Basic Statistical Concepts

• Statistics


  A body of knowledge (science) that deals with the following methods: Collection, Organization, Presentation, Analysis, Interpretation of data
• John W. Tukey: 'Statistics is a science in my opinion, and it is no more a branch of mathematics than physics, chemistry, and economics; for if its methods fail the test of experience – not the test of logic – they will be discarded.'
• Statistics


  • Population count
  • Vital statistics (birth rate, mortality rate, etc.)
  • Crime rate per province
  • The average daily hour spent on social media
  • Percentage of Filipinos who are in favor of "same-sex marriage"
• Uses of Statistics


  • Describe the general characteristics of the collection of elements under study called the population
  • Compare different subpopulations
  • Explain a phenomenon that has taken place in the population
  • Predict future phenomena that will take place in the population
  • Describe the relationships between the different characteristics of the elements in the population
  • Study cause-and-effect
• Population


  A collection of all the elements under consideration in any statistical study
• Sample


  A part (or subset) of the population from which information is collected
• Population and Sample


  • A study on the voting behavior and preferences in the Philippines
  • Population: all registered Filipino voters
  • Sample: a subset of registered Filipino voters
• Variable


  A characteristic or an attribute of the elements in a collection that can assume different values for different elements
• Observation


  Realized value of a variable
• Data


  The collection of observations
• Variables


  • Sex of students
  • Household size
  • Favorite color of women
  • Support for marijuana legalization (Yes, No)
  • Number of cups of rice consumed per meal
  • Length of service (in years) of employees
• Qualitative Variable


  Have labels or names assigned to their respective categories
• Quantitative Variable


  Any characteristic that can be measured or counted in numbers
• Highest educational attainment of HH head, monthly income (in pesos), type of waste (dried leaves, recyclables, food scraps, etc.), and type of disposal (compost pits, dump in open pits, garbage collector, etc.) are variables in the study on socio-demographic characteristics and waste management practices of households
• Social class (poor, middle, rich), number of years in the community, the primary source of income (e.g. fishing, marketing, etc.), and satisfaction level on the implementation of the Laguna de Bay conservation program (unsatisfied, satisfied, highly satisfied) are variables in the study on resource utilization
• Levels of Measurement


  • Nominal
  • Ordinal
  • Interval
  • Ratio
• Nominal


  The numbers in the measurement system are used to classify an element into distinct, non-overlapping, and exhaustive categories. Categories are of equal importance.
• Ordinal


  The numbers in the measurement system are used to classify an element into distinct categories. The system arranges the categories according to magnitude (ordering matters).
• Interval


  The numbers in the measurement system are used to classify an element into distinct categories. The system arranges the categories according to the magnitude. The system has a fixed unit of measurement representing a set size throughout the scale. The system has no true zero.
• Ratio


  The numbers in the measurement system are used to classify an element into distinct categories. The system arranges the categories according to the magnitude. The system has a fixed unit of measurement representing a set size throughout the scale. The system has an absolute zero.
• The level of measurement is one of the considerations in choosing the appropriate statistical tool to analyze the data
• Parameter


  A summary measure describing a specific characteristic of the population
• Statistic


  A summary measure describing a specific characteristic of the sample
• The values 90% and 80% are parameter and statistic, respectively
• Descriptive Statistics


  Includes all the techniques used in organizing, summarizing, and presenting the data on hand collected from either sample or a population
• Descriptive Statistics


  • A change in the number of Filipino immigrants coming to the United States between 2014 and 2019
  • The gender distribution of Ph.D. students across discipline were presented using the enrollment data this year to show that the gender gap exists in doctoral degree completion
• Inferential Statistics


  Includes all the techniques used in analyzing the sample data that will lead to generalizations about a population from which the sample came from
• Inferential Statistics


  • Based on an experiment conducted using a random sample of rats, it was concluded that rats are smart and are comparable to humans when it comes to decision-making
  • A sociologist interviewed a random sample of 50 UPLB students to determine whether they can handle stress or not. Results found that the majority of all UPLB students cannot handle their stress alone and need strong social support
• Staff X used descriptive statistics by asking all 93 resident doctors and reporting that 89% gave a good rating on the training
• Staff Y used descriptive statistics by asking a random sample of 15 resident doctors and reporting that 70% gave a good rating on the training
• Out of 290 randomly selected students, 33% of them are still undecided to enroll this semester in a remote learning setting is an example of descriptive statistics