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Chapter 4: Problem 2

Explain what is meant by a lurking variable. Provide an example.

Short Answer

Expert verified
A lurking variable is an unconsidered variable that affects the relationship between studied variables. For example, temperature is a lurking variable influencing both ice cream sales and drowning incidents.

Step by step solution

01

Define a Lurking Variable

A lurking variable, also known as a confounding variable, is an unseen or unconsidered variable that might influence the relationship between the variables being studied. It can cause a false perception of a relationship or mask the true relationship.
02

Understand the Effects

A lurking variable can make it appear that there is a direct cause-and-effect relationship between the variables being studied, even if there is none. Alternatively, it can obscure the true relationship between studied variables by adding an additional layer of complexity.
03

Recognize Lurking Variables in Analysis

In statistical analysis, it's crucial to identify and control for lurking variables to avoid misinterpretation of the results. This often involves carefully designing experiments or studies to minimize the impact of these confounding factors.
04

Provide an Example with Explanation

Suppose we observe that ice cream sales and drowning incidents both increase during summer. At first glance, it might seem like ice cream sales directly affect drowning incidents. However, the lurking variable here is the temperature. Hot weather both increases ice cream sales and encourages people to swim, leading to more drowning incidents.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Confounding Variable
A confounding variable is an outside influence that can distort the results of an experiment or study. It is different from the independent and dependent variables directly observed. Confounding variables can cause misleading conclusions by either hiding the true relationship or making one appear where none exists. For example, in a study examining the link between coffee consumption and heart disease, stress could be a confounding variable. Both stress and coffee consumption might contribute to heart disease, giving a false impression of a direct connection between coffee intake and heart disease.
Statistical Analysis
Statistical analysis is the process of collecting and interpreting data to test hypotheses and infer relationships between variables. It involves different techniques to summarize, visualize, and determine patterns in the data.
猞� Descriptive statistics: Mean, median, mode, and standard deviation help summarize the data.
猞� Inferential statistics: Methods like t-tests, chi-square tests, and regression analysis help draw conclusions about the population based on sample data.
Effective statistical analysis requires awareness of potential confounding variables. Techniques such as randomization, stratification, and statistical controls can help account for these variables, ensuring more accurate results.
Experiment Design
Experiment design is crucial in any scientific study. It involves structuring experiments to test hypotheses while minimizing bias and errors. Proper design helps identify and control for lurking variables, which can affect the outcomes.
猞� Randomization: Assigning subjects randomly to different groups ensures that confounding variables are evenly distributed.
猞� Control Groups: Having a control group helps isolate the effects of the independent variable on the dependent variable.
猞� Blinding: Single or double-blind studies prevent bias by ensuring that neither the participants nor the researchers know who belongs to which group during the experiment. These strategies help produce more reliable and valid results, leading to a better understanding of the relationships between the studied variables.

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Most popular questions from this chapter

Lyme Disease versus Drownings Lyme disease is an inflammatory disease that results in skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning deaths for a rural county in the United States. $$\begin{array}{lllllllllllll} \text { Month } & \mathbf{J} & \mathbf{F} & \mathbf{M} & \mathbf{A} & \mathbf{M} & \mathbf{J} & \mathbf{J} & \mathbf{A} & \mathbf{S} & \mathbf{O} & \mathbf{N} & \mathbf{D} \\ \hline \text { Cases of } & & & & & & & & & \\ \text { Lyme Disease } & 3 & 2 & 2 & 4 & 5 & 15 & 22 & 13 & 6 & 5 & 4 & 1 \\ \hline \text { Drowning } & & & & & & & & & & & & \\ \text { Deaths } & 0 & 1 & 2 & 1 & 2 & 9 & 16 & 5 & 3 & 3 & 1 & 0 \end{array}$$ (a) Draw a scatter diagram of the data using cases of Lyme disease as the explanatory variable. (b) Compute the correlation coefficient for the data. (c) Based on your results from parts (a) and (b), what type of relation appears to exist between the number of reported cases of Lyme disease and drowning deaths? Do you believe that an increase in cases of Lyme disease causes an increase in drowning deaths?

For each of the following statements, explain whether you think the variables will have positive correlation, negative correlation, or no correlation. Support your opinion. (a) Number of children in the household under the age of 3 and expenditures on diapers (b) Interest rates on car loans and number of cars sold (c) Number of hours per week on the treadmill and cholesterol level (d) Price of a Big Mac and number of McDonald's french fries sold in a week (c) Shoe size and IQ

(a) Draw a scatter diagram treating \(x\) as the explanatory variable and \(y\) as the response variable. (b) Select two points from the scatter diagram and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on the scatter diagram. (d) Determine the least-squares regression line. (e) Graph the least-squares regression line on the scatter diagram. (f) Compute the sum of the squared residuals for the line found in part (b). (g) Compute the sum of the squared residuals for the least-squares regression line found in part (d). (h) Comment on the fit of the line found in part (b) versus the least-squares regression line found in part (d). $$\begin{array}{l|ccccc}x & 5 & 10 & 15 & 20 & 25 \\\\\hline y & 2 & 4 & 7 & 11 & 18\end{array}$$

Describe the difference between univariate and bivariate data.

For the data set $$\begin{array}{cccccc}x & 2 & 4 & 8 & 8 & 9 \\\\\hline y & 1.4 & 1.8 & 2.1 & 2.3 & 2.6\end{array}$$ (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between \(x\) and \(y\). (b) Given \(\bar{x}=6.2, s_{x}=3.03315, \bar{y}=2.04,\) that \(s_{y}=0.461519,\) and \(r=0.957241,\) determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a).
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