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Statistics 101: Principles of Statistics11 chapters | 141 lessons | 9 flashcard sets

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Lesson Transcript

Instructor:
*Jessica McCallister*

The Pearson correlation coefficient is just one of many types of coefficients in the field of statistics. The following lesson provides the formula, examples of when the coefficient is used, its significance, and a quiz to assess your knowledge of the topic.

The **Pearson correlation coefficient** is a very helpful statistical formula that measures the strength between variables and relationships. In the field of statistics, this formula is often referred to as the **Pearson R test**. When conducting a statistical test between two variables, it is a good idea to conduct a Pearson correlation coefficient value to determine just how strong that relationship is between those two variables.

In order to determine how strong the relationship is between two variables, a formula must be followed to produce what is referred to as the **coefficient value**. The coefficient value can range between -1.00 and 1.00. If the coefficient value is in the negative range, then that means the relationship between the variables is negatively correlated, or as one value increases, the other decreases. If the value is in the positive range, then that means the relationship between the variables is positively correlated, or both values increase or decrease together. Let's look at the formula for conducting the Pearson correlation coefficient value.

Step one: Make a chart with your data for two variables, labeling the variables (*x*) and (*y*), and add three more columns labeled (*xy*), (*x*^2), and (*y*^2). A simple data chart might look like this:

Person | Age (x) |
Score (y) |
(xy) |
(x^2) |
(y^2) |
---|---|---|---|---|---|

1 | |||||

2 | |||||

3 |

More data would be needed, but only three samples are shown for purposes of example.

Step two: Complete the chart using basic multiplication of the variable values.

Person | Age (x) |
Score (y) |
(xy) |
(x^2) |
(y^2) |
---|---|---|---|---|---|

1 | 20 | 30 | 600 | 400 | 900 |

2 | 24 | 20 | 480 | 576 | 400 |

3 | 17 | 27 | 459 | 289 | 729 |

Step three: After you have multiplied all the values to complete the chart, add up all of the columns from top to bottom.

Person | Age (x) |
Score (y) |
(xy) |
(x^2) |
(y^2) |
---|---|---|---|---|---|

1 | 20 | 30 | 600 | 400 | 900 |

2 | 24 | 20 | 480 | 576 | 400 |

3 | 17 | 27 | 459 | 289 | 729 |

Total | 61 | 77 | 1539 | 1265 | 2029 |

Step four: Use this formula to find the Pearson correlation coefficient value.

Step five: Once you complete the formula above by plugging in all the correct values, the result is your coefficient value! If the value is a negative number, then there is a negative correlation of relationship strength, and if the value is a positive number, then there is a positive correlation of relationship strength. Note: The above examples only show data for three people, but the ideal sample size to calculate a Pearson correlation coefficient should be more than ten people.

Let's say you were analyzing the relationship between your participants' age and reported level of income. You're curious as to if there is a positive or negative relationship between someone's age and their income level. After conducting the test, your Pearson correlation coefficient value is +.20. Therefore, you would have a slightly positive correlation between the two variables, so the strength of the relationship is also positive and considered strong. You could confidently conclude there is a strong relationship and positive correlation between one's age and their income. In other words, as people grow older, their income tends to increase as well.

Perhaps you were interested in learning more about the relationship strength of your participants' anxiety score and the number of hours they work each week. After conducting the test, your Pearson correlation coefficient value is -.80. Therefore, you would have a negative correlation between the two variables, and the strength of the relationship would be weak. You could confidently conclude there is a weak relationship and negative correlation between one's anxiety score and how many hours a week they report working. Therefore, those who scored high on anxiety would tend to report less hours of work per week, while those who scored lower on anxiety would tend to report more hours of work each week.

A discussion on the Pearson correlation coefficient wouldn't be complete if we didn't talk about **statistical significance**. When conducting statistical tests, statistical significance must be present in order to establish a probability of the results without error.

The statistical symbol for significance is denoted as *p*. The *p* stands for **probability**. In the field of social sciences, the value associated with *p* is generally set to represent .05 or below. What does this mean? Setting a *p*-value at .05 or below means that there is less of a chance of error. This error-reporting system (probability) establishes statistical significance and accuracy among results of statistical tests.

If the *p*-value results in .04, then there is an even smaller chance of error in the results. The lower the *p*-value, the more accurate the statistical significance is and the less chance of error. Ideally, you want your statistical tests to result in as small a *p*-value as possible. You must find statistical significance in order to continue moving forward conducting the Pearson correlation coefficient.

The **Pearson correlation coefficient**, often referred to as the **Pearson R test**, is a statistical formula that measures the strength between variables and relationships. To determine how strong the relationship is between two variables, you need to find the **coefficient value**, which can range between -1.00 and 1.00. If the coefficient value is in the negative range, then that means the relationship between the variables is **negatively correlated** - as one value increases, the other decreases. If the value is in the positive range, then that means the relationship between the variables is **positively correlated**, or both values increase or decrease together.

The formula for conducting the Pearson correlation coefficient value follows these steps:

- Make a chart with your data for two variables, labeling the variables (
*x*) and (*y*), and add three more columns labeled (*xy*), (*x*^2), and (*y*^2). - Complete the chart using basic multiplication of the variable values.
- After you have multiplied all the values to complete the chart, add up all the columns from top to bottom.
- Use this formula to find the Pearson correlation coefficient value.
- Once you complete the formula above by plugging in all the correct values, the result is your coefficient value!

When you are done, you should be able to:

- State the purpose of the Pearson correlation coefficient
- Recall another name for the Pearson correlation coefficient
- Explain how to determine if two variables are negatively or positively correlated
- State the Pearson correlation coefficient formula
- Describe statistical significance and what
*p*-values mean

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Statistics 101: Principles of Statistics11 chapters | 141 lessons | 9 flashcard sets

- Go to Probability

- Go to Sampling

- Creating & Interpreting Scatterplots: Process & Examples 6:14
- 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
- Interpreting Linear Relationships Using Data: Practice Problems 6:15
- 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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