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Statistics 101: Principles of Statistics11 chapters | 136 lessons | 3 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.

When conducting experiments and analyzing data, many people often confuse the concepts of correlation and causation. In this lesson, you will learn the differences between the two and how to identify one over the other.

Brandy works in a clothing store. As she is restocking shelves, she notices that the sweaters are completely gone. She goes into the inventory area of the store and finds the sweater boxes. In the meantime, she gets a call: another one of her co-workers is calling in sick. That's the third person this week! As she restocks the sweaters, Brandy has a thought. Are the sweater sales causing her coworkers to become ill? Brandy is faced with a common problem, correlation versus causation.

In this lesson, you will learn about correlation and causation, the differences between the two and when to tell if something is a correlation or a causation.

First, correlation and causation both need an independent and dependent variable. An **independent variable** is a condition or piece of data in an experiment that can be controlled or changed. A **dependent variable** is a condition or piece of data in an experiment that is controlled or influenced by an outside factor, most often the independent variable.

If there is a correlation, then sometimes we can assume that the dependent variable changes solely because the independent variables change. This is where the debate between correlation and causation occurs. However, there is a difference between cause and effect (causation) and relationship (correlation). Sometimes these areas can be confused and muddled when analyzing data.

You probably know that a **correlation** is the relationship between two sets of variables used to describe or predict information. There is an emphasis here on relationship. Sometimes we can use correlation to find causality, but not always. Remember that correlation can either be positive or negative.

Graph 1 is called a **positive correlation**, where the dependent variables and independent variables in a data set increase or decrease together.

This means that there is a positive relationship between the number of sweaters sold at Brandy's store and the frequency of illnesses that occur with Brandy's coworkers.

If the numbers sloped downward, like the line in Graph 2, then you have a data set with a **negative correlation**, where the dependent variables and independent variables in a data set either increase or decrease opposite from one another.

That means if the independent variables decrease, then the dependent variable would increase, and vice versa. In this example, Brandy notices that the more shorts that are sold, the fewer illnesses there are, but the more vacation time her coworkers use.

So the question is: do shorts or sweater sales cause illnesses or vacation? You might have guessed that it isn't the clothing that is causing this change; these things are just correlated, but not cause and effect.

**Causation**, also known as cause and effect, is when an observed event or action appears to have caused a second event or action. For example, I bought a brand new bed comforter and placed it in my washing machine to be cleaned. After cleaning the comforter, my washing machine stopped working. I may assume that the first action, washing the comforter, caused the second action, broken washing machine.

Brandy decides to rearrange the inventory on her floor. She puts the athletic wear and shoes in a prominent spot in the store, puts the swimwear next to the front register and moves the business attire to a less conspicuous spot. Over the next few weeks she notices a change in her employees. They are more active, eat healthier and take walks on their breaks. Could the athletic wear in a prominent spot cause the employees to have the motivation to be healthier? She tries an experiment, exchanging the athletic wear and the business wear. Over the next few weeks, Brandy doesn't notice a change in the employees' behavior. She asks them what caused them to suddenly want to work out and live a healthier life style. Was it the athletic wear? No, they tell her. It was the swimsuits by the front register reminding them that spring break was coming around the corner.

Unfortunately, there is no tried and true way of identifying causation. We can find many correlations in research, but the causation often requires a separate experiment. For example, Brandy did not know if the athletic wear was the causation or just a correlation until she rearranged the inventory a second time. However, you can identify instances of likely causation. Let's look at a few examples.

Brandy has noticed that she is having trouble keeping certain sizes of footwear inventory up. In sizes six and seven, she frequently runs out of high heels for women. In sizes eight and nine, she frequently runs out of athletic footwear for women. Brandy notices this and wonders if having a certain foot size causes a person to be more athletic. Given the information, is this a likely causation? Pause the video here if you need to review the information and think about your answer.

So what do you think? Is a person's foot size a cause of a person's athletic ability? No; given the information, we can only say that this is a correlation, especially since the sizes in both types of foot wear are common women's foot sizes.

Okay, let's try another one. Brandy is having trouble selling a new shirt in the store's stock. She notices the people that purchase the shirt take it straight off the rack, and many return it in a few days. She also notices that the shirt is often hanging in the discard rack in the dressing room. Brandy hypothesizes that there is something happening when the customers try on the shirt. Later, she asks a few employees to try on the shirt; they all report that the shirt has an itchy lining that they don't like. Brandy believes that this is the cause for the shirt's lack of sales. Given the information, is this a likely causation? Pause the video here if you need to review the information and think about your answer.

So what do you think? Is the scratchy lining the likely cause of poor sales? Given the information, this is probably true. There is a correlation between the shirt's low sales and the frequency it is found on the discard rack. But this information alone is not enough to determine causation. Brandy had to take it a step further to gather more information.

You will find both correlation and causation in everyday life, as we learned from Brandy's experiences. A **correlation** is the relationship between two sets of variables used to describe or predict information. A correlation can either be positive or negative. A **positive correlation** is where the dependent variables and independent variables in a data set increase or decrease together. A **negative correlation** occurs where the dependent variables and independent variables in a data set either increase or decrease opposite from one another.

Sometimes when there is a correlation, you may think that you have found a causation. **Causation**, also known as cause and effect, is when an observed event or action appears to have caused a second event or action. Remember when Brandy was rearranging the clothing in the department? She thought that the athletic wear was likely the cause of her employee's fitness routines, but it turned out to be the swimsuit display. Speaking of which... I think I'd better go hit the gym.

Once you've finished with this lesson, you will have the ability to:

- Define correlation and causation
- Differentiate between positive and negative correlations
- Explain why it is difficult to determine causation

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Statistics 101: Principles of Statistics11 chapters | 136 lessons | 3 flashcard sets

- Go to Probability

- Go to Sampling

- Creating & Interpreting Scatterplots: Process & Examples 6:14
- Simple Linear Regression: Definition, Formula & Examples 9:52
- Problem Solving Using Linear Regression: Steps & Examples 8:38
- Analyzing Residuals: Process & Examples 5:30
- Interpreting the Slope & Intercept of a Linear Model 8:05
- The Correlation Coefficient: Definition, Formula & Example 9:57
- The Correlation Coefficient: Practice Problems 8:14
- How to Interpret Correlations in Research Results 14:31
- Correlation vs. Causation: Differences & Definition 7:27
- Transforming Nonlinear Data: Steps & Examples 9:25
- Coefficient of Determination: Definition, Formula & Example 5:21
- Pearson Correlation Coefficient: Formula, Example & Significance 6:31
- Go to Regression & Correlation

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