The Purpose of Statistical Models

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  • 0:25 Purpose Of Statistics
  • 2:40 Types Of Statistical Models
  • 4:35 Types Of Variables
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Understanding statistics requires that you understand statistical models. This lesson will help you understand the purpose of statistics, statistical models, and types of variables.

Purpose of Statistics

Benjamin is working on a project for his agriculture class. He found research that shows that under the right conditions, plants will grow a consistent amount every day. Benjamin wants to test this information and see if he can predict the height of his plants after 10 days.

Benjamin needs to understand statistical models and the purpose of statistics before he can properly analyze this information. In this lesson, we will discuss the purpose of statistics and how you can use statistical models to achieve this purpose.

First, let's discuss the purpose of statistics. The purpose of statistics is to describe and predict information. This can be divided into descriptive statistics and inferential statistics. Sometimes we collect data in an attempt to describe the characteristics of a population. For example, Benjamin can collect data on the colors of the flowers of certain types of plants. Over time, he may have enough information to say that the plant produces a white flower 56% of the time, a purple flower 34% of the time, and a blue flower 10% of the time. This is an example of how Benjamin used statistics to describe the plant.

Statistics is also used to predict information. Benjamin can use the same information that he collected to predict the color of flower that the plant would produce. If Benjamin has a plant that hasn't yet produced a flower, he can say that it is most likely to produce a white flower and least likely to produce a blue flower.

Now that you understand that the purpose of statistics is to describe and/or predict, let's discuss the role that statistical model plays in that purpose.

A statistical model is a combination of inferences based on collected data and population understanding used to predict information in an idealized form. This means that a statistical model can be an equation or a visual representation of information based on research that's already been collected over time. Notice that the definition mentions the words 'idealized form'. This means that there are always exceptions to the rules.

For example, let's say that Benjamin waters his plants for 10 days with the correct amount of water under the correct conditions. However, what if someone accidentally knocks over one of the plants? Or what if an animal breaks into the greenhouse and starts feeding on the plant? These are extreme examples, but often unexpected conditions can interfere with collecting data.

Now let's talk about types of statistical models and how they are used.

Types of Statistical Models

Before you can understand the types of statistical models, you must first understand the reason these models exist. Statistical models exist because we are looking for a relationship between two, or sometimes more, variables. For example, in Benjamin's case there are two variables: the number of days the plants grow and the height of the plants. We know from earlier that the more days the plants grow, the taller they get. Of course, there is the matter of the condition of the plants, the amount of water, the amount of light, etc. These are all other variables that could affect the experiment. But for now, let's limit these two variables, just to keep things simple. The relationship between the height of the plants and the number of days the plants grow is known as a correlation, which is the relationship between two variables or sets of data. A correlation test is one type of statistical model.

Essentially, all statistical models exist to find inferences between different types of variables and because there are different types of variables, there are different types of statistical models. For example, let's say that Benjamin was collecting information about the different types of plants that grow in his region. He would be collecting data that would be grouped into categories, which is known as categorical data. In this experiment, Benjamin would have to use a different statistical model to analyze his data than the one he used to find a correlation between the height of the plants and the number of days they spent growing.

Some of the types of models, or statistical tests, include regression, analysis of variance, analysis of covariance, and chi-square. These are just a few examples of statistical models; there are many different ways we can analyze data depending on the variables. We will discuss many of these models in depth in future lessons.

Now let's talk more about the types of variables involved in different statistical models.

Types of Variables

Benjamin has been experimenting with his plants. He has added a different type of fertilizer, different amounts of water, and different amounts of humidity and sunlight to some of the plants. Now one of the plants has started to bloom only blue flowers, which is very rare. Unfortunately, Benjamin isn't sure which of the changes or combination of changes caused the plant to bloom blue flowers. To understand this phenomenon, Benjamin needs to understand two types of variables: response and explanatory.

A response variable is the observed variable, or variable in question. In Benjamin's case, the blue flowers would be the response variable. This is similar to a dependent variable, which is a condition or piece of data in an experiment that is controlled or influenced by an outside factor, most often the independent variable. However, sometimes data can be collected without doing an experiment and in these cases, there is still a response variable.

When analyzing data, we often ask, 'What is causing the response variable?' Benjamin has been asking the same question: 'What is causing the blue flowers?' To answer his question, you'll need to understand explanatory variables.

An explanatory variable is a variable or set of variables that can influence the response variable. In Benjamin's case, this refers to all of the things he did to his plants, such as watering, adding fertilizer, and changing humidity and sunlight. All of these factors could have influenced the blue flower's appearance.

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