# MA.912.DP.1.3

Explain the difference between correlation and causation in the contexts of both numerical and categorical data.

### Examples

Algebra 1 Example: There is a strong positive correlation between the number of Nobel prizes won by country and the per capita chocolate consumption by country. Does this mean that increased chocolate consumption in America will increase the United States of America’s chances of a Nobel prize winner?
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Categorical Data
• Numerical Data

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 8, students first analyzed bivariate numerical data using scatter plots. In Algebra I, students study association between variables in bivariate data and learn that there is a difference between two variables being strongly associated and one of them having a causative effect on the other. In later courses, students will learn how to design statistical experiments that can show causation.
• The intent of this benchmark includes the ability to informally draw conclusions about whether causation is justified when two variables are correlated.
• Correlation and causation are often misunderstood. It is important for students to understand their relationship. Causation and correlation can exist at the same time; however, correlation does not imply causation. Causation explicitly applies to cases where an action causes an outcome. Correlation is simply a relationship observed in bivariate data. One action may relate to the other, but that action doesn’t necessarily cause the other to happen, because both of them may be the result of a third “hidden variable.”
• Causation is possible, but it is also possible that correlation occurs from a third variable.
• For example, if one states, “On days when I drink coffee, I feel more productive.” it may be that one feels more productive because of the caffeine (causation) or because they spent time in the coffee shop drinking coffee where there are fewer distractions (third variable). Since one cannot determine whether the causation or the third variable results in correlation, then causation is not confirmed.
• Causation seems unlikely and a third variable seems likely.
• For example, there is a strong correlation between the number of Nobel prizes won by country and the per capita chocolate consumption by country. However, there are many possibilities a third variable, such as a strong economy, that can result in this correlation so causation can be ruled out.
• Causation is likely because there is a reasonable explanation for the causation.
• For example, if one states, “After I exercise, I feel physically exhausted.” it is reasonable to consider this to be a cause-and-effect. Causation can be confirmed by the explanation that because one is purposefully pushing their body to physical exhaustion when doing exercise, the muscles used to exercise are exhausted (effect) after they exercise (cause).
• When correlation is apparent in a bivariate data set, students are encouraged to seek a reasonable explanation that either identifies a hidden variable or a reasonable explanation for causation. Further investigation may be required to confirm or disconfirm causation.
• In Algebra I, the term correlation is used to describe an association between two variables and does not necessarily imply a linear relationship.
• Instruction includes asking the following questions while students investigate correlation and causation.
• Does this correlation make sense? Is there an actual connection between these variables? Will the correlation hold if I look at some new data that I haven’t used in my current analysis?
• Is the relationship between these variables direct, or are they both a result of some other variable?

### Common Misconceptions or Errors

• Even though students may not be able to reasonably explain why a causal relationship exists, they may assume that correlation implies causation.

### Strategies to Support Tiered Instruction

• Instruction includes co-creating and discussing examples and non-examples of causal relationships in numerical and categorical data.
• For example, a non-causal relationship could be a person’s shoe size and approximate number of vocabulary words they know.
• For example, a causal relationship could be a person’s shoe size and their age.
• Teachers provides instruction to increase understanding the relationship between correlation and causation. Teachers provides students with context that demonstrates when both correlation and causation are present. They may also provide context when only correlation is represented in the given context.

• Data from a certain city shows that the size of an individual’s home is positively correlated with the individual's life expectancy. Which of the following factors would best explain why this correlation does not necessarily imply that the size of an individual’s home is the main cause of increased life expectancy?
• a. Larger homes have more safety features and amenities, which lead to increased life expectancy.
• b. The ability to afford a larger home and better healthcare is a direct effect of having more wealth.
• c. The citizens were not selected at random for the study.
• d. There are more people living in small homes than large homes in the city. Some responses may have been lost during the data collection process.

### Instructional Items

Instructional Item 1
• Dr. Larry has noticed that when he carries around his lucky rock, his students seem to be nicer to him. Can one conclude that this positive correlation shows a causal relationship?
• a. Yes, because Larry decides whether or not to put his lucky rock in his pocket before he encounters people during the day.
• b. Yes, because it is not a negative correlation.
• c. No, because lucky rocks only work for children.
• d. No, because it is possible that people are nice to Larry because of another factor that also causes him to put the rock in his pocket.

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## Related Courses

This benchmark is part of these courses.
1200310: Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200320: Algebra 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200370: Algebra 1-A (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1210300: Probability and Statistics Honors (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 and beyond (current))
7912080: Access Algebra 1A (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1200315: Algebra 1 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1200375: Algebra 1-A for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912075: Access Algebra 1 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))
1210305: Mathematics for College Statistics (Specifically in versions: 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.DP.1.AP.3: Identify whether the data are explained by correlation or causation in the contexts of both numerical and categorical data.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Students are asked to interpret a correlation coefficient in context and describe a possible causal relationship.

Type: Formative Assessment

Listing All Possible Causal Relationships:

Students are asked to identify all possible causal relationships between two correlated variables.

Type: Formative Assessment

Does the Drug Cause Diabetes?:

Students are given a statement of association between two variables and are asked to determine if one variable is a cause of the other.

Type: Formative Assessment

Does Studying Pay?:

Students are given a scenario describing an association between two variables and are asked to determine if one variable is a cause of the other.

Type: Formative Assessment

## Lesson Plans

Students will explore voter turnout data for three gubernatorial general elections before and after the passage of the 19th Amendment. They will interpret the correlation of raw voter turnout vs. eligible population using a scatterplot, determine its direction by analyzing the slope and informally determine its strength by analyzing the residuals. Students will draw some conclusions and discuss what a correlation means and how it differs from causation in the context of elections in this integrated lesson.

Type: Lesson Plan

Spreading the Vote - Part 2:

Students will explore voter turnout data for three gubernatorial general elections before and after the passage of the 19th Amendment. They will interpret the correlation of eligible population vs. percentage of voter turnout using a scatterplot, determine its direction by analyzing the slope and informally determine its strength by analyzing the residuals. Students will draw some conclusions and discuss what a correlation means and how it differs from causation in the context of elections in this integrated lesson.

Type: Lesson Plan

Do Credit Cards Make You Gain Weight? What is Correlation, and How to Distinguish It from Causation:

This lesson introduces the students to the concepts of correlation and causation, and the difference between the two. The main learning objective is to encourage students to think critically about various possible explanations for a correlation, and to evaluate their plausibility, rather than passively taking presented information on faith. To give students the right tools for such analysis, the lesson covers most common reasons behind a correlation, and different possible types of causation.

Type: Lesson Plan

Height vs. Shoe Size:

This resource provides an introductory lesson on Correlation, the Correlation Coefficient, and Correlation vs. Causation. The lesson is structured around collecting data from a survey at the beginning of class to be used in creating scatter plots and analyzing them using technology. Students engage in discussion activities that challenge their thoughts on linked variables in the media.

Type: Lesson Plan

Heart Rate and Exercise: Is there a correlation?:

Students will use supplied heart rate data to determine if heart rate and the amount of time spent exercising each week are correlated. Students will use GeoGebra to create scatter plots and lines of fit for the data and examine the correlation. Students will gather evidence to support or refute statistical statements made about correlation. The lesson provides easy to follow steps for using GeoGebra, a free online application, to generate a correlation coefficient for two given variables.

Type: Lesson Plan

Correlation or Causation: That is the question:

Students will learn how to analyze whether two events/properties demonstrate a correlation or causation or both. They will learn what factors are involved when evaluating whether correlated events demonstrate causation. If two events are claimed to be causal when they are not, they will be able to determine why, and which (if any) causal fallacies are present. At the close of the lesson students will be given situational data and develop a newscast that assumes causation when in fact there is no causal link. Students who are observing will analyze each presentation and determine which (if any) causal fallacy was used (or explain why the newscast is correct in their assumption of causality).

Type: Lesson Plan

Smarter than a Statistician: Correlations and Causation in the Real World!:

Students will learn to distinguish between correlation and causation. They will build their skills by playing two interactive digital games that are included in the lesson. The lesson culminates with a research project that requires students to find and explain the correlation between two real world events.

Type: Lesson Plan

Is Milk Killing People?:

Students will explore correlation and causation from data through class discussions of real-world examples. They will know positive, negative, strong, and weak correlations. Students make predictions regarding the feasibility of causation by analyzing graphs and scatter plots of data.

Students will participate in an experiment where they will generate and analyze their own data. They will come to conclusion regarding variations in data, correlation and causation. Students are encouraged to explain and justify their responses. The teacher will facilitate discussion of leading question to be geared towards the learning objectives.

During the lesson, students will be assessed by several formative assessments and a summative assessment at the conclusion. The lesson includes a worksheet and data collection sheets.

Type: Lesson Plan

Sustainability and Tourism Location MEA:

This MEA gives the students an opportunity to learn about sustainability and then apply that knowledge to help EcoAthletica determine the location for their next sustainable tourism resort. The students will use a variety of criteria and the definition of sustainability and sustainable tourism to create a model for choosing locations.

Type: Lesson Plan

## Perspectives Video: Experts

PTSD: Correlation vs Causation:

Jens Foell discusses the link between correlation and causation in PTSD patients.

Type: Perspectives Video: Expert

The Criminal Brain and Correlation vs. Causation:

Florida State Researcher, Jens Foell, discusses the importance of understanding correlation versus causation when researching personality traits and criminal behavior.

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiast

Correlation and Causation in a Scientific Study:

Watching this video will cause your critical thinking skills to improve. You might also have a great day, but that's just correlation.

Type: Perspectives Video: Professional/Enthusiast

Golf and Divorce:

This is a simple task addressing the distinction between correlation and causation. Students are given information indicating a correlation between two variables, and are asked to reason out whether or not a causation can be inferred.

Coffee and Crime:

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

The Titanic 3:

This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic using a table of data.

## STEM Lessons - Model Eliciting Activity

Sustainability and Tourism Location MEA:

This MEA gives the students an opportunity to learn about sustainability and then apply that knowledge to help EcoAthletica determine the location for their next sustainable tourism resort. The students will use a variety of criteria and the definition of sustainability and sustainable tourism to create a model for choosing locations.

## MFAS Formative Assessments

Does Studying Pay?:

Students are given a scenario describing an association between two variables and are asked to determine if one variable is a cause of the other.

Does the Drug Cause Diabetes?:

Students are given a statement of association between two variables and are asked to determine if one variable is a cause of the other.

Listing All Possible Causal Relationships:

Students are asked to identify all possible causal relationships between two correlated variables.

Students are asked to interpret a correlation coefficient in context and describe a possible causal relationship.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Lesson Plan

Do Credit Cards Make You Gain Weight? What is Correlation, and How to Distinguish It from Causation:

This lesson introduces the students to the concepts of correlation and causation, and the difference between the two. The main learning objective is to encourage students to think critically about various possible explanations for a correlation, and to evaluate their plausibility, rather than passively taking presented information on faith. To give students the right tools for such analysis, the lesson covers most common reasons behind a correlation, and different possible types of causation.

Type: Lesson Plan

## Perspectives Video: Professional/Enthusiast

Correlation and Causation in a Scientific Study:

Watching this video will cause your critical thinking skills to improve. You might also have a great day, but that's just correlation.

Type: Perspectives Video: Professional/Enthusiast

Golf and Divorce:

This is a simple task addressing the distinction between correlation and causation. Students are given information indicating a correlation between two variables, and are asked to reason out whether or not a causation can be inferred.

Coffee and Crime:

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

The Titanic 3:

This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic using a table of data.

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

## Perspectives Video: Professional/Enthusiast

Correlation and Causation in a Scientific Study:

Watching this video will cause your critical thinking skills to improve. You might also have a great day, but that's just correlation.

Type: Perspectives Video: Professional/Enthusiast

Golf and Divorce:

This is a simple task addressing the distinction between correlation and causation. Students are given information indicating a correlation between two variables, and are asked to reason out whether or not a causation can be inferred.