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- 1. Chapter 1 Introduction to Statistics Definition Basic Areas of Statistics Types of Data Sets & Measurements Types of Data & Level of Measurements
- 2. Learning Objectives At the end of this chapter, the student is expected to: 1) define statistics; 2) summarize the different classification of variables and data; and 3) appreciate the importance and uses of statistics in all fields of work.
- 3. - the science of collecting, organizing, analyzing, and interpreting data - set of figures or measures Statistics
- 4. - a person who collects information or one who prepares analysis or interpretations He may be a scholar who develops a mathematical theory on which the science of statistics is based. Statistician
- 5. Areas of Statistics 1. Descriptive Statistics 2. Inferential Statistics
- 6. Descriptive Statistics - deals with methods of organizing, summarizing, and presenting numerical data in a convenient form - statistician tries to describe a situation For example Getting census of the population is or of little value if it is just a mass of numerical data. It can be meaningful if it can be organized into a sort of table called the frequency distribution or of some kind of graphs.
- 7. Descriptive Statistics Descriptive statistical methods could be used to summarize the data. For example Actual sales level An average weekly sales levels, and The degree of variation from this average that weekly sales undergo
- 8. Inferential Statistics - consist of generalizing from samples to populations performing hypothesis testing, determining relationships among variables, and making predictions - main concern is to analyze the organized data leading to prediction or inferences
- 9. Inferential Statistics It implies that before carrying out an inference, appropriate and correct descriptive measures or methods are employed to bring out good results. For example Predicting the life span of a mechanical toy gun is based on the performance of several similar toy guns. Its prediction depends on the descriptive statistical tools to be undertaken.
- 10. Inferential Statistics Another example A researcher may wish to know if a new drug will be effective in reducing the number of heart attacks in men over 60 years of age. For this study, two groups of men over 60 would be selected. One group would be given the drug, and the other would be given a placebo. The number of heart attacks in men would be counted. Statistical test would then be applied.
- 11. Basic Terms in Statistics 1. Universe 2. Variable 3. Population 4. Sample 5. Parameter 6. Statistic
- 12. Universe - the collection of things or observational units under consideration
- 13. Variable - a characteristic observed or measured on every unit of the universe
- 14. Population - the set of all possible values of the variable of interest
- 15. Sample - the portion of the population that has been selected for analysis - a subset of a population
- 16. Example Suppose we are interested in studying the factors related to the student’s performance in Math 28 at Central Philippine University. Universe: students of CPU Variables: Math 28 performance and factors such as age, grade in College Algebra, year level, gender
- 17. Example Suppose we are interested in studying the factors related to the student’s performance in Math 28 at Central Philippine University. Population: ages of all students of CPU enrolled in Math 28, grades of all students of CPU enrolled in Math 28 Sample: performance or ages or grades of students in one section of Math 28
- 18. Parameter - a numerical measurement obtained using the population data set
- 19. Statistic - a numerical measurement obtained using the sample data set
- 20. Types of Data or Variables 1. Qualitative Variables or Categorical 2. Quantitative Variables or Numerical
- 21. Qualitative Variables - yield categorical responses and answers to “what kind” questions, non-numerical characteristics or labels - represent differences in quality, character, or kind but not in amount Examples eye color, favorite movie, political party affiliation, blood type, brand of computer, level of customer’s satisfaction, nationality, student ID number
- 22. Quantitative Variables - yield numerical responses and answers to “how many” and “how much” questions, numerical measurements or quantities - numerical in nature and can be ordered or ranked Examples height, weight, income, resting pulse rate, number of cell phones owned, household size, number of students in a Statistics class, proportion of students who passed Math 28 last semester
- 23. Classifications of Quantitative Variable 1. Discrete Variable 2. Continuous Variable
- 24. Discrete Variable - a quantitative variable that can assume a finite number or utmost countable number of values - produces numerical responses that arise from a counting process Examples number of magazine subscriber, number of typhoons, amount of cash in the cash registry, number of satisfied customers, graduates in a certain college, number of students in a classroom
- 25. Continuous Variable - a quantitative variable that can assume an infinite number of values associated with the values within a continuum or interval, depending on the precision of the measuring instrument Examples height, length of hair, length of longest long-distance call made per month, monthly charge of water consumption
- 26. Levels of Measurement Data can also be described in terms of the level of measurement attained.
- 27. Levels of Measurement 1. Nominal Scale 2. Ordinal Scale 3. Interval Scale 4. Ratio Scale
- 28. Nominal Scale - classifies data into various distinct categories in which no ordering is implied - uses numbers for the purpose of identifying name or membership in a group or category - observations can be classified and counted without particular order or ranking imposed on the data Examples blood type, course, breed of dog, shape of bacteria in a Petri dish, internet provider, political party, religion, telephone number, preferred hobbies
- 29. Nominal Scale Nominal scaling is the weakest form of measurement because no attempt can be made to account differences within a particular category or to specify any ordering or direction across the various categories. All qualitative variables are measured on a nominal scale.
- 30. Ordinal Scale - has the characteristics of a nominal scale with an additional characteristic that categories are ordered Examples UAAP basketball ranking, calamity threat level, level of performance, letter grades, ordering of food by preference, income category, birth order
- 31. Ordinal Scale Ordinal scaling is somewhat a stronger form of measurement because an observed value classified into one category possesses more of a property being scaled than does an observed value classified into another category. Ordinal scaling is still relatively weak though because no attempt is made to account for differences between the classified values.
- 32. Note!!! Data obtained from categorical variables are considered to be measured on nominal scale or on an ordinal scale.
- 33. Interval Scale - a scale of measure used for data values that are numerical - indicates an actual amount and there is equal unit of measurement separating each data, specifically equal interval Examples temperature, score, grade
- 34. Interval Scale Ratio between two data values is meaningless. This occurs when zero is an arbitrary measurement rather than actually indicating “nothing”.
- 35. Ratio Scale - the same with the interval scale - zero measurement indicates absence of the quantity being measured Examples weight, height, number of children, election votes, length, area, volume, velocity, money, duration
- 36. Note!!! Data obtained from numerical variables usually assumed to have been measured either on an interval scale or a ratio scale. These scales constitute the highest levels of measurement. They are stronger forms of measurement than an ordinal scale because you can determine not only which observed value is the largest but also by how much.
- 37. 37 Summary Chart for the Classification of Data Variables Qualitative (categorical) Quantitative (numerical) Nominal Ordinal Discrete Continuous Interval Ratio