library(readr)
Final_Data<- 
  read_csv("~/StatswApps/Final/Final - Sheet1 (1).csv")
head(Final_Data,n=2)

Introduction

In this study, I looked at the following research question: Does taking a 250mg supplement of magnesium help improve tension symptoms in adults from the ages of 18 to 65? I used two binary categorical variables, treatment vs no treatment and improvement vs no improvement to record the difference in proportions of the amount of improvement between the treatment and no treatment groups.

Anxiety is a very common issue that many researchers have been testing to try and find ways to reduce anxiety symptoms in todays adults. As presented by Boyle et al in his review, The Effects of Magnesium Supplementation on Subjective Anxiety and Stress—A Systematic Review, “Anxiety related conditions are the most common affective disorders present in the general population with a lifetime prevalence of over 15%.” (1) Boyle claims that based on the 18 valid studies that him and his group analyzed, there is a correlation between magnesium and lessening anxiety symptoms. However, he does state that this needs to be studied more in depth to guarantee this statement for all people. Rukat states a similar claim in their review titled, The Relationship Between Magnesium Deficiency and Anxiety, the Therapeutic Effects of Magnesium Supplementation – Literature Review. They claim that “Evidence of a link between magnesium levels and anxiety has led to increased interest in the potential efficacy of magnesium supplementation to alleviate anxiety symptoms.” (2) Again, they stress that there seems to be a correlation yet this needs to be studied more.

My research is inspired by my own experience having anxiety. I have always wondered if there was a natural way to reduce my tension symptoms, and have been pointed towards magnesium in the past. This research further peaked my interest in this topic because there seems to be an obvious correlation that we may be able to see in the Islands. Obviously, the Islands is not an exact study and is not to be used for actual medical advice, but I am curious as to its effects on the Islanders and to see if the Islanders trends match those of current research.

Data Collection Methods

The observational units of this study were the Islanders on the Islands. The variables in this study are two binary categoricals: Treatment vs Control and Improvement vs No Improvement. I took 54 volunteers total, with 6 islanders from 3 towns on each of the 3 islands. To split the treatment vs control group, 3 random islanders from each town will be doing the 250mg Magnesium treatment and 3 random islanders from each town will take a placebo sugar pill. To measure their levels of tension, I will ask the participants each of the following questions: “How anxious are you feeling?”, “How restless are you feeling?”, and “How tense are you feeling?”. From the Islands guide, their responses include feeling “not at all” (coded as 0), feeling “a little” (coded as 1), “moderately” (coded as 2), “quite a bit” (coded as 3) and “extremely” (coded as 4). Based on their response, they will recieve a score from 0-4 for each question which will be summed to give their final score for the day out of 12. I will record these scores in a spread sheet and then once the study is over, I will change the quantitative variable to a categorical variable of either improvement or no improvement for each islander. The only thing that went wrong during my study was that two of my participants dropped out of the study, so my total participants for my treatment group was 27 and my total participants for my control group was 25.

Descriptive Statistics

As we can see in the two-way table, there is a pretty even distribution between each cell, indicating little to no association between the variables. The mosaic plot also displays this, with very little association being shown.

tally(Treatment ~ Improvement, data=Final_Data)
##            Improvement
## Treatment   IMPROVEMENT NONE
##   Control            11   14
##   Treatment          13   14
library(vcd)
mosaic(Treatment ~ Improvement, data = Final_Data, direction = "v")

Analysis of Results

The population is adults on the islands from ages 18-65. The parameter is then the difference in proportions of improvement of individuals in the treatment group and the no treatment group. For my study, the null hypothesis is that there is no difference in the proportions of improvement between the two groups, represented in symbols as \(H_0: \pi_{control}=\pi_{treatment}\). The alternative hypothesis is that there is a larger proportion of improvement for the treatment group than the control group, represented in symbols as \(H_a: \pi_{control}<\pi_{treatment}\).

When doing analysis, it is important to consider possible errors. In this situation, a Type I error would look like concluding based on my significance tests that magnesium treatment does cause improvement in tension levels when it actually does not. A Type II error would look like concluding based on my significance tests that there was no correlation between improvement and magnesium treatment but there actually was.

As stated in the data collection methods section, this study used volunteers that were randomly assigned which means that it can be used as a representative sample for all islanders of ages 18-65. However, since this is a simulation, I am only comfortable generalizing this to all adult Islanders, and not real humans given that is not who we were sampling from.

As shown in the two-way table, there are 10 observations in each part of the table which meets the validity conditions for a theory-based test for a difference in two proportions. For a difference of two proportions, I used a z-statistic as the standardized statistic for analysis which resulted in a value of \(z=0.28\):

tally(Treatment ~ Improvement, data = Final_Data, format = "prop")
##            Improvement
## Treatment   IMPROVEMENT      NONE
##   Control     0.4583333 0.5000000
##   Treatment   0.5416667 0.5000000
-diffprop(Treatment ~ Improvement, success = "Treatment", data = Final_Data)
##   diffprop 
## 0.04166667
set.seed(4786)
treatment.null <-do(500) * diffprop(shuffle(Treatment) ~ Improvement, success = "Treatment",
data = Final_Data)
head(treatment.null, 2)
diffprop=0.04
z<-diffprop/0.142
z
## [1] 0.2816901

The following displays a simulated Dot Plot given our with values higher than the observed difference in proportions highlighted in yellow:

dotPlot(~ diffprop, data = treatment.null,
groups = (diffprop >= 0.04),
width = 0.0001, cex = 2)

As shown below, the p-value was \(0.304\), which tells us the probability observing a difference in improvement proportions of 0.04 or higher assuming the null hypothesis is true. This p-value is extremely high which provides little to no evidence against the null hypothesis and therefore fail to reject the null hypothesis.

p.value<-prop(~ (diffprop >= 0.04), data = treatment.null)
p.value
## prop_TRUE 
##     0.304

Based on the p-value and the standardized statistic, there is little to no evidence against the null hypothesis, therefore concluding that magnesium does not improve tension symptoms in adults on the Islands.

The confidence interval for this study is as follows:

confint(prop.test(Treatment ~ Improvement, success="Treatment", data = Final_Data))

From \(-0.268\) to \(0.35\) which are the plausible values of our population parameter. This interval indicates that we are 95% confident that the true mean difference is between -0.269 to 0.35. This interval does include 0, and is quite centered on 0 which means that the null hypothesis is very plausible which agrees with the conclusion drawn from the p-value and the standardized statistic.

Conclusion

Based on the p-value, the standardized statistic and the confidence interval, I can confidently say that there is little to no evidence against the null hypothesis, therefore concluding that magnesium does not improve tension symptoms in adults on the Islands. This data did not behave the way I thought it would, based on the research that inspired this study. Both of the articles I used in my initial research concluded that there should be a correlation between magnesium treatment and alleviated anxiety symptoms such as tension (1)(2). However, we did not see this result at all. Based on the conclusion that magnesium does not have an impact on tension and the previous evidence which indicated that it does, this puts into question if the Islands are an accurate representation of real life mental health scenarios. Given that mental health is something that is still not very well understood in the real world, I wonder if the Islands are an adequate tool to test relationships between activities/supplements and mental health. This result can be generalized to the Islanders, but again, I would not be comfortable generalizing these results to real life individuals given the conflicting results between this study and real life results with similar studies. In the future, I would love to look into mental health on the Islands more in depth by testing the islanders mental health after doing an assortment of activities to see if there is change that is compatible with real life data.

Bibliography: references to literature mentioned in the introduction

  1. Boyle, Neil Bernard, Clare Lawton, and Louise Dye. 2017. “The Effects of Magnesium Supplementation on Subjective Anxiety and Stress—A Systematic Review” Nutrients 9, no. 5: 429. https://doi.org/10.3390/nu9050429

  2. Rukat, Mateusz, Kinga Przyborowska, Justyna Kwiecień, Beata Getka, Katarzyna Wiejak, and Michał Łata. 2024. “The Relationship Between Magnesium Deficiency and Anxiety, the Therapeutic Effects of Magnesium Supplementation – Literature Review”. Journal of Education, Health and Sport 53 (January):91-101. https://doi.org/10.12775/JEHS.2024.53.007.