Understanding Statistics: Types, Variables, and Sampling Methods
Understanding Statistics
Statistics is a branch of mathematics that deals with the study of a given feature in a population, data collection, organizing them into tables and illustrations, and analyzing them to draw conclusions about that population.
Types of Statistics
Descriptive Statistics: This involves studying the entire population, noting a feature of the same, and calculating parameters that give global information about the entire population.
Statistical Inference: This is a descriptive study performed on a subset of the population called a sample, and then extending the results to the entire population.
Biostatistics: This is a branch of statistics dealing with problems within the life sciences, such as biology and medicine.
Variables in Statistics
A variable is the property or attribute that is predicated of the unit of analysis.
Depending on the property, we can distinguish various types of variables:
- Qualitative Variable: This is a characteristic that cannot be expressed with numbers and must be expressed in words. For example, place of residence.
- Quantitative Variable: This is any characteristic that can be expressed with numbers. For example, the number of siblings or height. In this variable, we can distinguish two types:
- Discrete Quantitative Variable: This is a variable that can take only a finite number of values. For example, the number of siblings.
- Continuous Variable: This is a variable that can take any value within a real interval. For example, height.
Population and Sampling
Population: The set of all possible elements involved in an experiment or a study.
Types of Population
Finite Population: This indicates that it is possible to have reached or exceeded a limit. It includes a limited number of measurements and observations.
Infinite Population: This includes a large set of measurements and observations that cannot be achieved in the count. These are hypothetically infinite populations because there is no limit to the number of observations that each can generate.
Sample: A set of measurements or observations taken from a given population. It is a subset of the population.
Simple Random Sampling: This is one in which each element of the population has an equal chance of being selected for the sample.
A simple random sample is one in which its elements are selected by simple random sampling.
Sampling with Replacement: This is one in which an element can be selected more than once in the sample because after an element of the population is observed, it is returned to the population. This way, you can make unlimited withdrawals even though the population is finite.
Sampling without Replacement: This does not return the removed items to the population until all elements that make up the sample population are removed.
When taking a probability sample, two main aspects must be taken into account:
- The method of selection.
- The sample size.
Measurement Scales
Knowing the scale to which a measurement belongs is important in determining the appropriate method to describe and analyze the data.
Nominal Scale
This uses numbers to identify that data belongs to a group or category. There is no particular order or dimension to this scale; these are observations that can be classified or counted.
Ordinal Scale
On this scale, numbers represent a classification (greater than or less than), but do not represent a unit of measurement. It is implied that a number is a much higher degree of the attribute measured against a smaller number. This establishes a grading or natural order of categories, and each of the data can be located within any of the available categories.
Interval Scale
This scale, in addition to “greater than” and “less than,” also establishes a unit of measurement that allows us to ascertain how much is more or less. The unit of measurement is arbitrary, zero is conventional, and there may be negative numbers. Measuring temperature and IQ are examples of this type of scale.