Skip to main content
Ch. 2 - Exploring Data with Tables and Graphs
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
Chapter 2, Problem 2.4.2

Causation A study has shown that there is a correlation between body weight and blood pressure. Higher body weights are associated with higher blood pressure levels. Can we conclude that gaining weight is a cause of increased blood pressure?

Verified step by step guidance
1
Understand the concept of correlation: Correlation measures the strength and direction of a linear relationship between two variables. It does not imply causation. A positive correlation between body weight and blood pressure means that as body weight increases, blood pressure tends to increase as well, but this does not necessarily mean one causes the other.
Consider the principle of causation: Causation implies that changes in one variable directly result in changes in another. To establish causation, additional evidence is required beyond correlation, such as controlled experiments or longitudinal studies that rule out confounding variables.
Identify potential confounding variables: Confounding variables are factors that might influence both body weight and blood pressure, such as diet, physical activity, genetics, or underlying health conditions. These variables could explain the observed correlation without a direct causal relationship.
Evaluate the study design: Check whether the study used methods like randomized controlled trials or statistical techniques to control for confounding variables. If the study only reports correlation without addressing confounding factors, causation cannot be concluded.
Conclude based on evidence: Without further evidence from experimental or longitudinal studies that control for confounding variables, we cannot conclude that gaining weight is a direct cause of increased blood pressure. Correlation alone is insufficient to establish causation.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Correlation vs. Causation

Correlation refers to a statistical relationship between two variables, indicating that they tend to change together. However, this does not imply that one variable causes the other. Understanding this distinction is crucial, as it helps prevent misinterpretation of data, particularly in studies where external factors may influence both variables.
Recommended video:
Guided course
06:36
Scatterplots & Intro to Correlation

Confounding Variables

Confounding variables are external factors that may affect both the independent and dependent variables in a study, potentially leading to misleading conclusions. In the context of body weight and blood pressure, factors such as diet, exercise, and genetics could confound the relationship, making it essential to control for these variables to establish a true causal link.
Recommended video:
Guided course
07:09
Intro to Random Variables & Probability Distributions

Statistical Significance

Statistical significance assesses whether the observed relationship between variables is likely due to chance. In studies examining causation, researchers often use p-values to determine significance. A low p-value suggests that the correlation observed is unlikely to be random, but it does not confirm causation without further investigation into the underlying mechanisms.
Recommended video:
Guided course
05:53
Parameters vs. Statistics
Related Practice
Textbook Question

In Exercises 15 and 16, construct the frequency polygons.

Presidents Use the frequency distribution from Exercise 14 in Section 2-1 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?

151
views
Textbook Question

In Exercises 5–8, identify the class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. The frequency distributions are based on real data from Appendix B.

476
views
Textbook Question

In Exercises 9–12, using a loose interpretation of the criteria for determining whether a frequency distribution is approximately a normal distribution, determine whether the given frequency distribution is approximately a normal distribution. Give a brief explanation.

Blood Platelet Counts of Females Refer to the frequency distribution from Exercise 8

125
views
Textbook Question

In Exercises 5–8, answer the questions by referring to the following Minitab-generated histogram, which depicts the weights (grams) of all quarters listed in Data Set 40 “Coin Weights” in Appendix B. (Grams are actually units of mass and the values shown on the horizontal scale are rounded.)

Class Width and Class Limits Give the approximate values of the class width, and the lower and upper class limits of the class depicted in the bar farthest to the left.

229
views
Textbook Question

In Exercises 25 and 26, construct the cumulative frequency distribution that corresponds to the frequency distribution in the exercise indicated.


Exercise 5 (Age of Best Actress When Oscar Was Won)

202
views
Textbook Question

In Exercises 5–8, answer the questions by referring to the following Minitab-generated histogram, which depicts the weights (grams) of all quarters listed in Data Set 40 “Coin Weights” in Appendix B. (Grams are actually units of mass and the values shown on the horizontal scale are rounded.)


Relative Frequency Histogram How would the shape of the histogram change if the vertical scale uses relative frequencies expressed in percentages instead of the actual frequency counts as shown here?

182
views