Introduction

The detrimental effects of smoking on human health, as established by the Centers for Disease Control and Prevention (CDC, 2021), are widely acknowledged. Some scholars also wonder that whether smoking habit can influence IQ level. Lots of studies and literature has been delving into this subject across various demographics. Like Karin Wennerstad’s study on associations between IQ and cigarette smoking among Swedish male twins (Wennerstad,2010) , and other studies like Lawrence Whalley’s research which is across age span (Lawrence, 2005). It prompts a curiosity and inspired me to wonder whether similar pattern also applies to island populations, where the world is encoded and programmed to simulate the real world. This leads to my formulation of the research question: Would Smoking Habit influence the IQ level of islanders? The parameter in this scenario would be the difference in mean IQ level between smokers and non-smokers on the island. I conjecture an overall trends of a slightly lower average IQ level for smoker relative to non-smokers before the investigation.

Data Collection Methods

The observational units for this study were the islanders who participated in the research. Data for smokers and non-smokers was assessed through a self-report survey conducted via both newspaper advertisements in each town and a door-to-door approach on the island. This method was chosen due to its feasibility and accessibility for data collection within the island community. IQ level was quantitatively measured using standardized scales, specifically the Adult Intelligence Scale test administered to participants after completing the smoking status survey. The study was random in race, gender, and age without any control, which there might have been potential confounding variables influencing the results due to the lack of control over these demographic factors. However, possible sampling error may occur from the recruitment method using newspaper advertisements, which could introduced voluntary bias. Repeat visits, numbering between 3 to 4, were necessary to obtain the desired sample size, resulting in approximately 4-5 islanders responding to the newspaper advertisements in each town. This may have influenced the representativeness of the final sample.

Descriptive Statistics

library(readr)
SmokeIQ <- 
  read_csv("~/Documents/Eileen_STAT- Sheet2.csv")
head(SmokeIQ, n=10)

The explanatory variable, smoking status, is a binary categorical variable consisting of two levels: smokers and non-smokers. The response variable, IQ level, is quantitative, which is a standardized measurements.

bwplot(IQ ~ Smoker, 
       horizontal = FALSE, 
       main="Side-by-side boxplots",
       data = SmokeIQ)

From the side-by-side boxplot, the interquartile range (the length of the box) seems to be slightly wider for non-smokers compared to smokers, and a slightly larger range shows a slightly larger standard deviation for non-smokers. Non-smokers has a smaller median IQ level but a higher mean value compared to the smokers. The similar mean mean IQ levels between non-smokers and smokers suggest no immediate association, further analysis is necessary to confirm this observation.

data(SmokeIQ)
favstats(IQ ~ Smoker, data = SmokeIQ)

Analysis of Results

The population in this context refers to all individuals residing on the island who could potentially participate in the study. There are two distinct populations of interest: non-smokers and smokers. The parameters being investigated are the difference in mean IQ level for non-smokers and smokers. The null hypothesis posits that there is no difference in the mean IQ level between smokers and non-smokers among the islanders. \[H_0: \mu_{smoker} - \mu_{non-smoker} = 0\] The alternative hypothesis posits that there is a difference in the mean IQ level between smokers and non-smokers among the islanders.\[H_A: \mu_{smoker} - \mu_{non-smoker} \neq 0\]

In this case, a Type I error would occur if we incorrectly reject the null hypothesis when it is actually true, concluding that there is a significant difference in mean IQ levels between non-smokers and smokers when there isn’t one. On the other side, Type II error would occur if we fail to reject the null hypothesis when it is actually false, failing to detect a significant difference in mean IQ levels between non-smokers and smokers when there is one.

The sampling method utilizing newspaper ads for recruitment, introduces potential bias as certain segments of the population may be more inclined to respond to such ads, thus not yielding a purely random sample. This compromises the representativeness of the sample as it may not accurately capture the diversity of the population. However, the sample size is deemed adequate for providing reliable estimates of population parameters to some extent, suggesting that while the sample may not be perfectly representative, it still offers valuable insights into the population of interest. Therefore, while the measurements may not be entirely representative, they do provide valuable information, though with some limitations.

histogram(~IQ | Smoker, data = SmokeIQ, width = 6, layout = c(1, 2))

stat(t.test(IQ ~ Smoker, data = SmokeIQ))
##         t 
## 0.1583888

The t-statistics result of 0.158 indicates that the difference in mean IQ levels between non-smokers and smokers is not statistically significant. This suggests that there is insufficient evidence to reject the null hypothesis, which posits that there is no significant difference in mean IQ levels between the two groups. Additionally, the validity condition is met as there are 35 units for each group, and the histogram suggests that the data is not strongly skewed, further supporting the reliability of the t-test results.

two.sided.p.value<-pval(t.test(IQ ~ Smoker, data = SmokeIQ))
cat("the two-sided p-value is",two.sided.p.value)
## the two-sided p-value is 0.8746228

Furthermore, the two-sided p-value of 0.875 indicates that the probability of observing a difference in mean IQ levels between non-smokers and smokers as extreme as the one observed in the sample, assuming that there is truly no difference in the population, is approximately 87.5%. While it is below the significance level of 0.05, we fail to reject the null hypothesis.

The t-statistics and p-value suggests that there is no significant difference in mean IQ levels between non-smokers and smokers on the island.

library(pairwiseCI)
pairwiseCI(IQ ~ Smoker, data = SmokeIQ, method="Param.diff")
##   
## 95 %-confidence intervals 
##  Method:  Difference of means assuming Normal distribution, allowing unequal variances 
##   
##   
##        estimate lower upper
## YES-NO     -0.6 -8.16  6.96
##   
##

Last but not least, with a pairwiseCI test by R code, we obtain a 95% confidence interval of (-8,16, 6,96). Thus, we are 95% confident that the difference in mean IQ level between smokers and non-smokers on the island is between -8.16 and 6.96. This shows a possibility that the true difference in means between the two groups is zero, which suggest no difference in mean, which leads to the conlcusion that no sufficient evidence to conclude a statistically significant difference between the two groups. This is consistent with the outcomes get from t-statistics and p-value.

Conclusion

My study aimed to investigate the potential association between smoking status and IQ levels among islanders. Analysis of the data revealed that there was no significant difference in mean IQ levels between non-smokers and smokers on the island, as evidenced by a two-sided p-value of 0.875 and a t-test of 0.158. This suggests that the observed difference in mean IQ levels between the two groups could have occurred by chance alone, assuming that there is truly no difference in the population.

After the analysis and reflection, I learned and noticed that the findings are limited by several factors and suggest some potential improvements. The sample size of 35 units for each group was deemed sufficient, and the histogram of the data suggested that it was not strongly skewed. However, the sampling method, relying on newspaper ads for recruitment, introduced potential bias, as certain segments of the population may be more inclined to respond to such ads. Additionally, the lack of control over demographic factors such as race, gender, and age, as well as potential confounding variables, may have influenced the results. The use of self-report surveys for determining smoking status also introduced subjectivity and the possibility of voluntary bias.

To improve the study design in the future, I would recommend to increase the sample size and employ more rigorous data collection methods. Combining recruitment strategies, such as random digit dialing or door-to-door surveys, could enhance the representativeness of the sample. Furthermore, incorporating verification methods for smoking status, such as involving family members or health institutions, could reduce subjectivity and bias in the data. Controlling for demographic factors and categorizing smokers based on their smoking habits could also provide more nuanced insights into the association between smoking and IQ levels. In this way, it may reduce the bias and potentially lead to a more representative sample of the entire population.

In future studies, researchers may choose to investigate similar questions while building on these results by exploring additional factors that could influence IQ levels. It’s crucial to emphasize that not only this study, but any similar research, can only be generalized to the specific population under investigation (in this case, the islanders).

Bibliography: references to literature mentioned in the introduction

“Health Effects of Cigarette Smoking.” Centers for Disease Control and Prevention, 29 Oct. 2021, (www.cdc.gov/tobacco/data_statistics/fact_sheets/health_effects/effects_cig_smoking/index.htm#:~:text=Top%20of%20Page-,Smoking%20and%20Increased%20Health%20Risks,%2C%20stroke%2C%20and%20lung%20cancer.&text=Estimates%20show%20smoking%20increases%20the,by%202%20to%204%20times&text=For%20stroke%20by%202%20to%204%20times)

Karin Modig Wennerstad, et al., Associations between IQ and cigarette smoking among Swedish male twins, Social Science & Medicine, Volume 70, Issue 4, 2010, Pages 575-581, ISSN 0277-9536, (https://doi.org/10.1016/j.socscimed.2009.10.050.)

Lawrence J. Whalley, et al., Childhood IQ, smoking, and cognitive change from age 11 to 64 years, Addictive Behaviors, Volume 30, Issue 1, 2005, Pages 77-88, ISSN 0306-4603, (https://doi.org/10.1016/j.addbeh.2004.04.014.)