MATH4 - Statistics Reviewer made by Ruazol.pdf

What is STATISTICS? Sample is the subset of a population, it must be random. The field of Statistics deals with the collection, presentation, analysis, and use of data to make In a Random selection, every m...

What is STATISTICS? Sample is the subset of a population, it must be random. The field of Statistics deals with the collection, presentation, analysis, and use of data to make In a Random selection, every member of a population decisions, solve problems, and design products has the equal chance of being selected. and processes. (Montgomery and Runger) Variables is a characteristics that takes two or more In simple terms, Statistics is the science of data. values across individuals Where to use Statistics? 1. Qualitative Variables - represents differences in quality, character, or kind but not in amount Statisticians apply statistical thinking methods to a wide variety of scientific, social, and business Independent variables - cause and endeavors in almost every work field. predictor Engineering Statistics provides a scientific basis Dependent variables - effect, outputs, for decision-making in the engineering field. value being predicted Example Application in the Real-world 2. Quantitative Variables - are numerical in Problems: nature and can be ordered or ranked, a count of something 1. Predicting the Lifespan of Machinery Parts 2. Quality Control Continuous variables 3. Reliability Analysis - assume any numerical value over an interval/s. Scopes of Statistics - a measure of something - there is an infinite number of possible 1. Data Gathering / Collection - getting value information - not countable 2. Data Presentation - information to - e.g. weight, temperature, and height numerical data (tabular and graphs) 3. Data Analysis - resolution of information Discrete variables into simpler elements - whose value can be counted using 4. Data Interpretation - findings and relating integral values existing theories - there is only a finite number to pick from Two Main Branches of Statistics - e.g. dozen eggs and dice 1. Descriptive Statistics - collection and Four Levels of Measurement organization 1. Nominal Data - categories (no ordering or 2. Inferential Statistics - generalization and direction), e.g. marital status and types of car prediction (conclusion) owned Statistics is the practice of analyzing and 2. Ordinal Data - ordered categories (ranking, collecting numerical data in large quantities. order, or scaling), e.g. service quality service and student letter grades Population is the complete set of elements to be studied. 3. Interval Data - differences between measurements but no true zero, e.g.  temperature in fahrenheit and Accidental or Convenience standardized exam score sampling - obtained by selecting whosever 4. Ratio Data - differences between conveniently available measurements, true zero exists, e.g. height, age, weekly food spending Purposive sampling - selected subjectively to represents Data is a collection of values for particular the population variables, usually numerical. Quota sampling Two Main Types of Data - determine the size which should be filled up 1. Primary Data - are data collected directly by the researcher himself, e.g. interview Snowball sampling and experimentation. - starts with the known sources of information and turn give other 2. Secondary Data - are data taken from sources materials previously gathered by other researchers, e.g. books and thesis. Networking sampling - find socially devalued urban Sampling Design/Method populations such as addicts, usually hidden from the outsiders. 1. Probability Sampling - everyone has a chance of being included in the sample What do Engineers do? Simple Random sampling An engineer is some who solve problems of interest - obtained from population to society with the efficient application of scientific randomly principles: - Refining existing products Systematic sampling - Designing new products or processes - systematic order of appearance The Engineering Method Stratified sampling - divided into different strata, sample taken proportionally from the population Clustered sampling - formed into different cluster (Area sampling) Many aspects of engineering practice involve working Multi-stage sampling - used for with the data, obviously some knowledge of statistics national, regional, provincial or is important to any engineer. country level studies. Specifically, statistical techniques can be a 2. Non-probability Sampling - not everyone powerful aid in designing new products and the same chance of being included in systems, improving existing designs, and sample designing, developing, and improving production processes. It is the science of learning information from data. Two Direction of Reasoning Conducting Surveys Methods 1. Face-to-face interview - gives good response rates, fewer misunderstanding, and overall more complete 2. Self-administered - accomodates large number sample and gives more anonymity Statistical inference is one type of reasoning Five Simple Steps for Conducting Surveys Reasoning based on measurements from some objects to measurements on all objects can result 1. Identify the audience in error, called sampling error. - pre-survey research Collecting Engineering Data 2. Find a survey provider - use proper survey provider 1. Retrospective Study - it uses historical process data. 3. Conduct the survey - short but exact to the point and ensure 2. Observational Study - collects data from conveniency current operations without disturbing the system. 4. Create context for the survey - share and published your data 3. Designed Experiments - disturbs the system and observes the impacts. 5. Evaluate your research - revisit the efficiency of a survey Planning and Conducting Surveys Planning and Conducting Experiments Survey is the way to ask a lot of people a few well-constructed questions. It is a series of Experiments are the basis of all theoretical unbiased questions that the subject must answer. predictions. Without experiments, there would be no results, and without any tangible data, there Advantages of Survey would be no basis for the scientist and engineers to formulate a theory. The advancement of culture - efficient ways of collecting information and civilization depends on experiments which from large number of people bring about new technology. (P. Cuadra) - relatively easy to administer - wide variety of information can be Experiment is a series of tests conducted in a collected systematic manner to increase the understanding of an existing process or to explore a new product Disadvantages of Survey or process. - depends on the subject's motivation, Design of Experiments (DOE) honesty, memory, and ability to respond. - answer choices and survey questions - It is the method to create efficient could lead to vague data. experiments that maximize learning with minimal resources. It’s used in cross sciences and engineering to improve  processes, enhance yields, and reduce The general approach of planning and conducting variability, especially when there’s no the experiment is called Strategy of existing theory to guide the development Experimentation. of new products or processes. Guidelines for Designing an Experiments DOE helps in: 1. Recognition of _ and statement of the - Identifying relationships between cause problem and effect a. Factor screening - Providing an understanding of interactions b. Optimization among the causative factors c. Confirmation - Determining the levels at which to set the d. Discovery controllable factors in order to optimize e. Robustness reliability 2. Selection of the response variable - Minimizing the experimental error 3. Choice of factors, level, and ranges - Improving the robustness of the design or 4. Choice of experimental design process to variation 5. Performing the experiment 6. Statistical analysis of the data Stages of Design of Experiments (DOE) 7. Conclusions and recommendations 1. Planning - plan for the course of Experiments are used to study the performance experimentation of processes and systems. 2. Screening - identify the important factor that affects the process 3. Optimization - determine the best settings of these factors to achieve the objectives 4. Robustness Testing - make the product and process insensitive to variations that are likely to be experienced 5. Verification - validation of the best settings by conducting a few follow-up experimental runs Three Basic Principle Design Experiment 1. Randomization - experiments performed are randomly determined 2. Replication - independent repeat run of each factor combination 3. Blocking - improving the precision of the experiment