Introduction

For this study, I am interested in exploring the relationship between the intensity levels of exercising and circulating cortisol levels–an indicator of the body’s response to stress. The research question of interest is “do different exercise intensity levels affect the change in salivary cortisol levels, pre- and post-workout, in the Islanders (ages 18-65)?” For this experimental study, the population parameter of interest is the true difference in the long-run mean changes in salivary cortisol levels, before and after working out, between the high intensity (running) and low intensity (yoga) exercise groups. Prior to seeing any of the data, I suspected that the actual parameter value would be different than 0, with the average change in salivary cortisol levels of the high-intensity group being higher than that of the low-intensity group, since differing types of exercises and exercise intensities can have drastically varying physiological effects on humans.

As someone who practices both running and yoga on a weekly basis, I’m interested in what immediate effects these two opposing exercise intensities may have on my body and stress levels. Additionally, I have conducted summer research relating to hormones, taken a biology course on the endocrine system, and plan to pursue a career in medicine as an endocrinologist, and I find this system’s ability to respond to stress and be an overall indicator of our health fascinating. As an often stressed-out college student, the findings from this study may help to guide mine and others’ exercise habits in ways that adapt to both our mental and physiological states (e.g. avoiding exercise that increase cortisol levels and implementing ones that decrease it when I’m already stressed). While the islanders may not have the same cortisol response to exercise as humans do, this study may lead to further questions, which may involve longer study duration, such as the role of differing types of exercise intensity on chronically stressed individuals with consistently high cortisol levels. Results, again, may give insight into exercise’s role in stress management.

The stress response is greatly regulated by the secretion of cortisol from the adrenal glands, which are located on top of the kidneys (Thau et al., 2023). When met with stressors, the body will quickly release epinephrine (or adrenaline) to adaptively enter “fight or flight” mode; a few minutes later, cortisol will enter the bloodstream and cause the release of glucose necessary for maintaining the energy necessary for overcoming the stressful event. To some, exercising may not seem particularly stressful–people even use it to relieve stress–but this exact biological process is stimulated in order to adapt to the physiological stress induced by exercise.

According to a study conducted by E. E. Hill and colleagues, “cortisol levels increase at a rate relatively proportional to the exercise intensity, but reach a final level dependent upon the total duration of an exercise session” (p. 587). High-intensity exercises, such as running, will require an excess of cortisol in order to maintain the physiological capacities necessary for exercise and subsequent recovery. All things considered, the release of cortisol from high-intensity exercise is not always harmful to the body–rather, it is often classified as eustress capable of enhancing many biological processes (Hackney & Walz, 2013). Though, in sedentary individuals and those who already have high circulating cortisol levels, extra cortisol secretion during exercise can be harmful. According to another study conducted by J. Thirthalli and colleagues, while high-intensity exercise may increase cortisol levels, low-intensity exercise has the potential to decrease circulating cortisol levels (2013). While the mechanisms for this phenomenon are still being worked out, it’s suspected that yoga, as well as other mild exercise forms, have the ability to enhance the tone of the parasympathetic nervous system, which counteracts the “fight or flight” response with “rest and digest”. This rest and digest state is coupled with low cortisol levels within the body.

My research question is inspired by these multiple studies because missing from the current literature are studies that combine both low-intensity and high-intensity exercise into the same model. By taking a random sample of 18-65 year old Islanders, the findings from this study may be generalized across all groups on the islands, including people who incorporate exercise into their daily lives and those who suffer from chronic stress. Furthermore, these findings may help to guide stress management techniques and increase the overall health and well-being of the other islanders.

Data Collection Methods

The next step of this project was data collection. The observational units are the 60 islanders who participated in this study. The participants were recruited via a wanted ad posted in the newspaper of each village asking islanders, “are you between the ages of 18 and 65?” in order to isolate volunteers within the adult-aged population of interest. A list of each island’s volunteers was compiled and the villagers were each assigned a unique number. Using a random number generator, 20 islanders from each island (60 total participants) were chosen, at random, to participate in the study. Once the list of 60 participants was finalized, their names were imported into a random grouping generator, and they were randomly assigned into two experimental groups–each with 30 volunteers.

The two experimental groups are the binary categorical variables in question; one group was the “High Intensity (HI)” group and the other was the “Low Intensity (LI)” group. The intensity of exercise experienced by the islanders is also the explanatory variable in this case. The high intensity exercise group was tasked with going for a 30 minute run, and the low-intensity group was assigned to practice yoga for 30 minutes. The response variable, which is a quantitative variable, was the change in salivary cortisol levels of the islander before and after exercising. Prior to beginning the exercise task, a quantitative baseline salivary cortisol level was taken. Another salivary cortisol test was administered 5 minutes after the completion of the exercise activity to compare whether mean cortisol levels increased, decreased, or remained the same after the differing types of exercise. This five minute waiting period allows for any change in hormonal levels in the blood to transfer into the saliva. The post-exercise cortisol level was subtracted from the pre-exercise level in order to obtain the sample statistic of interest. The sex and age of each volunteer was also taken in case other aspects of this research wanted to be studied. Since this experimental protocol was quite involved and somewhat time consuming, trials were run in batches of 10 islanders at a time. Each testing period occurred during midday, between the hours of 11am and 1pm.

While nothing went wrong during the course of the study, an interesting thing to note is that while the average age of participants was 39.6–which is very near to the midpoint between 18 and 65–there was very few participants near 18 years of age. This may have been due to the recruitment method, as 18 year olds are probably less likely to read the newspaper than middle-aged and older people. Although rarely, in some cases, an islander would answer to my add in the newspaper, but they would decline to give consent to be in the study when chosen at random. Each island had around 400 responses to the newspaper adds, so in these cases, a new random number would be generated until a volunteer did consent to be in the study and the volunteers per island reached 20.

Descriptive Statistics

After collecting the data, numerical and visual summaries of it were created. This study looked at one binary categorical explanatory variable and one quantitative response variable. The binary categorical explanatory variable was the exercise intensity level experienced by the islanders; via randomly assigned groupings, participants were tasked with practicing low-intensity (LI) yoga for thirty minutes or high-intensity (HI) running for thirty minutes. The quantitative response variable was the difference in salivary cortisol levels of the participant before and after completing the exercise task. The average difference in cortisol levels for the LI group was -0.004 ug/dL, indicating that, on average, cortisol levels slightly decreased after low intensity exercise. For the HI group, the average difference in cortisol levels was 0.009 ug/dL, indicating that cortisol levels slightly increased after high intensity exercise. As we can see from the box plot below, the LI group’s five-number summary is shifted further left compared to the HI group (i.e. the minimum and maximum are much lower for the LI; -0.074 and 0.037 ug/dL, respectively, compared to -0.049 and 0.069 ug/dL for the HI group). The averages, though, hug zero and are very small in comparison to the overall range of salivary cortisol levels obtained (mostly 0.1-0.3 ug/dL), so we cannot draw conclusions about this data until a theory-based analysis is performed.

library(readr)
Exercise_Data <- read_csv("~/Mini Projects/Sramek - Mini Project Data Collection - Organized Sheet.csv")
head(Exercise_Data, n=2)
data(Exercise_Data)
favstats(Change_in_Salivary_Cortisol ~ Exercise_Intensity, data = Exercise_Data)
bwplot(Exercise_Intensity ~ Change_in_Salivary_Cortisol, 
       horizontal = TRUE, 
       main="Side-by-side boxplots",
       data = Exercise_Data)

histogram(~Change_in_Salivary_Cortisol | Exercise_Intensity, data = Exercise_Data, 
        main="Parallel histograms",
        layout = c(1, 2))

Analysis of Results

In this experimental study, the population of interest is the inhabitants of the Islands ages 18-65, and the parameter of interest is the true difference in the long-run mean changes in salivary cortisol levels, before and after working out, between the high intensity (running) and low intensity (yoga) exercise groups. Additionally, my null hypothesis states that the mean change in salivary cortisol levels for the high intensity exercise group is the same as the mean change in salivary cortisol levels for the low intensity exercise group. My alternative hypothesis was that the mean change in salivary cortisol levels for the high intensity exercise group is greater than the mean change in cortisol levels for the low intensity group.

\[H_0: \mu_{High~Intensity} = \mu_{Low~Intensity} \]

\[H_A: \mu_{High~Intensity} > \mu_{Low~Intensity} \]

It is also important to discuss type I and type II errors, and how they may relate to my experimental study. A type I error may occur where we would find significant evidence that the difference in mean cortisol levels between the low intensity and high intensity exercise groups is different than 0, when it is actually 0. This would lead us to falsely reject our null hypothesis. A type II error would occur in a scenario where we do not find any significant evidence that the true difference in mean cortisol levels between the two experimental groups is different than 0, when it is actually different than 0. In this case, we would falsely fail to reject our null hypothesis.

Regarding whether this study can be representative of the population of interest, I unfortunately do not believe that the presented findings can be generalized for the entire population of Islanders aged 18-65. Initially, I believed that putting an ad in the newspaper would attract a wide variety of participants and that a response rate of about 400 people per island would be representative of the larger population. When looking at the data even closer, though, I noticed that there were very few respondents on the lower end of the age range, even though the observed average age of participants neared the expected average age. This indicates that recruitment via a newspaper ad may not have achieved full representation of the entire Islander population. It seems as if younger people may not read the newspaper to the same degree that middle-aged or older Islanders do. Along with age, it is reasonable to assume that other confounding variables may arise due to the methods of participant recruitment. Another interesting one may be the baseline cortisol levels of newspaper readers–does reading the newspaper daily have any effect on how stressed an individual is? Since random sampling was utilized to choose the final participants from the pool of initial recruits, and random assignment was used to group participants into either low intensity or high intensity exercise groups, we can only generalize these findings to the population of respondents to the newspaper ad.

In my experimental study, the validity conditions for using a theory-based approach to conducting a t-test on the observed data were met. There were 30 participants per experimental group, which exceeds the required 20 observations per group. Additionally, we can see in the parallel histograms of the data that there is some slight left skewness in the low intensity exercise group. The skewness is not strong, though, so this component of the required conditions is also met. Using the theory-based approach, a standardized t-statistic was found to compare the difference between the two means. The standardized t-statistic was found to be 1.59, indicating little to no evidence against the null hypothesis.

#sample sizes
n.LI<- 30
n.HI<- 30

x.bar.LI<- -0.004
x.bar.HI<- 0.00857
  
SD.LI<- 0.0311
SD.HI<- 0.0303
  
# difference between the sample proportions of Low Intensity vs High Intensity
x.bar.diff<-x.bar.HI-x.bar.LI
cat("difference in sample means is",x.bar.diff)
## difference in sample means is 0.01257
SE.x.bar.diff<-sqrt(SD.LI^2/n.LI + SD.HI^2/n.HI)
cat("standard error of the difference in sample means is",round(SE.x.bar.diff,5))
## standard error of the difference in sample means is 0.00793
t.stat<-x.bar.diff/SE.x.bar.diff
cat("standardized statistic t is",round(t.stat,2))
## standardized statistic t is 1.59

The standardized t-statistic was then used to find the one-sided p-value. I am using a one-sided p-value since our alternative hypothesis predicts that the average change in salivary cortisol levels for the high-intensity exercise group will be greater than the average change in salivary cortisol levels for the low-intensity exercise group. We are not only predicting that the values will be different, in which case a 2-sided p-value would have been calculated. The one-sided p-value was found to be 0.059. Since it is above 0.05 but below 0.1, this signifies moderate evidence against the null hypothesis. Even still, it fails to reject the null hypothesis. The p-value of 0.059 is the probability of observing a difference in means of salivary cortisol levels between each of the exercise groups as extreme or greater than 0.0126, assuming that the null hypothesis is true. Since we fail to reject our null hypothesis, we do not have significant evidence that the population’s mean changes in salivary cortisol levels between the low intensity and high intensity exercise groups are different (i.e. the alternative hypothesis is not supported).

p.value<-(pval(t.test(Change_in_Salivary_Cortisol ~ Exercise_Intensity, data = Exercise_Data))/2)
cat("the p-value is", p.value)
## the p-value is 0.0591086

In some cases, it may be necessary to conduct a simulation-based approach for the standardized statistic and p-value. This would ensure that both the simulation-based and the theory-based approaches at calculating the p-value are within agreeance with one another. In this case, though, the validity conditions for conducting a theory-based approach are met, so doing a simulation-based approach or bootstrap is not necessary for this analysis.

Lastly, a 95% confidence interval was found. The confidence interval included values between -0.003 and 0.028, meaning that we are 95% confident that the true difference in the population’s mean changes in salivary cortisol levels between the low intensity and high intensity exercise groups is between -0.003 and 0.028 ug/dL. Since the confidence interval contains the value 0, this means that it is plausible for the two means to actually be the same in which the null hypothesis would be true.

x.bar.diff <- 0.01257

# simulated standard deviation
SE.x.bar.diff <- 0.00793

# margin of error for 95% CI
MoE <- 2 * SE.x.bar.diff

LB<-x.bar.diff - MoE # lower limit of 95% CI
UB<-x.bar.diff + MoE # upper limit of 95% CI
round(cbind(LB,UB),3)
##          LB    UB
## [1,] -0.003 0.028

Both the 95% confidence and the one-sided p-value are in agreeance with one another, so we fail to reject the null hypothesis. In other words, both the p-value and the 95% confidence interval do not provide significant evidence against the null hypothesis that “the mean change in salivary cortisol levels for the high intensity exercise group is the same as the mean change in salivary cortisol levels for the low intensity exercise group.”

Conclusion

Based on the one-sided p-value of 0.059, which is above the significance level of 0.05, and the zero-containing confidence interval of -0.003 to 0.028, we fail to reject our null hypothesis that the mean change in salivary cortisol levels for the high intensity exercise group is equal to the mean change in salivary cortisol levels for the low intensity exercise group. The data from this experimental study does not provide sufficient evidence in support of our alternative hypothesis. The standardized t-statistic of 1.59, which was used to calculate the p-value, is below 2, and therefore, it also provides little to no evidence against our null hypothesis. Regarding my original conjecture, the results of the theory-based analysis do not align with my expectations. Initially, I predicted that the high intensity exercise group would have higher average changes in cortisol levels before and after working out than the low intensity exercise group. This conjecture was based off of literature stating that ““cortisol levels increase at a rate relatively proportional to the exercise intensity” (Hill et al., 2008) and that “while high-intensity exercise may increase cortisol levels, low-intensity exercise has the potential to decrease circulating cortisol levels” (Thirthalli et al., 2013). However, through the theory based analysis, we fail to reject the null hypothesis, which was in opposition of my conjecture.

Because the newspaper ad strategy used to recruit participants may have introduced bias into the sample, the findings from this study can only be generalized among the respondents to the newspaper ad between the ages of 18 and 65. Among the newspaper ad respondents, random sampling and random assignment was utilized. In future studies, I would use completely random sampling so that the findings may be generalized over a larger population. I would also like to collect more observational units, since the data was close to providing significant evidence (our p-value was near 0.05 and the confidence interval lower limit of -0.003 is very close to 0). Additionally, I may look at changing the types of low intensity and high intensity exercises, and I would like to use circulating cortisol levels rather than salivary cortisol levels, as I would like to see if this may provide more accurate results. A further research question that may build upon my results would look into whether similar results are seen in Islanders who suffer from chronic stress. Results from this study may provide evidence for effective stress-management techniques.

Bibliography: references to literature mentioned in the introduction

Hill, E. E., Zack, E., Battagliini, C., Viru, M., Viru, A., & Hackney, A.C. (2008). Exercise and Circulating Cortisol Levels: The Intensity Threshold Effect. Journal of Endocrinology, Vol 31, 587-591. https://link.springer.com/article/10.1007/BF03345606

Hackney, A.C. & Walz, E.A. (2013). Hormonal Adaptation and the Stress of Exercise Training: The Role of Glucocorticoids. Trends in Sports Sciences, vol 20(4), 65-171. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5988244/

Thau, L., Gandhi, J., & Sharma S. (2023). Physiology, Cortisol. StatPearls. https://www.ncbi.nlm.nih.gov/books/NBK538239/

Thirthalli, J., Naveen, G. H., Rao, M. G., Varambally, S., Christopher R., & Gangadhar B. N. (2013). Cortisol and Antidepressant Effects of Yoga. Indian Journal of Psychiatry, 55(Suppl 3), 405–408. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3768222/