Estadística II: Research concepts and stages

• These are study notes for Estadística II, taught on Saturdays from 9:00 am to 11:59 am by Luis Uriel Rojas Pinzón.

Concepts and Stages of the Research Process

• Focuses on scientific methodology and basic statistical concepts.

Research Objectives

• The main idea is to distinguish and identify the steps of the scientific method in the research process.

What is Research?

• Research is a systematic and methodical inquiry process.
• Research aims to generate new knowledge, solve problems, validate existing theories, or develop new ones.
• It relies on data collection, analysis, and the application of scientific methods for reliable and valid results.

Importance of Research

• It is fundamental for the advancement of knowledge in any discipline.
• Research enables discovering new facts and establishing relationships between phenomena.
• It enables developing theories for natural and social behaviors.
• Research is essential for identifying and resolving specific issues, especially in professional settings.
• Research provides data and evidence for guiding decision-making.
• Research informs policy formulation and practical solution implementation.
• Research promotes continuous improvement of practices, products, and services.
• Organizations investing in R&D are likely to innovate, adapt, and remain relevant in competitive markets.

Examples of Research Topics

• Example research topic: impact of social media on the mental health of adolescents.

Steps of the Scientific Method

• Observation
• Problem Statement
• Literature Review
• Hypothesis Formulation
• Experiment or Investigation Design
• Data Collection
• Data Analysis
• Conclusions
• Result Publication

The Scientific Method

• The scientific method systematically acquires knowledge through observation, hypothesis formulation, experimentation, and analysis.
• The process is objective, reproducible, and verifies results to generate theories and laws.
• In poverty research in Colombia, this method identifies and measures poverty dimensions, such as education, health, and housing.
• Data collection and analysis test the stated hypotheses.

Problem Formulation

• The initial crucial step is to clearly define the question or problem to be resolved.
• This is applicable when addressing how multidimensional poverty in Colombia has changed and its influential factors.
• Focus on specifying the population, time frame, and dimensions for analysis

Dimensions to Analyze for poverty in Columbia

• Education: School lag, illiteracy
• Childhood and Youth: School absenteeism, access to early childhood services, developmental delays, youth unemployment
• Employment: Long-term unemployment, informal work, inadequate employment
• Health: Barriers to healthcare access, unmet health needs, access to childcare for children under 5

Literature Review

• This is a fundamental stage in scientific research.
• Compile, evaluate, and analyze previous studies and theories relevant to the study topic.
• Identify contributions, detect gaps, and place research within academic and practical contexts.
• It refines research questions, hypothesis formulation, and the selection of appropriate methodologies.
• Previous studies analyzing Multidimensional Poverty Index (MPI) on both global and national levels are examined.
• Reports from United Nations Development Programme (UNDP) and academic publications are reviewed.
• Studies comparing multidimensional poverty with monetary poverty, Unsatisfied Basic Needs (NBI), and housing deficits are analyzed.

Formulation of Hypothesis

• Propose an educated guess or explanation for the relationship between variables, grounded in observation and literature review.
• The hypothesis should be specific, testable, and serve as a foundation for designing experiments or investigations.
• A hypothesis for the Multidimensional Poverty Index (MPI) could be: rural areas in Colombia exhibit higher levels of multidimensional poverty than urban areas due to limited access to services and education.
• Hypotheses are based on prior literature and are tested through data collection and analysis.

Experiment/Investigation Design

• Plan methods and procedures for collecting and analyzing data to test the formulated hypothesis.
• Selection of variables, sample definition, measuring instruments, and analysis techniques is part of this experimentation
• Design a study that collects data through surveys like GEIH (Gran Encuesta Integrada de Hogares), ECV (Encuesta de Calidad de Vida), and CPV (Censo de Población y Vivienda) to measure MPI.
• Select representative samples of households in rural and urban areas, measuring the five dimensions of the IPM-C: education, health, employment, childhood and youth, and access to services.

Data Compilation

• Gathering necessary data to address the formulated question.
• In Colombia, sources like the Gran Encuesta Integrada de Hogares (GEIH) and other national surveys (ECV) measure Multidimensional Poverty.
• Organizing and cleaning data is important for ensuring its quality and relevance for analysis.

Data Analysis

• Data analysis uses statistical and computational tools to explore and model data.
• Descriptive and predictive analyses can understand trends and patterns in multidimensional poverty.
• Identification of the most affected dimensions and variation of poverty rates across different regions is an example.

Conclusions

• Analysis results should be interpreted within the context of the formulated problem.
• Assess the significance of findings and their response to the initial question.
• For instance, interpreting a decrease in multidimensional poverty and its relation to public policies, or identifying areas to be improved.

Result Publication

• Effective communication of results is essential for their usefulness and actionability.
• Prepare reports, data visualizations, and clear presentations.
• For example, present multidimensional poverty findings to government decision-makers and international organizations using graphs and key statistics.

Application of the Scientific Method: Examples

Example 1: Unemployment Rate

• Observation: An increase in the unemployment rate in a specific region.
• Question: What factors contribute to the increased unemployment rate there?
• Literature Review: Review previous studies on factors affecting unemployment.
• Hypothesis: Increased unemployment results primarily from job automation in manufacturing.
• Experiment Design: Gathering economic data and surveying local businesses.
• Data Collection: Obtaining job statistics, industrial production data, and survey responses.
• Data Analysis: Using econometric techniques to find correlations between automation and unemployment.
• Conclusions: Confirming automation has a significant impact on the increase in unemployment.

Example 2: Football Team Performance

• Observation: A soccer team's inconsistent performance in recent games.
• Question: What factors are affecting team performance?
• Literature Review: Study investigations into sports performance and factors involved in performance.
• Hypothesis: Inconsistent performance is due to poor team cohesion and physical condition.
• Experiment Design: Analyze individual player performance data, team cohesion, and physical fitness.
• Data Collection: Collecting game statistics, physical evaluations, and team cohesion surveys.
• Data Analysis: Use statistical analyses to find the influence of cohesion and fitness on performance.
• Conclusion: Confirmation that the lack of cohesion and poor physical condition is negatively affecting performance.

Example 3: Customer Satisfaction

• Observation: A company has noted a decrease in customer satisfaction.
• Question: What factors contribute to the decrease in customer satisfaction?
• Literature Review: Analyze studies on customer satisfaction and quality management.
• Hypothesis: Decreased customer satisfaction is due to increased wait times for service.
• Experiment Design: Survey customers and analyze waiting times for service.
• Data Collection: Conduct surveys and record wait times in different service points.
• Data Analysis: Statistically evaluate the relationship between waiting times and satisfaction levels.
• Conclusion: Identify a strong correlation between long waiting times and low customer satisfaction.

Basic Statistical Concepts

What is Statistics?

• Statistics is learning from data, measuring, controlling, and communicating uncertainty, according to Mendenhall, Beaver & Beaver (2003).
• Statistics is collecting, organizing, analyzing, and interpreting to make informed decisions, according to Anderson, Sweeney & Williams (2008).
• Statistics is the science of collecting, organizing, analyzing, and interpreting data for more effective decision-making, according to Lind, Marchal & Mason (2004).

Importance of Statistics

• Statistics are used in areas like economics, business administration, and public accounting.
• Statistics aids in making informed decisions based on data.

Population

• Population is the complete set of individuals or elements under study, according to Mendenhall, Beaver & Beaver (2003).
• Population is the complete set of all units of interest in a study, according to Anderson, Sweeney & Williams (2008).
• Population is the total set of elements or individuals being studied, according to Lind, Marchal & Mason (2004).

Importance of a Population

• The population is fundamental in statistics as it represents the complete universe of observations relevant to a specific investigation.
• Understanding the population is crucial for defining the study's scope and ensuring the results are generally applicable to the group of interest.
• Statistical inference may be questionable and lack validity without clear population definition.

Population Examples

• Students enrolled in the Statistics II course at U Central.
• Residents of Bogotá.
• Customers of a restaurant during July.
• Employees of Coca-Cola Colombia.
• Students in engineering, medicine, and humanities at Universidad Nacional.
• Households in Colombia divided by region and socioeconomic level.
• Cardiology, oncology, and pediatrics patients at the Hospital General.
• Consumers of a new smartphone in Colombia, segmented by age and gender.
• Internet users in a city, divided by daily, weekly, and occasional users, classified by activities.
• Farmers in the Cauca Valley region cultivating sugarcane, coffee, and flowers.

Census

• A census is an exhaustive study that compiles information from all elements of a population, according to Mendenhall, Beaver & Beaver (2003).
• A census is a data collection procedure that involves enumerating all elements of a population, according to Anderson, Sweeney & Williams (2008).
• A census is a method of data collection in which information is obtained from all members of a defined population, according to Lind, Marchal & Mason (2004).

Importance of a Census

• A census is important because it gives complete and accurate data from the whole population.
• A census eliminates sampling errors and allows for direct inferences.
• Censuses are for formulating public policies, planning, and informed decision-making at a national and local level.

Census Examples

• National Population and Housing Census (2018): Conducted by DANE, collects demographic and socioeconomic data of the Colombian population.
• Agricultural Census (2014): Also conducted by DANE, gathers details on agricultural production, land use, and living conditions in rural areas.
• National Population and Housing Census (2005): Provided data on the distribution, characteristics, and living conditions of Colombians.
• Building Census: Conducted by DANE, collects construction data.
• United States Census (2020): Conducted every 10 years, collects detailed data on the population and housing.
• United Kingdom Census (2021): Conducted by the ONS, collects information on demographic and socioeconomic characteristics.
• China Census (2020): Conducted by the National Bureau of Statistics, one of the largest in the world, collects data on population and housing.
• India Census (2011): Conducted by the Office of the Census of India, collects detailed information including the demographic, social, and economic characteristics.

Sample

• A sample is a subset of the population.
• The sample provides information on the entire population (Mendenhall, Beaver & Beaver, 2003)
• A sample is the subset of people selected for the study to provide information (Anderson, Sweeney & Williams, 2008)
• Data from a sample can realize inferences (Lind, Marchal, and Mason, 2004)

Examples of Samples

• Sample of 200 students from engineering, medicine, and humanities.
• Sample of 500 households in Colombia, selected randomly from the Andean, Caribbean, and Pacific regions, of different socioeconomic levels.
• Sample of 150 patients from cardiology, oncology, and pediatrics.
• Sample of 300 consumers selected randomly from different age and gender groups.
• Sample of 100 farmers from the Cauca Valley region, selected randomly from sugarcane, coffee, and flower cultivators.

Examples of Surveys

• Encuesta Nacional de Demografía y Salud (ENDS): Conducted by Profamilia, this survey collects data on health, family planning, fertility, infant and maternal mortality of households in Colombia.
• Encuesta Nacional de Calidad de Vida (ECV): Conducted by DANE, this survey focuses on measuring the living conditions of Colombia's population.
• Encuesta de Opinión del Consumidor (EOC): Conducted by Fedesarrollo, this monthly survey measures the perception and expectations of Colombian consumers regarding the country's economic situation
• Encuesta Nacional de Consumo de Sustancias Psicoactivas: Conducted by the Ministry of Justice and DANE, researches drug usage in the Colombian population.
• Gran Encuesta Integrada de Hogares (GEIH): Conducted by DANE, surveys employment, unemployment, income, and working conditions.

Parameter

• A parameter describes a population characteristic using a number (Mendenhall, Beaver & Beaver, 2003).
• A descriptive measure that serves a population description is what defines a parameter (Anderson, Sweeney & Williams, 2008).
• A numerical measure describes a characteristic of a complete population (Lind, Marchal & Mason, 2004).

Examples of Parameters

• The average age of all the students at the Universidad Nacional.
• The proportion of Colombian households with internet access.
• The standard deviation of the monthly income of all families in Bogotá.
• The variance in scores of all students on a national mathematics exam.
• The percentage of satisfied employees in a multinational company.
• The median blood pressure of all patients in a hospital.
• The average monthly sales of all points of sale in a supermarket chain.

Further Examples of Parameters

• Infant Mortality Rate (ENDS): This parameter measures the number of deaths of children under one year old per 1,000 live births in a determined year.
• Life Quality Index (ECV): This composite parameter reflects the level of well-being of households
• Consumer Confidence Index (EOC): This parameter measures the level of optimism that consumers have in the economy and their finances
• Unemployment Rate (GEIH): This parameter measures the percentage of unemployed people that are seeking jobs
• Average Children per Women (ENDS): This parameter measures the average children that women will have
• Average Income per household: Measures household income

Statistic

• A statistic is a measure calculated from sample data used to estimate a population parameter (Mendenhall, Beaver & Beaver, 2003).
• A statistic is a descriptive measure calculated from the data of a sample" (Anderson, Sweeney & Williams, 2008).
• A numerical measure calculated from the data of a sample (Lind, Marchal & Mason, 2004).

Examples of Statistics

• Average age of a sample of 200 students from the Universidad Nacional.
• Proportion of households with internet access from a sample of 500 Colombian households.
• Standard deviation of monthly income from a sample of 300 families in Bogotá.
• Variance of scores for a sample of 150 students from a national mathematics exam.
• Percentage of satisfied employees from a sample of 500 employees in a multinational company.
• Median blood pressure from a sample of 100 patients in a hospital.
• Average monthly sales from a sample of 50 points of sale in a supermarket chain.

Further Examples of Statistics

• Average Income
• Median Age of the population
• Standard Deviation of Psychoactive Substances Consumption
• Rate of unemployed
• Coefficient of Gini

Notation

• Mathematical and statistical symbols are used to represent data and functions (Mendenhall, Beaver & Beaver, 2003).
• Standard symbols, like population or standard deviation measure are used to define sizes (Anderson, Sweeney & Williams, 2008).
• Standard notation is used for the mean sample, and standard deviation parameters that include the samples (Lind, Marchal & Mason, 2004).

Examples of Notation

Media sample

• Average of a variable in a sample

Standard deviation sample

• Used in studies, measure the dispersion in the data

Proportion sample

• Reflect a Gran Encuesta Integrada Homes

Sample Size

• It is the number of observations or even individuals in a home

T Student value

• A hypothesis and confidence interval appliance to sample of any area

Data

• Numerical number
• Represents the characteristics of a person in statistical analysis
• The data can measure

Importance of Data

• Los datos is the base of any statistical analysis

Variable

• Variables can be measured by number of statistics

La variable

• Fundamental information
• Measurements can be analyzed

Examples of variables

• Monthly income:
• Level of educations

Type of Variables

Variables in quantitative

• They can be measured mathematically

Variables in cualitativa

• They can have attributes without numbers

Examples of Types of variables

• Monthly Income = (ECV), quantitative
• Level of education achieved is variable (ENDS), qualitative

Variable quantitatives

• Any kind, as long as they’re measurable with a scale

Variable Continua

• Values that can be on many numbers

Variable Discreta

• Value to define the value that you can put into work

Bases de Datos Database

• It has connections where the data helps with application
• Database are very important

Database information

• They are data on electronic devices

Data structure

• This data haves form and definitions

Non structure data base (not data)

• The datas haves a form, content is videos pictures and files, its requiere advanced techniques

Data Base Types

Estructurados Data Base

Estructure and data base are the most importatn parts of data storage

• They are easy to access

No estructured Data base

They required to use a method that its faster

Formas de Realizar Preguntas en Encuestas (Survey)

Escala Likert(Scale Likert)

• is a great appliance to indicate degree

Preguntas abietras Open Questions

• is great information
• They provide the richest and the most detail information
• They show and present themes and opinions that aren’t considered.
• The question is long and not effective

Reguntas esencibles Sensitive Questions

• Thematic that can be important a sensitive

Datos No Agrupados y Agrupados (Data that aren’t grouped and not grouped)

Dates no are grouped

• present tal is how you can

Dates that are grouped

• The days are organize

Definición de Distribución Estadística

• (Definition of Statistical Distribution) Describes the value of variables in numbers or days that are the value of values.

Distribución Estadística

• (Statistical Disturbation)
• Distribution Direct = Is variables that can or can’t values
• Sample- the number of client attention to the call center receipt by the hour

Distribución Continua

• Is referred to valuable that can make value the same day