What is Statistics and its relationship with other disciplines. Difference between Descriptive and Inferential Statistics.
The study of a phenomenon often begins with the analysis of data obtained from various sources, including observational data collected from observations of existing events and experimental data obtained from planned experiments. Statistics is the discipline that deals with processing, summarizing, and highlighting the relevant aspects within this data, as well as assessing the degree of uncertainty associated with the conclusions that can be drawn from the analysis of such data.
In the current digital world, where data availability is exponentially expanding (big data), the importance of statistics is continually growing. Statistics plays a crucial role in interpreting, extracting meaning, and making informed decisions from this vast flow of information. It helps discover trends, identify correlations, predict future behaviors, and support decision-making in various fields, including science, economics, medicine, technology, and many other sectors. Statistics is a fundamental tool for the information age in which we live.
Descriptive Statistics:
Descriptive statistics focuses on the presentation and synthesis of observed data through tables, charts, and appropriate indices. This branch of statistics provides a clear and understandable overview of the data, whether it represents a sample or the entire population. Descriptive statistics is used to summarize the main characteristics of the data, highlighting trends and patterns. It does not rely on probabilistic models.
Inferential Statistics:
Conversely, inferential statistics aims to draw conclusions about the entire phenomenon based on data collected from a limited sample of the population. This type of statistics is used for making predictions, testing hypotheses, and decision-making, often with a predetermined quantification of error. For example, in electoral projections, estimates of election results are provided along with margins of error. Inferential statistics is based on probability theory and provides tools for managing and quantifying uncertainty in results.
In general, descriptive statistics focuses on data representation and interpretation, while inferential statistics aims to draw general conclusions and predictions based on limited samples. Both branches are crucial for understanding and analyzing data, and each has its specific role in the statistical process. Error is an integral part of inferential statistics and is taken into account in results and predictions. For example, a small variation in data does not always indicate a significant change, and this is where inferential statistics plays a crucial role in assessing uncertainty.
Describe the concepts of Population, Sample Attribute, Variable, Level of measurement and Dataset.
Data refers to individuals or statistical units that, when considered as a whole, constitute what is referred to as the “population.” This terminology originates from the early statistical studies, which predominantly had a demographic nature. Within the population, it is possible to identify a subset known as a “sample.” Researchers often utilize samples because it is frequently impractical or impossible to gather data from every individual in the population. Sampling enables a more efficient collection and analysis of data. However, it is of paramount importance that the sample is of high quality and representative of the original population, as this is a key element in drawing meaningful conclusions that can be generalized to the entire population.
An attribute is an intrinsic characteristic or specific quality of an element within a dataset. Attributes represent measurable or categorizable aspects of entities or individuals included in the data. These attributes are often used to describe, classify, or quantify elements within the dataset.
In the context of a given population, a statistical variable is defined as a characteristic of its units that is of interest for examination. Depending on the values that the variable can take, often referred to as the variable’s modes, a distinction is made between:
Qualitative Variables (or Categorical Variables): These variables assume non-numeric values, although they are sometimes encoded with numbers for convenience. When these values do not have a natural order, the variable is termed “nominal.” For example, nominal variables include color, religious belief, political party affiliation, and gender (male or female).
Ordinal Variables: When these values have a natural order, the variable is termed “ordinal.” In surveys, ordinal data is often obtained using Likert scales (for example, surveys about courses use scales like “strongly agree, agree more than disagree, disagree more than agree, strongly disagree”). Other examples of ordinal variables include educational level, military rank, and days of the week.
Quantitative Variables: These variables have inherently numeric values. Depending on the range of possible values, two distinctions are made:
- Discrete Variables: These variables can assume only a finite number of values or, at most, a countable infinity of values. Examples of discrete variables include the number of children and the number of pages in a book.
- Continuous Variables: These variables can potentially take on any real number as values (even though they may effectively assume only certain values), or all real numbers within a certain interval. Examples of continuous variables include height, weight, and temperature. Continuous data often arises from measurements.
A dataset, or data set, is a structured collection of information that includes values or measurements for multiple attributes or variables. Datasets are typically organized in tabular form, with rows representing individual observations or cases, and columns representing specific variables or attributes. These datasets are used for statistical analysis, research, and various data-driven activities in a wide range of fields.