Introduction
My research question is: How can engaging in low-intensity exercise outside affect mood (in terms of depression level), and would these mood effects visible after only exercising once?
The population parameter I am using is the difference between the two proportions, which are the change in depression level of those who exercised vs. the change in depression level of those who did not exercise. This population proportion should be 0, under the null hypothesis that both proportions (for the exercise group and no exercise/control group) are the same, so the difference between them would be 0.
Mini Literature Review
I read three different papers about the effects of exercise on mood when I was designing my study. I also used them to formulate a hypothesis to test through my study based on the results they described.
A review article I read (Callaghan, 2004) inspired me to think about exercise as a potential therapy for mental health, not just as something that can boost your mood when you’re having a bad day. However, I would still like to further extend this with participants who do not necessarily have a mental health condition to see if they would still be able to benefit. In this review article Callaghan referenced several studies that saw decreased depression levels after exercise among participants and positive associations between exercise and mental health and well-being in general.
One of the research papers I read (Keating et al., 2018) inspired me to consider focusing my study on people who have mental health conditions, but I decided to further extend this to include people without mental health conditions to see if exercise can help improve their mood as well, also including people who don’t exercise at all during the study (as a control group), some of which may have mental health conditions and some of which don’t. The authors of this paper reported seeing a significant decrease in depressive symptoms among the participants from the beginning to the end of the study, so I hoped to see the same in my study, even if the participants in my study had not been diagnosed with depression.
Another research paper (Jimenez et al., 2021) inspired me to have the walk that I would have my participants go on be outside to enhance the mood benefits of the exercise. The authors of this paper found that walking in nature had many benefits, including leading to mood improvements.
Based on these articles I read, I suspected that the actual parameter would be different in that those who exercised would not experience an increase in their depression levels resulting from exercising, while the depression levels of those who didn’t exercise would be more likely to increase than that of those who did exercise.
Data Collection Methods
The observational units were the 57 participants in my study, not including one participant that withdrew after completing the first survey. I found these participants by visiting various towns scattered around each island, trying to recruit a diverse and representative group of people, but I did not do random sampling when selecting these participants.
I measured the response variable by asking participants to fill out a survey at the very beginning of the study and then having participants do exercise (going on a relaxing walk outside for 30 minutes) if they were in the exercise group and finally fill out the same survey again to see how their moods changed after exercising (but participants in the control condition just filled out the survey again at the same time as the exercise group but after not exercising), based on their responses to the survey. In the survey I asked participants how depressed they felt at the time of survey completion on a scale from 1 to 10. I wanted to see if the walk would lead to decreases in ratings for depression levels. I chose depression levels as the mood I would measure out of many that I could have chosen, so it would be interesting to do this kind of study again but with levels of other moods being measured instead of depression. As long as participants are showing signs of decreased depression, I am still counting that as a sign of improved mood, even if it isn’t necessarily an increase in happiness.
Thankfully nothing went wrong with this study. Each participant responded to the first survey, so the response rate was 100%. However, one participant withdrew from my study when I was about to ask my participants in the experimental condition to go on a walk. As a result, I had to eliminate that participant from my study and not use the data I collected based on his response to the first survey. Everyone else remained and completed the exercise and second survey. With everyone except for the participant who withdrew responding to my second survey, my response rate for the second survey was 98.28%.
No sampling errors (aside from probably having too small of a sample size) were made, but I didn’t do random sampling when I selected my participants because I was trying to recruit participants from a variety of ages and locations (I selected participants from several towns from each island) and also trying to keep the sex ratio even to avoid having my results be confounded by these factors. I realize now that I still should have done random sampling so that my results could be more generalizable, but I did randomly assign participants to groups. The randomness would probably also eliminate these confounding factors, but in a better way since it would allow my results to be more generalizable. It is also better as a research practice in general to always do random sampling whenever possible. Since I realize that not doing random sampling can compromise the generalizability and representativeness of my results, if I were to do this again I would do random sampling, even if that might not result in as even of a distribution of ages and genders.
Descriptive Statistics for Two Categorical Variables
My explanatory variable is whether or not my participants took a relaxing walk outside for 30 minutes (the exercise group) or did not (the control group), while my response variable is whether the participants’ depression level increased or not based on their responses to the second survey I asked them to fill out. A “success” in this case is no increase in depression level following exercise, with more participants experiencing this in the exercise group than the control group because this would show that exercise can have a positive influence on mood overall, on average, in terms of depression levels.
The proportion of those who exercised and did not experience an increase in their depression level was 14/28, while the proportion of those who did not exercise and also did not experience an increase in their depression level was 15/29 (Table 1). Given how similar these two proportions are, there is unlikely to be an association between these variables and the null hypothesis is plausible.
Table 1. Two-way table of results comparing depression level changes in those who did vs. did not exercise.
| Exercised | Did not exercise | Total | |
|---|---|---|---|
| Depression level did not increase | 14 | 15 | 29 |
| Depression level increased | 14 | 14 | 28 |
| Total | 28 | 29 | 57 |
Analysis of Results
The population my sample represents is all Islanders since I selected participants from a wide age range (from 6 to 106) and all over each island and also equally represented males and females. However, since I did not do random sampling, my sample may not necessarily be representative of the population. Random sampling would lead to a more representative sample.
My population parameter is a difference in proportions. More specifically in the context of my study, it is the difference between the change in depression levels after exercise (going on a relaxing walk for 30 minutes outside) vs. after no exercise.
My null hypothesis in symbols is: \(H_0: \pi_{exercise} = \pi_{control}\), while my null hypothesis in words is that there is no association between exercise and depression level, so the two explanatory variable groups are the same and so are their proportions.
My alternative hypothesis in symbols is: \(H_A: \pi_{exercise} < \pi_{control}\), while my alternative hypothesis in words is that there is an association between exercise and depression level, so the two explanatory variable groups are not the same and neither are their proportions. The exercise group has a smaller proportion than the control group that did not exercise because depression levels would mostly either stay the same or decrease after exercise (rather than increase), resulting in a smaller average proportion than after no exercise, where depression levels may be more likely to increase.
A type I error in this case would be a “false positive” (meaning that a false association between variables was made) and occur if I concluded that I can reject the null hypothesis (that there was no association between exercise and depression level) when the null hypothesis is actually plausible, while a type II error would be a “false negative” (meaning that a real association was missed) and occur if I concluded that the null hypothesis is plausible when it is actually not plausible.
My measurements cannot reasonably be considered a representative sample of the population because I did not do random sampling, even though I tried to be representative through my sampling method because a random sample still tends to be the most representative and lead to the most generalizable results.
Theory-based Approach
The appropriate (theory-based) standardized statistic for the difference of two proportions for two categorical variables is the z-statistic. There are more than 10 observations in each of the cells, so the validity condition for this theory-based test has been met and this would be an appropriate test for me to use for my data.
library(readr)
Exercise_Mood_Data <- read_csv("~/MATH-247/Exercise + Mood Data.csv")
head(Exercise_Mood_Data, n=2)#sample sizes
n.exercise<- 28
n.control<- 29
# counts
noincreasedep.exercise<- 14
noincreasedep.control<- 15
#sample proportions
p.hat.exercise <- noincreasedep.exercise/n.exercise
p.hat.control <- noincreasedep.control/n.control
# difference between the sample proportions
p.hat.diff<-p.hat.exercise-p.hat.control
cat("The difference in sample proportions is",p.hat.diff)## The difference in sample proportions is -0.01724138#pooled proportion (total successes/combined sample size)
p.hat.pooled<- (noincreasedep.exercise+noincreasedep.control)/(n.exercise + n.control)
# Standard error of the theoretical sampling distribution based on a pooled proportion
SE.diff.null<-sqrt((p.hat.pooled*(1-p.hat.pooled))/n.exercise
+ (p.hat.pooled*(1-p.hat.pooled))/n.control)
# Standardized statistic, z
z <- p.hat.diff/SE.diff.null
cat("The standardized statistic z is",round(z,2))## The standardized statistic z is -0.13\(\hat{p} = -0.01724138, z = -0.13\)
p.value<-pnorm(-0.13, 0, 1)
p.value## [1] 0.4482832According to the p-value of 0.4482832, the probability of observing -0.01724138 as the difference in proportions assuming the null hypothesis is true is 0.4482832. This means that, under the null hypothesis, the likelihood that this (or a larger difference) would be the difference between the proportion of people who exercised and experienced no increase in their depression levels and those who did not exercise and experienced no increase in their depression levels is 0.4482832. This very high p-value would lead me to fail to reject the null hypothesis because this shows that exercise and mood are not associated because results like mine could be observed under the null hypothesis ~44.83% of the time.
The alternative hypothesis that exercise and depression level are associated and that exercise can improve mood is not plausible because there is little difference between the groups, based on the p-value. Instead, the null hypothesis that there is no association between exercise and depression level is plausible and I have very weak evidence against it, so I fail to reject it.
The validity conditions for a theory-based test were satisfied because all of the cells of the two-way table had at least 10 observations, so my theory-based and simulation-based values should be similar to each other and lead me to the same conclusion. However, I am doing a simulation-based analysis anyway for comparison to test the validity and reliability of my results that came from the theory-based approach.
Simulation-based Approach
set.seed(2875)
Exercise_Mood_Data.null <-do(5000) * diffprop(shuffle(Exercise_Mood_Data$'Inc/Not inc Depression level')
~ Exercise, success = "Not increased", data = Exercise_Mood_Data)
head(Exercise_Mood_Data.null, 2)p.value<-prop(~(diffprop < -0.01724138 | diffprop > 0.01724138), data = Exercise_Mood_Data.null)
p.value## prop_TRUE
## 0.7922My simulation-based p-value is 0.7922. This is a much larger value than my theory-based p-value of 0.4482832, but the conclusion I can make from each is the same since both p-values are large, meaning that I fail to reject the null hypothesis.
Confidence Interval
# simulated standard deviation
SE <- sd(~ diffprop, data = Exercise_Mood_Data.null)
cat("The standard deviation is ",SE)## The standard deviation is 0.1325685# margin of error for 95% CI
MoE <- 2 * SE
#MoE
LB<-p.hat.diff - MoE # lower limit of 95% CI
UB<-p.hat.diff + MoE # upper limit of 95% CI
cat("The 95% confidence interval for the difference in population proportions is ",
round(cbind(LB,UB),2))## The 95% confidence interval for the difference in population proportions is -0.28 0.25My 95% confidence interval is (-0.28, 0.25). This means that I am 95% confident that the difference in population proportions between those who exercise and those who don’t for a change in depression levels is between -0.28 and 0.25. This interval includes 0, which means that I have very little evidence against the null and fail to reject it. This is the same conclusion that I came to in 5d.
Conclusion
I had no significant results (there were no significant differences between the change in depression levels exercise and no exercise groups) and my original predictions were not reflected in my results. My data did not behave how I expected it to because, based on past studies that I reviewed (Callaghan, 2004; Keating et al., 2018; Jimenez et al., 2021), I had expected that there would be a difference between the exercise and control groups in terms of how their depression levels changed. More specifically, I had expected that the exercise group would experience, on average, a larger decrease in depression levels than the control group, but that is not what I found. Instead, the two groups were almost identical in terms of the results.
I learned several things through this project, such as how to apply what I have been learning in this class to my own research project as well as practice and build general good research practices. However, I should have done random sampling instead of trying to choose participants so that my sample would be what I thought was representative because that limited the generalizability and validity of my results. A larger sample size also would have been better and more representative. Something I learned more specifically from the results of my project is that the Islanders are not the best participants to use for research if you want to get realistic results and conduct studies not on real people but get results that could mimic what we would get if we studied real people. This is because aside from the Islanders not being real people, they seem to have randomized responses/values for many questions we might want to ask them, so if you want to determine whether or not there is a relationship between two variables this can make it seem like there is no relationship even though there may be in reality. Myself as well as most of the other students in the class were unable to get significant results despite previous research backing up our alternative hypotheses.
Someone who may choose to build on my results may use a larger sample size and do random sampling and may also test this over a longer period to see if maybe the effects of exercise are more long-term. The effects may not be able to be seen after just one round of exercise but instead after people practice regular exercise over a longer period of time. Testing this would also make the control results a better comparison and allow for larger differences between the groups since after doing nothing in particular that could affect depression levels in the control group and only exercising once in the exercise group it makes sense that there is not a large difference in depression level changes between the groups. It may also be interesting to test with different negative moods/feelings other than depression levels or test with positive ones to see if certain moods/feelings can be more affected. They could also choose to compare the means rather than difference in proportions or measure depression (or other mood/feeling) decrease or not rather than increase or not or choose to include individuals whose depression (or other mood/feeling) level stayed the same in a third group. Doing this may lead to more meaningful and clear results since the way I did it in this study groups the people who experienced no change in their depression level into the same category as those who experienced a decrease in their depression level. Because of this, you can’t tell by looking at my results how many people actually experienced a decrease in their depression level vs. just didn’t experience any change in their depression level. I set up my results this way for simplicity, but this change would reduce some ambiguity.
Bibliography
P. Callaghan, Exercise: a neglected intervention in mental health care?, Journal of Psychiatric and Mental Health Nursing, Volume 11, Issue 4, 2004, Pages 476-483, (https://onlinelibrary.wiley.com/doi/10.1111/j.1365-2850.2004.00751.x)
Laura E Keating, Suzanna Becker, Katie McCabe, Jeff Whattam, Laura Garrick, Roberto B Sassi, Benicio N Frey, and Margaret C McKinnon, Effects of a 12-week running programme in youth and adults with complex mood disorders, BMJ Open Sport & Exercise Medicine, Volume 4, Issue 1, 2018, Pages 1-7, (https://doi.org/10.1136/bmjsem-2017-000314)
Marcia P. Jimenez, Nicole V. DeVille, Elise G. Elliott, Jessica E. Schiff, Grete E. Wilt, Jaime E. Hart, and Peter James, Associations between Nature Exposure and Health: A Review of the Evidence, Volume 18, Issue 9, 2021, (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8125471/)