CHAPTER I. Introduction - PDF

CHAPTER I. INTRODUCTION Florence Nightingale on Statistics “...the most important science in the whole world: for upon it depends the practical application of every other science and of every art: the one science essential to all politica...

CHAPTER I. INTRODUCTION Florence Nightingale on Statistics “...the most important science in the whole world: for upon it depends the practical application of every other science and of every art: the one science essential to all political and social administration, all education, all organization based on experience, for it only gives results of our experience.” “To understand God's thoughts, we must study statistics, for these are the measures of His purpose.” Definition of Statistics In its plural sense, statistics is a set of numerical data (e.g., vital statistics in a beauty contest, monthly sales of a company, daily peso-dollar exchange rate). In its singular sense, statistics is a branch of science that deals with the collection, presentation, analysis and interpretation of data. General Uses of Statistics 1. Statistics aids in decision making. Provides comparison Explains action that has taken place Justifies a claim or assertion Predicts future outcome Estimates unknown quantities 2. Statistics summarizes data for public use. Application of Statistics Diverse applications “During the 20th Century statistical thinking and methodology have become the scientific framework for literally dozens of fields including education, agriculture, economics, biology, and medicine, and with increasing influence recently on the hard sciences such as astronomy, geology, and physics. In other words, we have grown from a small obscure field into a big obscure field.” – Brad Efron Role of Statistics In biological sciences and medical sciences, it can help researchers discover relationships of variables and determine if a certain treatment is better than the others. Example. A doctor can use Statistics to determine to what extent is an increase in blood pressure dependent upon age.  In social sciences, it can help and guide researchers support theories and models that cannot be just rationalized. Example. Empirical studies are using Statistics to obtain socio-economic profile of the middle class to form new socio-political theories on classes as the existing theories apparently are no longer valid. In business, a company can use Statistics to forecast sales, design products, and produce goods more efficiently. Example. A pharmaceutical company can apply statistical procedures to find only if a new formula is indeed more effective than one being used. Results can help company decide whether to market the new formula or not. In engineering, it can be used to test properties of various materials. Example. A quality controller can use statistics to estimate the average lifetime of the products produced by their current equipment. Fields of Statistics 1. Statistical Methods of Applied Statistics – refer to procedures and techniques used in the collection, presentation, analysis and interpretation of data. 2. Statistical Theory of Mathematical Statistics – deals with the development and exposition of theories that serve as bases of statistical methods. Major Areas of Statistics 1. Descriptive Statistics Methods concerned with the collection, description and analysis of a set of data without drawing conclusions or inferences about a larger set The main concern is simply to describe the set of data such that the otherwise obscure information is brought about clearly Conclusions apply only to the data on hand Example of Descriptive Statistics Present the Philippine population by constructing a graph indicating the total number of Filipinos counted during the last census by age group and sex. Present the number and percentage of summa cum laude, magna cum laude and cum laude in all UP units in year 2023. 2. Inferential Statistics Methods concerned with making predictions or inferences about a larger set of data using only the information gathered from a subset of this larger set The main concern is not merely to describe but actually predict and make inferences based on the information gathered  Conclusions are applicable to a larger set of data which the data on hand is only a subset Example of Inferential Statistics A new milk formulation designed to improve the psychomotor development of infants was tested on randomly selected infants. Based on the results, it was concluded that the new milk formulation is effective in improving the psychomotor development of infants. Problems: Determine if the following is Descriptive or Inferential Statistics. 1) Einstein Covido is studying turbulence in the laboratory needs the average quantities that vary over small intervals of time. Answer: Descriptive 2) Gwenn Davide is interested in examining how many classes in Statistics have been taken on the average by the incoming graduating students at Central Visayas colleges and universities during their four years in school. Answer: Inferential 3) Sara Marcos is interested in studying the experiences of mothers in time of calamities. Answer: Inferential 4) Robin Zubiri wants to determine the range of ages of females who got married from January to June 2023 in Cebu City. Answer: Descriptive Do Self-Assessment Questions (SAQ) 1.1 SAQ 1.1 Determine if the following is Descriptive or Inferential Statistics. 1) Lenie wants to know the average salaries received by her workers in her company 2) An experiment comparing the effectiveness of hybrid (face-to-face and online) classes against pure face-to-face type of teaching-learning. 3) You have been hired by an NGO to examine how the Filipino people feels about the performance of the current mayors and barangay chairmen in the country 4) Determining the shooting percentage of PBA players in the time of pandemic. Definition of Population and Sample A population is a collection of all elements under consideration in a statistical study. A sample is a part or subset of the population from which the information is collected. Definition of Parameter and Statistic A parameter is a numerical characteristic of a population. A statistic is a numerical characteristic of the sample. Examples: The population mean µ , population variance s 2 and population standard deviation σ are parameters while the sample mean X , sample variance S2 and sample standard deviation S are statistics (plural form of statistic; it is different from the subject Statistics). Problems: 1. A study was conducted at UP Cebu to analyze the grade weighted average (GWA) of students who marched in the graduation rites last July 21, 2023. POPULATION: all students UP Cebu who marched in the graduation rites last July 21, 2023 SAMPLE: a group of UP Cebu students who marched in the graduation rites last July 21, 2023, randomly selected PARAMETER: the GWA of UP Cebu students who marched in the graduation rites last July 21, 2023 STATISTIC: the GWA of students in the study who graduated from UP Cebu last year 2. Cars crashed into a tree at a speed of 100 kilometers per hour. We want to know the proportion of persons in the driver’s seat that would have had head injuries. We start with a simple random sample of 75 cars. POPULATION: All cars that crashed into a tree at a speed of 100 kilometers in Year 2019. SAMPLE: The 75 cars that were selected by simple random sampling. PARAMETER: The proportion of persons who would have suffered head injuries in the population. STATISTIC: The proportion of persons who would have suffered head injuries in the sample. Do SAQ 1.2 SAQ 1.2 Identify the population, sample, parameter and statistic in the given problem. 1) We want to know the average (mean) amount of money first year college students spend at ABC College on school supplies that do not include books. We randomly surveyed 100 first year students at the college. Three of those students spent 1500 pesos, 2000 pesos, and 2250 pesos, respectively. 2) An insurance company would like to determine the proportion of all medical doctors who have been involved in one or more malpractice lawsuits. The company selects 500 doctors at random from a professional directory and determines the number in the sample who have been involved in a malpractice lawsuit. Steps in a Statistical Inquiry 1. Define the problem 2. Formulate the research design 3. Collect the data 4. Code and analyze the collected data 5. Interpret the results and make conclusion. Watch this video clip 1.1 on Statistical Inquiry: https://www.youtube.com/watch?v=ybjWptmneFw