LESSON 1.pdf

LESSON 1 Constant is a characteristic or property of a population or sample which is common to all members of the group. INTRODUCTION TO STATISTICS AND DATA ANALY...

LESSON 1 Constant is a characteristic or property of a population or sample which is common to all members of the group. INTRODUCTION TO STATISTICS AND DATA ANALYSIS Grouped Data are raw data organized into groups or categories with corresponding frequencies. SCIENTIFIC DATA - Statistical methods are used to analyze data from a process to gain more sense of where Parameter is the descriptive measure of a characteristic in the process changes may be made to improve the of a population. quality of the process. Variable is a measure or characteristic or property of a - These statistical methods are designed to population or sample that may have a number of contribute to the process of making scientific different values. It differentiates a particular member judgments in the face of uncertainty and from the rest of the group. variation. PROBABILITY AND STATISTICAL INFERENCE INFERENTIAL STATISTICS - Involves using data Descriptive or deductive statistics – provides general from the sample to make interferences or prediction information about the fundamental statistical properties about a larger population. of data (mean, median, mode, variance, standard Variability in Scientific Data - If the observed product deviation etc.) density in the process were always the same and were Pedadogy-wise, probability is essential in inferential always on target, there would be no need for statistical statistics because it quantifies the uncertainty in drawing methods. conclusions about a population from a sample, enabling Descriptive Statistics us to estimate the likelihood of various outcomes and make informed decisions. Mean – The arithmetic average of all the numbers Methods of Data Collection Median – The value in the center when the numbers are arranged least to greatest. - Collection of the data is the first step in conducting statistical inquiry. It simply refers to Mode – The most commonly appearing value. the data gathering, a systematic method of Range – The difference between the largest and smallest collecting and measuring data from different number. sources of information in order to provide STATISTICAL TERMS answers to relevant questions. - In the field of engineering, the three basic Data are facts, figures and information collected on some methods of collecting data are through characteristics of a population or sample. These can be retrospective study, observational study and classified as qualitative or quantitative data through a designed experiment. Ungrouped (or raw) data are data which are not Retrospective Study - use the population or sample of the organized in any specific way. They are simply the historical data which had been archived over some collection of data as they are gathered. period of time. Statistic is a measure of a characteristic of sample. Observational study - Process or population is observed knowledge and understanding of the research question at and disturbed as little as possible, and the quantities of hand or their goals. interests are recorded. Snowball or Referral Sampling - People recruited to be Design Experiment – very important in engineering part of a sample are asked to invite those they know to design and development and in the improvement of take part, who are then asked to invite their friends and manufacturing processes in which statistical thinking and family and so on. statistical methods play an important role in planning, Statistical Analysis conducting, and analyzing the data. Descriptive Statistics Measures of central tendency such TYPES OF SAMPLING as the mean, median, and mode summarize the PROBABILITY SAMPLING METHODS performance level of a group of scores, and measures of variability describe the spread of scores among Simple random sampling - Every element in the participants. population has an equal chance of being selected as part of the sample. It’s something like picking a name out of Measures of Central Tendency a hat. The Mean - Known as the arithmetic average, consists of Systematic Sampling - With systematic sampling the the sum of all scores divided by the number of scores. random selection only applies to the first item chosen. A rule then applies so that every nth item or person after that is picked. Stratified Sampling - Stratified sampling involves random selection within predefined groups. It’s a useful method The Median - To find the median, you arrange the values for researchers wanting to determine what aspects of a of the variable in order—either ascending or descending— sample are highly correlated with what’s being measured. and then count down (n + 1) / 2 scores. Cluster Sampling - With cluster sampling, groups rather than individual units of the target population are selected at random for the sample. These might be pre-existing groups, such as people in certain zip codes or students The Mean vs Median - the mean is influenced belonging to an academic year. considerably by the presence of the extreme observation, NON-PROBABILITY SAMPLING METHODS 14.7, whereas the median places emphasis on the true “center” of the data set. Convenience Sampling - People or elements in a sample are selected on the basis of and availability. Quota sampling - This approach aims to achieve a spread across the target population by specifying who should be recruited for a survey according to certain groups or criteria. Purposive sampling - Participants for the sample are chosen consciously by researchers based on their The Mode - A rarely used measure of central tendency, VERIFICATION - This final stage involves validation of the mode simply represents the most frequent score in a the optimum settings by conducting a few follow-ups distribution. experimental runs. This is to confirm that the process functions as expected and all objectives are achieved. The Standard Deviation - is a measure of the dispersion of data points in a dataset, indicating how much the LESSON 2 values typically differ from the mean PROBABILITY - This is simply how likely an event is to happen. - The likelihood of an outcome is measured by assigning a number from the interval [0, 1] or as The Variance - is a statistical measure that represents the percentage from 0 to 100%. average of the squared differences between each data point and the mean, indicating the spread of data in a dataset. EXPERIMENT – used to describe any process that generates a set of data. EVENT – consists of a set of possible outcomes of a probability experiment. INTRODUCTION TO DESIGN EXPERIMENTS 1. SIMPLE EVENT – an event with one outcome. Design of Experiments, or DOE, is a tool to develop an 2. COMPOUND EVENT – an event with more than experimentation strategy that maximizes learning using one outcome. minimum resources. SAMPLE SPACE & EVENT SAMPLE SPACE - is the PLANNING - Identification of the objectives of set of all possible outcomes or results of a random conducting the experiment or investigation, assessment experiment. of time and available resources to achieve the objectives. Sample space is represented by letter S. SCREENING - experiments are used to identify the Each outcome in the sample space is called an element important factors that affect the process under of that set. investigation out of the large pool of potential factors. EVENT - is the subset of this sample space, and it is OPTIMIZATION - The objectives may be to either represented by letter E. increase yield or decrease variability or to find settings OPERATIONS OF EVENTS that achieve both at the same time depending on the product or process under investigation INTERSECTION OF EVENTS (common sa given) ROBUSTNESSTESTING - It is important to identify - The intersection of two events A and B is sources of variation and take measures to ensure that the denoted by the symbol A ∩ B. product or process is made robust or insensitive to these - It is the event containing all elements that are factors. common to A and B. MUTUALLY EXCLUSIVE EVENTS (walang COUNTING RULES common) MULTIPLICATIVE RULE - We can say that an event is mutually exclusive if - The probability of occurrence of both the events they have no elements in common. A and B is equal to the product of the probability UNION OF EVENTS (sama sama sa dalwang group) of B occurring and the conditional probability that event A occurring given that event B - The union of events A and B is the event containing all the elements that belong to A or to B or to both and is denoted by the symbol A ∪ B. The elements A ∪ B maybe listed or defined by the rule A ∪ B = { x | x ∈ A or x ∈ B}. COMPLEMENT OF AN EVENT - The complement of an event A with respect to S is the set of all elements of S that are not in A and is denoted by A’ PROBABILITY OF AN EVENT - Sample space and events play important roles in probability. Once we have sample space and event, we can easily find the probability of that event. PERMUTATION RULE - Permutation refers to the arrangement of all or part of a set of objects, with regard to the order of the arrangement. While dealing with permutation, one should concern about the selection, as well as arrangement. COMBINATIONS RULE - The combination formula is used to find the number of ways of selecting items from a collection, such that the order of selection does not matter. In simple words, combination involves the selection of objects or things out of a larger group where order doesn’t matter.