Note that the written report should have the style of a research paper. That means that there needs to be a continuing storyline. Do not include the questions, just your answers to them. Do not use bullet points. Have connective narratives between the sentences.

Introduction

Could taking a 10 minute long cold-air exposure at negative 20 degrees Celsius reduce cortisol levels? This is the research question that this project aims to answer via an statistical tests on a population of computer-generated individuals that are created on an application called “The Islands.” The inspiration for this topic comes from pre-existing research on cold-water exposure. According to existing literature, “cold water immersion has been used in an intentional and controlled manner for centuries across multiple disciplines” (Reed et al). Cold water exposure is touted to “relieve stress, bolster the immune system, improve sleep quality, and give rise to calmness” (Lindfors). This has led to people adopting cold-water-plunging techniques into their daily lives, with individuals such as Wim Hof taking the perceived benefits of cold water plunging to extreme limits. However, despite the few individuals who brave the cold waters stating that the plunging has extensive benefits, some studies have sought to quantify just how much cold water plunging helps people with anxiety levels and general health.

One study have suggested that “a single bout of cold water immersion may not serve as a modality to target vascular function, but could be a means to reduce cortisol following immersion and contribute to less negative feelings” (Reed et al). The greatest changes in vascular shear stress occured 30 minutes after the immersion (ibid). Another study targeted how cold water plunging affects mental health, finding that “practice of cold-water immersion was found to be related to better mental health and shorter upper respiratory tract infections compared to control group” (Czarnecki et al).

This research question is inspired by these articles because they each speak about cold water plunging from a different perspective. Lindfors discusses cold water plunges with respect to how humans have historically performed them, Czarnecki et. al. discusses cold water plunges with respect to how they affect anxiety and stress, and Reed et al discusses cold water plunges with respect to how they affect our physical well-being. While the study is measuring cold exposure, not cold plunging (the islanders will be exposed to cold air, as opposed to cold water), the primary interest lies in the concept of cold exposure to understand if being exposed to cold air for 10 minutes will decrease cortisol levels. Thus, the population parameter of interest is that the Islander participants’ cortisol levels will increase or decrease after being exposed to this cold air. The Islanders provide a medium wherein we can study this ethically, and with the opportunity to generalize results to all of the Islanders regardless of age.

Data Collection Methods

The observational units are the 40 islanders whom I collected data from. The variable was measured by taking 20 control samples and 20 non-control samples. I first asked all of them a questionnaire which included questions about their gender, perceived health, anxiety, age, and birthplace. Then, I measured all of the subjects’ cortisol levels and recorded it. I then randomly chose 20 of the 40 islanders to expose to -20 degrees Celsius temperatures for 10 minutes. I waited 45 minutes, and then measured their cortisol levels again, recording them for all subjects, even the control group. In the literature, studies which conducted similar tests but with cold plunges measured cortisol levels 30 minutes post-plunge. Once I retrieved all of the data, I put it into an excel spreadsheet and then took the difference in cortisol levels pre and post cold exposure. This is the value that I am measuring.

Originally, my study was supposed to study cold plunging exposure, but because the Islands do not have that as an option, I pivoted to cold air exposure. Something else which went wrong in my data collection is that one of my participants (in the control group) opted out of my study.

Potential sources of sampling errors could lie in the timing when I took cortisol levels, as I could not take all measurements exactly 45 minutes after they were exposed to the cold temperatures. Furthermore, since there is little research on cold air exposure and cortisol levels, a non-sampling error could surface in the time I took to measure cortisol levels post-exposure

Descriptive Statistics

Considering that this study is focusing on a quantitative response variable (cortisol levels) and a binary response categorical variable (whether the subject was exposed to the cold air), it is most appropriate to portray the data collected in a side-by-side boxplot. The three chunks of code below include the raw data, summary statistics, and the side by side boxplot, with cortisol levels on the x-axis, and group type on the y-axis. A more positive value means that the subject had increased cortisol levels (proportional to increased stress levels) after being exposed to the cold conditions. With a median of 1.35 for the control compared to a median of 0.26 for the treatment, this plot suggests that the central tendency for the treatment group was to generally have lower cortisol levels than the control group post-cold exposure. With this said, neither group is decreasing in cortisol levels at the median. The plot suggests there is a slight association that the treatment group’s cortisol is lowering after the cold exposure when compared to the control group, but we need to find a way to quantify this.

library(readr)
finalproject <-read_csv("~/mini projects/finalproject4 - Sheet1.csv")
head(finalproject, n=2)
favstats(Cortisol ~ type, data = finalproject)
bwplot(type ~ Cortisol, 
       horizontal = TRUE, 
       main="Side-by-side boxplots",
       data = finalproject)

Analysis of Results

To best quantify the relationship between the two groups, we will use a theory-based approach to determine the t-statistic and p-value for statistical significance. Considering the random sampling method used to choose the subjects, the sample population will be the 40 islanders randomly chosen, with a potential to expand results to all of the islanders. The population parameters that I will be looking at are if mu is going to be equal to or not equal to zero. The null hypothesis is: taking a 10 minute long cold exposure at -20 degrees Celsius does not affect cortisol levels. The alternative hypothesis is: taking a 10 minute long cold exposure at -20 degrees Celsius does affect cortisol levels. These are symbolically expressed below. A type I error would be that we reject the null, even if the subject’s cortisol levels are not actually affected by the cold exposure. A type II error would be that we accept the null hypothesis despite the islanders’ cortisol levels actually being affected by the cold exposure. I would say that this study is representative for ages between 13-93 in the Islands, so, for most people on the islands. This is because I have a significant amount of samples, with more than 20 in the control and 20 in the treatment groups, and they were randomly chosen (to the best of my abilities). All in all, we have to remember that the islands are by no means a perfect method and that we should not generalize to a human audience.

null: \[H_0: \mu = 0\] alternative: \[H_A: \mu =/= 0\]

We conduct our theory-based approach first by finding an appropriate test statistic, or a t-test. Validity conditions are satisfied, as we have 20 or more samples for both the treatment and control group. From this test, we get a t-value of 1.632. This shows us that there is not a significant difference between the control and treatment group. To further our significance tests, null distribution for the change in cortisol levels is made. . To get this distribution, we need to calculate the difference in the sample means, which were found above by using the favstats function in R Studio. By taking the mean of the control (1.375) and subtracting it by the mean of our treatment (0.535), we get a difference in means of -0.840. The null distribution is then created from this value, and is shown graphically with a center at 0. This shows us that if we were to complete this study 1000 times on a group that is based purely on chance, then most of our results would have a difference in sample means of 0. If we use this null distribution and compare our actual result of -0.84 to it, we can obtain a p-value. Our reported p-value is 0.119, which is over twice the desired p-value for rejecting the null hypothesis. Thus, we cannot reject the null hypothesis that a 10 minute exposure to -20 degrees Celsius will affect the cortisol levels of the islanders. To understand where our population parameter lies, a 95% confidence interval test was conducted. With a confidence interval between -0.203 and 1.883, we are 95% confident that our population parameter lies between these values. Notice that we include zero in the confidence interval. This further suggests that we cannot reject the null hypothesis, because it lies at zero.

stat(t.test(Cortisol ~ type, data = finalproject))
##        t 
## 1.632802
#sample sizes
n.yes<- 20
n.no<- 20

x.bar.yes<- 0.535
x.bar.no<- 1.375
  
SD.yes<- 1.81
SD.no<-   1.42
  
# difference between the sample proportions of males vs females
x.bar.diff<-x.bar.yes-x.bar.no
cat("difference in sample means is",x.bar.diff)
set.rseed(498) 
cortisol.null <- do(1000) * diffmean(shuffle(Cortisol) ~ type, data = finalproject)
dotPlot(~ diffmean, data = cortisol.null,
        main="Simulated Null Distribution of the difference in sample means",
        xlab="difference in sample means",
        width = 0.01, cex = 1)

p_value<-prop(~(diffmean <= -0.84|diffmean >= 0.84), data = cortisol.null)
cat("two-sided p-value is",p_value)
## two-sided p-value is 0.119
confint(t.test(Cortisol ~ type, data = finalproject))

Conclusion

To conclude, this study sought to investigate the potential impact of a 10-minute exposure to cold air at -20 degrees Celsius on cortisol levels among a population of islanders. With literature inspiration that looked at cold water exposure as opposed to cold air exposure, there was not a set of established rules that this study sought to follow. Rather, it built upon the observations from these other studies. Despite this challenging pivot, we were still able to achieve some interesting statistical analysis. While the data behaved somewhat liked I expected, it did not perform how I expected in the statistical analysis. With the t-test and p-values found, we could not reject the null hypothesis, and thus could not say that cold air exposure results in a decrease in stress levels. I do believe that the data could be generalized to the Islanders due to it meeting the validity conditions of 20 treatment and 20 controls with no strong skew, though I would not generalize it to a human audience. Next time, I would attempt longer periods of time before and after cortisol testing and cold air exposure, as well as cold air exposure at less intense temerpatures. If somebody were to build on my results, I would guide them towards questions of temperature (that is to say, what temperatures provide the more destressing) or questions of preconditioned stress that the subjects may have before being studied.

Bibliography: references to literature mentioned in the introduction

Jan Czarnecki, Katarzyna Nowakowska-Domagała & Łukasz Mokros, Combined cold-water immersion and breathwork may be associated with improved mental health and reduction in the duration of upper respiratory tract infection - a case–control study, International Journal of Circumpolar Health, Volume 83:1, 2024, pages 1-6. 2330741, (10.1080/22423982.2024.2330741)

Emma L. Reed , Christopher L. Chapman , Emma K. Whittman , Talia E. Park , Emily A. Larson , Brendan W. Kaiser, Lindan N. Comrada , Karen Wiedenfeld Needham , John R. Halliwill , Christopher T. Minson, Cardiovascular and mood responses to an acute bout of cold water immersion, Journal of Thermal Biology, Volume 118, 2023, pages 1-11, (https://doi.org/10.1016/j.jtherbio.2023.103727)

Antti Lindfors, Qualia of Stress and Bodily Enregisterment in Ice Swimming, Signs and Society, pages 156-175, (https://doi.org/10.1086/714857).