Intro to Statistics Nature of Statistics Statistics is used in almost all fields of human endeavor. In sports, a statistic may keep records of the number of free throws each player in a basketball game, or the number of hits a baseball player gets in a league. In other areas, such as public health an administrator might be concerned with the number of residents who contract a new strain of flu virus during a certain year, just like the agency of the Department of Health is doing right now. In education, a researcher might want to know if new methods of teaching are better than the traditional one. Lesson 1. Descriptive and Inferential Statistics Statistics is a set of ideas and techniques that enable the user to collect data efficiently. It is also used as an aid in decision making, like controlling manufacturing processes and to measure success of those processes. It is also used to calculate premiums on insurance policies, identifying criminals, finding a new statistical relationship between two or more variables, to formulate economic policy and to make decisions about trading stocks and bonds. In short, statistics is the essential science, no matter what your career is an understanding of statistical methods will help us make decisions effectively. To further improve our ideas in statistics, at the end of the lesson you will be learning to: 1. Define statistics 2. Differentiate the types of statistics Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data (Bluman, 2012). Data can be used in different ways. Statistics are divided into two main areas depending on how data are used — Descriptive Statistics and Inferential Statistics. Descriptive statistics consists of the collection, organization, summarization, and presentation of data. In descriptive statistics, statistician tries to describe a situation by using Measures of Central Tendency (mean, median, mode); Measures of Variability (range, MAD, SD, coefficient of variance); Measures of Position (quartiles, quintiles, deciles, percentiles). For example, getting the census of the population and organizing the data gathered using graphs and make a generalization about the population (Bluman, 2012, Jabilles et. al., 2018). Examples of Descriptive Statistics 1. The weekly mean sales of TV sets in a certain store 2. Alcohol is the most frequent disinfectant against COVID-19. 3. At least 5% discount is deducted on the online sale. 4. The rice importation was doubled last year compared to the rice importation two years ago. Inferential statistics consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions. In this area, statistical tries to infer the characteristics of the population from the sample. For example, predicting the life span of a newly released automobile model as compared to the last year’s released. Its prediction depends on the descriptive tools to be undertaken. Examples of Inferential Statistics 1. Salary predicts the life satisfaction of businessmen in Antique. 2. Productivity of crops is a factor in determining the choice of students to go into farming. 3. Awareness of COVID-19 symptoms is directly related to resiliency of the residents living in Cebu City. 4. Number of received calls predicts the number of orders in a flower shop. Exercise 01. Classify whether the given situation belongs to the area of descriptive statistics or statistical inference. 1. Over-all average of student grades in his seven subjects. 2. Effect of music in the production of chickens. 3. To find the more effective method between the lecture type and cooperative learning. 4. The median sale for the month of January. 5. At least 5% of the crops were destroyed by insects. 6. Assuming that 10% of the crops were destroyed by rain this rainy season, we would expect an increase in the prices of rice by the end of the year. 7. Fifty percent of patients reported to have side-effect in the use of a certain drug. 8. The chance that a person will be robbed in a certain city is 15%. 9. The average number of students in a class at the University of Antique is 45. 10. A recent study showed that eating garlic can lower blood pressure. Lesson 2. Variables and Types of Data There are data everywhere, and large data sets need techniques on how to collect and analyze them. Today, several computer applications can be use in generating information from the data collected. Collecting useful data of course is not easy, which is one of the major thing that we will be learning in this module. In this lesson you will be learning the following: 1. Identify the types of variables as to its nature, and measure 2. Categorize and classify each of the variable collected as to its nature, and measure 3. Identify the level of measurement of variables Statisticians collect information for variables that describe the situation. A variable is a characteristic or attribute that can assume different values. This may include: age, municipality, sex, nationality and so on, which can be found mostly in forms we fill-in. Data are values (measurements or observations) that the variable can assume. Say for age, you fill-in 25, and Sibalom for municipality. Both 20 and Sibalom are called data. A collection of data values forms a data set. Each value in the data set is called a data value or a datum. Kinds of Variable There are basically two kinds of variables— QUALITATIVE and QUANTITATIVE Variables. Qualitative variables result in information that describes or categorizes an element of a population. For example, a sample of four hair-salon customers was surveyed for their “hair color”, “hometown”, and “level of satisfaction” with the results of their salon treatment. Arithmetic operations are not meaningful for data that result from a qualitative variable. Quantitative variables result in information that quantifies an element of a population. For example, “total cost” of textbooks purchased by each student. Other examples are weight, height, body temperature, time and many more. Arithmetic operations are meaningful for data that result from a quantitative variable. Type of Quantitative Variable as to its Measure Quantitative variables can further be categorized as to its measure — Discrete and Continuous. Discrete variables can be an assigned values such as 0, 1, 2, 3, and the said to be countable (taken as a whole). Examples are— the number of flowering pots in a garden, the number of students in a classroom, and the number of calls received. While, continuous variables by comparison, can assume an infinite number of values in an interval between any two specific values (taken as part of a whole). Example is the temperature since the variable can assume an infinite number of values between any two given temperatures. The classification of variables can be summarized using the diagram below: Dichotomic Polynomic Levels of Measurement In addition, qualitative and quantitative variables can further be classified using measurement scales these are — nominal, ordinal, interval, and ratio. The first level of measurement is called the nominal level of measurement. This classifies data in categories which are in no logical order and have no particular relationship. This is also the most basic or lowest level of measurement in which the numerals assigned to each category stand for the name of the category, but they have no implied order or value. Examples are: college instructors classified according to subject taught (English, History, Math, Psychology, or Filipino). Also, classifying as to sex male or female or residents according to zip codes. Even though numbers are assigned as zip codes, there is no meaningful order or ranking. The next of measurement is called the ordinal level. Data measured at this level can be placed into categories that can be ordered, or ranked. For example, from students’ evaluation, their faculty might be ranked according to them performance as excellent, very satisfactory, satisfactory, fair, and poor. Note that precise measurement of differences in this level does not exist. For instance, when people are classified according to their build (small, medium, or large), a large variation exists among the individuals in each class. The third level of measurement is called the interval level. This level ranks data and precise differences between units of measure exist, however there is no meaningful zero. For example, standardized psychological tests yield values measured on an interval, such as IQ. There is no meaningful difference of 1 point between an IQ of 109 and an IQ of 110. Temperature is another example of interval measurement. One property is lacking in the interval scale: There is no true zero. For example, IQ test do not measure people who have no intelligence. Another is temperature, 0°C does not mean no heat at all. The highest level of measurement is called the ratio level. This scale possesses all the characteristics of interval measurement, and there exist a true zero. Examples are those used to measure height, weight, area, and number of phone calls received. Another way of presenting ratio is when a person can lift 100kilograms and another can lift 50kilograms, then the ratio between them is 2 to 1 or the first person can lift twice as much as the second person. The following table gives the summary for the types of measurements (Lopez, 2002): Exercises 02. Categorize each of the following data collected by filling-in the table that follows.
