Introduction

The purpose of this study was to see whether people who live on the islands can have their systolic blood pressured lowered by listening to classical music. To understand this we wanted to figure out what happened to individuals blood pressures after listening to classical music so we compared pre and post classical music blood pressure measurements. The current literature indicates that there is statisticaly signifcance between listening to classical music and lowering of blood pressure. (Cyrus, et al., 2022) studied adults where they played classical music for 90 seconds and measured blood pressure. This study showed statistical signifcance of p-value of under 0.05 indicating the effects of classical music on adults. (Bekiroglu, et al., 2013) study was conducted on elderly hypertensive patients and shows similar results. (Saing, et al., 2016) study also showed statistical significance of the lowering effect of classial music on blood pressure but this study focused specifcally on children. These three studies give good evidence that this trend can be seen for people of all ages.

Since the islanders are not real people and we do not know how in depth the algorithsm are that make up the simulation, we suspected that actual parameter would be lower (there would be a small or no existant change in blood presssure) then what has been observed in real studies.

Data Collection Methods

The observational units in this study are individual residence of the Islands who participated. Blood pressure was measured before and after 10 minutes of music and sitting. Both the control group and the test group sat for 10 minutes between blood pressure checks to maintain that consistency between the two groups; but only the test group actually listened to classical music during that 10 minutes. Then we compared the blood pressure from before and after and looked to see if their had been a decrease. We measured 2 binary categorical variables. The explanatory variable was whether or not subjects listened to classical music or not and the response variable was whether blood pressure decreased or not. Samples were collected by randomly going to different cities on the islands and then scrolling randomly and clicking on houses randomly and then choosing random people from each house to be in the study. There was a total of 40 participants in the study, 20 in the control and 20 in the treatment group. One issue that we ran into was that young children were not able to listen to music so they could not be included in the study.

Descriptive Statistics

Numerical and visual summaries that are appropriate for your data.

For two categorical variables in your data set, describe them, and include a two-way table, and discuss any relevant proportions. Does there appear to be an association between the two variables?

library(readr)
Exploration_2_3_Data_Collection <- 
  read_csv("~/miniproject3 - blood pressure.csv")
data(miniproject3)
head(Exploration_2_3_Data_Collection, n=2)
tally(Decrease ~ Music, data = Exploration_2_3_Data_Collection, format = "count", margin = TRUE)
##           Music
## Decrease   no yes
##   decrease  7  16
##   no       13   4
##   Total    20  20
tally(Decrease ~ Music, data = Exploration_2_3_Data_Collection, format = "prop")
##           Music
## Decrease     no  yes
##   decrease 0.35 0.80
##   no       0.65 0.20
-diffprop(Decrease ~ Music, success = "decrease", data = Exploration_2_3_Data_Collection)
## diffprop 
##    -0.45
# creating a 5000 repetitions of shuffles
set.seed(4786)
Blood.null <-do(5000) * diffprop(shuffle(Decrease) ~ Music, success = "decrease",
data = Exploration_2_3_Data_Collection)
head(Blood.null, 2)
# Creating the null distribution of the difference in proportions
dotPlot(~ diffprop,
        data = Blood.null,
        width = 0.0001,
        cex = 2)

# Finding the p-value in the null distribution of the difference in proportions
dotPlot(~ diffprop, data = Blood.null,
groups = (diffprop <= -0.45 | diffprop >= 0.45),
width = 0.0001, cex = 2)

round(favstats(~diffprop, data = Blood.null)[c("mean","sd")],3)
#Calculating the p-value
p.value<-prop(~(diffprop <= -0.45 |diffprop >= 0.45), data = Blood.null)
p.value
## prop_TRUE 
##    0.0118
diffprop=-0.45 
z<-diffprop/0.161
z
## [1] -2.795031
confint(prop.test(Decrease ~ Music, success="decrease", data = Exploration_2_3_Data_Collection))
bargraph(~Music, groups = Decrease, data = Exploration_2_3_Data_Collection, auto.key = TRUE, stack = TRUE)

Here on the stacked bar plot blue represents number of subjects who’s heart rate decreased. On the right we have the treatment group and on the left we have the control group who just sat but did not listen to music. With this bar plot we can see that there is a difference in the amounts of decreases in blood pressure between the two groups. 80% of treatment group experienced decrease blood pressure while only 35% of control groups blood pressure decreased. This indicates that there is an association between classical music and decreased blood pressure in the data

The population is the islanders and the parameter is the different in change in blood pressure between those who listen to music versus those who didn’t.

The null hypothesis of this study states that there is no difference in change in blood pressure between those who sat and listened to classical music for 10 minutes and those who just sat for 10 minutes. \[H_0: \pi_{music} = \pi_{nomusic}\]

The alternative hypothesis of this study states that blood pressure decreased more in those who sat and listened to classical music for 10 minutes over those who just sat for 10 minutes \[H_A: \pi_{music} > \pi_{nomusic}\]

If there is not enough data, we could see a type 1 error where a trend that shows that there was a difference between those who listened to music vs those who didn’t and then reject the null even tho it was just due to not enough data. A type 2 error would occur if we failed to reject the null hypothesis but there was actually a good reason to due so in the population but we did not see this trend in the data. Possibly because we did not do a good enough of a random sample or something.

Although I tried my best when sampling to do it randomly, I did not use a specific random sampling method so there definitely could be bias from my sampling method. I also did not get an even number of samples from each city and each island. Because of these factors I wouldn’t want to generalize this study past the group that participated.

The Z - Statistic for this study was calculated as 2.795031. We have a somewhat random sample but not a truly randomized method for sample. The distribution of the null hypothesis is approximately normal and there are greater then 10 participants in both the control and treatment group which is good. The P - Value for this study is equal to 0.0118 which is a very small value. This value means that the probability of getting the observed statistic under the null hypothesis is 0.0118 which is very low and leads us to reject the null hypothesis in favor of the alternative one.

I also calculated the 95% confidence interval which indicates what range of difference in proportions there might be in the population. The range is ((0.1271846, 0.7728154)) and does not include zero. Zero is the null hypothesized value, so since we are 95% confident that the population proportion does not fall within the null hypothesis range we are given more reason to reject the null hypothesis.

Conclusion

Based on the data that we see, the results are significant and we can see that listening to classical music can have an effect in lowering blood pressure for the islanders. The p-value and confidence interval both indicate we should reject the null hypothesis in favor of this alternative conclusion. Surprises: We were surprised that we were actually able to reject the null hypothesis since this is based on a simulation of the islands. One main point that should be made about this research is that we did not actually quantify the amount of decrease in blood pressure for each individual. If blood pressure went down we counted it as a success and if it didn’t we counted it as a failure but we did not compare the level of change between successes and failures. A further question to ask would be about whether these changes in blood pressure are a significant change or not. Does the music have an important level of influence that could affect how someone feels or improve someones health?

Cyrus, D., Riley, J., Dadabhoy, D. P., Amir, D., & Garetto, J. (2022). The effect of classical music on heart rate, blood pressure, and mood. Cureus, 14(7) doi:https://doi.org/10.7759/cureus.27348

Bekiroglu, T., Ovayolu, N., Ergün, Y., & Ekerbiçer, H. Ç. (2013). Effect of turkish classical music on blood pressure: A randomized controlled trial in hypertensive elderly patients. Complementary Therapies in Medicine, 21(3), 147-54. doi:https://doi.org/10.1016/j.ctim.2013.03.005

Saing, S. K., Rina, O., Ramayati, R., & Rusdidjas, R. (2016). Effect of classical music on reducing blood pressure in children. Paediatrica Indonesiana, 48(3), 142–146. https://doi.org/10.14238/pi48.3.2008.142-6