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Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

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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.

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.

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.

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.

This is similar to an **independent variable**, which is a condition or piece of data in an experiment that can be controlled or changed. The difference between explanatory variables and independent variables is that explanatory variables can't always be controlled or changed. For example, if Benjamin has no control over the humidity in his greenhouse, then the humidity is not an independent variable that Benjamin can control, but it could still be a factor in the blue flower's appearance.

Variables are collected in the form of data, which can either be categorical or quantitative. Each type of categorical data can either be ordinal or nominal, and each type of quantitative data can be either discrete or continuous. **Nominal data** is categorical data that assigns numerical values as an attribute to an object, animal, person, or any other non-number. They are used to identify the objects only; they cannot be manipulated as numbers. **Ordinal data** is data that can be ordered and ranked but not measured, such as levels of achievement, prizes, rankings, and placements.

**Discrete data** is data that cannot be divided. It is distinct and can only occur in certain values. For example, you can only have a whole person, not a half or a quarter of a person, when collecting data. **Continuous data** is data that can be divided infinitely; it does not have any value distinction such as time, height, and weight.

As you can see, the many types of data lend themselves to many combinations of explanatory and response variables, and that is why we have different statistical models to analyze this data.

The purpose of statistics is to describe and predict information. This can be divided into descriptive statistics and inferential statistics, which just means that sometimes we collect data in an attempt to describe the characteristics of a population and sometimes we collect data and analyze it to predict information. For both of these purposes, we have to use a statistical model.

A **statistical model** is a combination of inferences based on collected data and population understanding used to predict information in an idealized form. There are different types of statistical models known as tests that can be used to analyze data.

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. Some of the types of models, or statistical tests, include regression, analysis of variance, analysis of covariance, and chi-square.

There are many different ways we can use the models to analyze data, depending on the types of variables. A **response variable** is the observed variable or variable in question. In Benjamin's experiment, the blue flowers were 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.

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. This is similar to an **independent variable**, which is a condition or piece of data in an experiment that can be controlled or changed.

Remember, variables are collected in the form of data, which can either be categorical or quantitative. Each type of categorical data can either be **ordinal** or **nominal**, and each type of quantitative data can be either **discrete** or **continuous**. This can result in needing many different types of statistical models to analyze each combination of data properly.

If you are wondering about the different types of statistical models or confused by any of these concepts presented in this lesson, don't worry! Keep going, and we will talk about all of these concepts in greater detail in other lessons.

Once you've completed this lesson, you will be able to:

- Identify the purpose of statistics and statistical models
- List different types of statistical models
- Define the characteristics of response variable and explanatory variable
- Compare explanatory variables and independent variables
- Describe categorical and quantitative data
- Differentiate between ordinal and nominal data
- Distinguish that differences between discrete and continuous data

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Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

- Descriptive & Inferential Statistics: Definition, Differences & Examples 5:11
- Difference between Populations & Samples in Statistics 3:24
- Defining the Difference between Parameters & Statistics 5:18
- Estimating a Parameter from Sample Data: Process & Examples 7:46
- What is Quantitative Data? - Definition & Examples 4:11
- What is Categorical Data? - Definition & Examples 5:25
- Discrete & Continuous Data: Definition & Examples 3:32
- Nominal, Ordinal, Interval & Ratio Measurements: Definition & Examples 8:29
- The Purpose of Statistical Models 10:20
- Random Selection & Random Allocation: Differences, Benefits & Examples 6:13
- Convenience Sampling in Statistics: Definition & Limitations 6:27
- How Randomized Experiments Are Designed 8:21
- Analyzing & Interpreting the Results of Randomized Experiments 4:46
- Confounding & Bias in Statistics: Definition & Examples 3:59
- Confounding Variables in Statistics: Definition & Examples 5:20
- Bias in Statistics: Definition & Examples 7:24
- Bias in Polls & Surveys: Definition, Common Sources & Examples 4:36
- Misleading Uses of Statistics 8:14
- Go to Overview of Statistics

- Go to Probability

- Go to Sampling

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