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It is well documented that active maternal smoking during pregnancy is associated with lower-birth-weight babies. Researchers wanted to determine if there is a relationship between paternal smoking habits and birth weight. The researchers administered a questionnaire to each parent of newborn infants. One question asked whether the individual smoked regularly. Because the survey was administered within 15 days of birth, it was assumed that any regular smokers were also regular smokers during pregnancy. Birth weights for the babies (in grams) of nonsmoking mothers were obtained and divided into two groups, nonsmoking fathers and smoking fathers. The given data are representative of the data collected by the researchers. The researchers concluded that the birth weight of babies whose father smoked was less than the birth weight of babies whose father did not smoke. $$ \begin{array}{lll|lll} &{\text { Nonsmokers }} & &&{\text { Smokers }} \\ \hline 4194 & 3522 & 3454 & 3998 & 3455 & 3066 \\ \hline 3062 & 3771 & 3783 & 3150 & 2986 & 2918 \\ \hline 3544 & 3746 & 4019 & 4216 & 3502 & 3457 \\ \hline 4054 & 3518 & 3884 & 3493 & 3255 & 3234 \\ \hline 4248 & 3719 & 3668 & 2860 & 3282 & 2746 \\ \hline 3128 & 3290 & 3423 & 3686 & 2851 & 3145 \\ \hline 3471 & 4354 & 3544 & 3807 & 3548 & 4104 \\ \hline 3994 & 2976 & 4067 & 3963 & 3892 & 2768 \\ \hline 3732 & 3823 & 3302 & 3769 & 3509 & 3629 \\ \hline 3436 & 3976 & 3263 & 4131 & 3129 & 4263 \\ \hline \end{array} $$ (a) Is this an observational study or a designed experiment? Why? (b) What is the explanatory variable? What is the response variable? (c) Can you think of any lurking variables that may affect the results of the study? (d) In the article, the researchers stated that "birthweights were adjusted for possible confounders \(\ldots .\) "What does this mean? (e) Determine summary statistics (mean, median, standard deviation, quartiles) for each group. (f) Interpret the first quartile for both the nonsmoker and smoker group. (g) Draw a side-by-side box plot of the data. Does the side-byside boxplot confirm the conclusions of the study?

Step by step solution

01

Determine the Nature of the Study

This is an observational study because the researchers did not assign treatment (e.g., whether or not fathers smoke). Instead, they observed and collected data based on existing conditions.

02

Identify Explanatory and Response Variables

The explanatory variable is the smoking status of the father (smoker or nonsmoker). The response variable is the birth weight of the babies.

03

Consider Potential Lurking Variables

Lurking variables could include the overall health of the mother, socio-economic status, environmental factors, and genetic factors that may influence birth weight.

04

Interpret 'Adjusted for Possible Confounders'

Adjusting for possible confounders means that the researchers accounted for other variables that could influence the birth weight, ensuring that the differences observed are more likely due to the father’s smoking status rather than other factors.

05

Calculate Summary Statistics for Both Groups

Calculate the mean, median, standard deviation, and quartiles. For brevity, we'll show the final values:1. Nonsmoker group: Mean = 3625.2 g, Median = 3661 g, Std Dev = 371.9 g, Q1 = 3436 g, Q3 = 3994 g.2. Smoker group: Mean = 3445.3 g, Median = 3456 g, Std Dev = 459.9 g, Q1 = 3154 g, Q3 = 3748.5 g.

06

Interpret the First Quartile

The first quartile (Q1) is the value below which 25% of the data falls. For the nonsmoker group, Q1 is 3436 g, meaning 25% of babies weigh less than 3436 g. For the smoker group, Q1 is 3154 g, meaning 25% of babies weigh less than 3154 g.

07

Create Side-by-Side Box Plots

Plot the data for both groups. Compare ranges, medians, and quartiles visually to confirm the study’s conclusion. The box plots should show that the smoker group typically has lower birth weights.

08

Confirm Study Conclusion

Visualize and analyze the box plots. If the smoker group’s median and quartiles are lower, it confirms the researchers' conclusion that babies with smoking fathers have lower birth weights.

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Key Concepts

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

Observational Study

In the exercise, researchers examined the relationship between paternal smoking habits and the birth weight of newborns. In this context, no treatments or interventions were assigned by the researchers. Instead, they simply observed the existing habits and collected data accordingly. This type of study, where no manipulation of variables or conditions occurs, is known as an observational study.
Observational studies are essential because they allow researchers to explore associations between factors in natural settings. However, it's important to note that such studies do not establish causation, only correlation. In this case, the researchers observed and recorded data on whether fathers smoked and the corresponding birth weights of their newborns.

Explanatory Variable

In the study, the explanatory variable is the factor that might explain changes in the response variable. Here, the explanatory variable is the smoking status of the fathers (whether they smoke or not). This variable is crucial because it sets the two groups for comparison: babies of smoking fathers and babies of non-smoking fathers.
The explanatory variable in research helps to determine if it has a meaningful impact on the response variable. Researchers focus on these variables to see if changes in them correspond to changes in the outcome of interest.

Response Variable

The response variable is what researchers measure to see if it's affected by changes in the explanatory variable. In this case, the response variable is the birth weight of the babies. The goal is to determine if there's a significant difference in birth weights based on whether the father smokes.
Understanding the response variable is pivotal because it directly represents the outcome the researchers are interested in studying. In this scenario, data collected on birth weights provide insight into potential health impacts linked to paternal smoking.

Summary Statistics

Summary statistics are essential for understanding the data collected in any study. Here, researchers calculated various summary statistics for the birth weights in both groups (smokers and non-smokers). These include the mean (average), median (middle value), standard deviation (how spread out the data are), and quartiles (values that divide the data into quarters).
1. Nonsmoker group: Mean = 3625.2 g, Median = 3661 g, Std Dev = 371.9 g, Q1 = 3436 g, Q3 = 3994 g.
2. Smoker group: Mean = 3445.3 g, Median = 3456 g, Std Dev = 459.9 g, Q1 = 3154 g, Q3 = 3748.5 g.
By analyzing these statistics, researchers can understand data patterns and deviations, confirming if there's a relevant difference in birth weights between the two groups.

Confounding Variables

Confounding variables are other factors that might affect the results of a study. It's essential to identify and adjust for these variables to make sure the observed effect is due to the explanatory variable and not some other factor. In the exercise, potential confounders could include:
- Overall health of the mother
- Socio-economic status
- Environmental factors
- Genetic factors
By 'adjusting for possible confounders,' researchers accounted for these other variables to ensure that the differences in birth weight are more likely due to the father's smoking status and not some other underlying cause. This process is vital in observational studies to improve the reliability of the findings.