27/29 Exercises: Categorize each of the following as nominal, ordinal, interval or ratio measurement. 1. Ranking of college athletic teams 2. Employee number 3. Number of vehicles registered 4. Brands of soft drinks 5. Number of car passers along C5 on a given day 28/29 References: I Statistics. Informed Decision using Data by Michael Sullivan, III,. Fifth Edition I Sampling: Design and Analysis by Sharon L. Lhr. Second Edition Thank You! 29/29