Introduction

Can 30 minutes of yoga a day help reduce tension levels for the Islanders? The parameter of interest for this study is the difference in proportions of tension level improvement between Islanders that do 30 minutes of yoga a day and Islanders that do not do 30 minutes of yoga a day.

Previous research has suggested that yoga may be beneficial for anxiety and tension. “Stress is an important triggering factor for tension headache. Yoga is one of the effective therapies in reducing stress levels. Studies had shown that shavasana is as effective as electromyography (EMG) biofeedback in reduction of tension headache”(Menon et al., 2013, p.1). This inspired me to use the POMS scale for anxiety-tension because it helped me recognize that yoga has physical and mental affects which could help reduce mental tension and physical tension. Many other related studies have also been done. “A systematic literature review was conducted to identify articles that assess the effect of yoga and yoga-related interventions on stress reduction in nonclinical populations. Studies were classified according to the length of the intervention, yoga type, and measures of outcome”(Wang et al., 2020, p.1). This inspired me because its about non-clinical affects of yoga on stress reduction. Using the islands supports answering this questions like this really well. I personally chose this reaserch question because I took a yoga class this semester and I feel that it has helped my anxiety and tension levels decrease.

From this previous research, I suspect that the proportion of tension level improvement will be higher for Islanders who do yoga.

Data Collection Methods

The observational units in this study are the Islanders that are 12-95. There were twelve Islanders randomly sampled from each Island using a random number generator. The Islanders were then randomly assigned into two groups, one group did yoga for 30 minutes a day and the other group had no treatment for one week. The measured variable was the tension-anxiety Profile of Mood States scale, which is determined by asking the Islanders three questions about their tension, anxiety, and restlessness. The Islanders produce a coded response from 0-4 for each question, which was averaged for each Islander. All of the Islanders were asked these questions at the beginning and end of the study which then produced the final variable of interest which was whether or not each Islanders tension levels improved over the course of the week.

Descriptive Statistics

Two categorical variables were used over the course of this study. The explanatory variable was whether or not the Islander did 30 minutes of yoga a day, and the response variable was whether or not the Islanders tensions levels decreased over a week. As you can see in the two way table and mosaic plot, there seems to be no association between the two variables.

library(readr)
Final_Data<- 
  read_csv("/Users/ianwalsh/Downloads/Stats project - Sheet1.csv")
tally(Treatment ~ Improvement, data=Final_Data)
##               Improvement
## Treatment      Improvement No Improvement
##   No Treatment           9              9
##   Treatment              8             10
library(vcd)
mosaic(Treatment ~ Improvement, data = Final_Data, direction = "v")

Analysis of Results

The population of this study are the Islanders 12-95, so any conclusions from this data can only be generalized to the Islanders in this age range. The parameter of interest is the difference in proportions of tension level improvement in Islanders who do 30 minutes of yoga a day and islanders who do not do 30 minutes of yoga a day.

The null hypothesis states that there is no difference between tension level improvement in Islanders who do 30 minutes of yoga a day and islanders who do not do 30 minutes of yoga a day; \(H_0: \pi_{control}=\pi_{yoga}\). The alternative hypothesis states that the proportion of improvement in Islanders who do 30 minutes of yoga a day is higher than islanders who do not do 30 minutes of yoga a day; \(H_a: \pi_{control}<\pi_{yoga}\).

In this study, Type I error would lead us to conclude that 30 minutes of yoga a day does increase tension improvement levels when it in fact does not, and Type II error would lead us to conclude that 30 minutes of yoga a day does not increase tension improvement levels when it in fact does.

The measurements in this study can reasonably be considered a representative sample because the study utilized random sampling and it is large enough. The validity conditions for a theory based z-test were not met for this study, which is at least 10 entries for each part of the two way table, but they were close enough to reasonably do the theory based test. The value of the standardized statistic in this study is z = -0.318

set.seed(1856)
treatment.null <-do(500) * diffprop(shuffle(Treatment) ~ Improvement, success = "Treatment",
data = Final_Data)
head(treatment.null, 2)
round(favstats(~diffprop, data = treatment.null)[c("mean","sd")],3)
diffprop=-0.056
z<-diffprop/0.176
z
## [1] -0.3181818

The p-value for this study is 0.734, and it represents the probability of observing a difference in proportions of -0.056 or larger assuming \(H_0\) is true. The standarized statistic and p-value of this study lead me to fail to reject the null hypothesis. Therefore, doing 30 minutes of yoga a day does not increase tension improvement levels for the islanders.

p.value<-prop(~ (diffprop >= -0.056), data = treatment.null)
p.value
## prop_TRUE 
##     0.734

Since the validity conditions are not met, I will also conduct a simulation based p-value test for this study. The p-values for the simulation and the theory based test are very similar which is reasonable because the validity conditions were almost met.

set.seed(1856)
final.null <- do(1000) * diffprop(shuffle(Treatment) ~ Improvement, data = Final_Data)
head(final.null, 2)
dotPlot(~ diffprop, data = final.null, groups = (diffprop >= -0.056),
        width = 1/15, cex = 5)

I am 95% confident that the difference in proportions of tension level improvement between Islanders that do 30 minutes of yoga a day and Islanders that do not do 30 minutes of yoga a day is between -0.438 and 0.327. Since this interval contains zero, there is no evidence against the null hypothesis which is consistent with all of the other tests.

prop(~(diffprop >= -0.056), data = final.null)
## prop_TRUE 
##     0.736
confint(prop.test(Treatment ~ Improvement, success="Treatment", data = Final_Data))

Conclusion

From this study, we can conclude that there is no evidence against \(H_0\) which means that there is no correlation between practicing yoga for 30 minutes a day and tension levels. This data did not behave as expected, however, that does not surprise me because it was collected from the Islands which cannot possibly simulate all human research topics accurately. I am only comfortable generalizing this data to the Islanders aged 12-95 because my sample was random. If I were to do this study again, I would restrict my population further to include only Islanders 18-65 and I would make sure I tested tension levels on the same weekday and time to avoid confounding variables. Another similar question I may ask in the future is if there is any immediate relief from tension symptoms after a 30 minute yoga session.

Bibliography:

Menon, Bindu, Vungarala Satyanand, and P. Karishma. “Effects of yoga on tension headache.” Journal of Dr. NTR University of Health Sciences 2, no. 3 (2013): 167. Gale Academic OneFile (accessed March 6, 2024). https://link-gale-com.ezproxy.whitman.edu/apps/doc/A349642608/AONE?u=whitman&sid=bookmark-AONE&xid=5ef2ceb4.

Wang, Feifei, M.Sc, and Szabo, Attila,PhD., D.Sc. 2020. “Effects of yoga on stress among healthy adults: A systematic review”. Alternative Therapies in Health and Medicine 26, (4) (Jul): 58-64, http://ezproxy.whitman.edu/login?url=https://www.proquest.com/scholarly-journals/effects-yoga-on-stress-among-healthy-adults/docview/2442969434/se-2 (accessed March 6, 2024).