Math 247 Final Project Report

Introduction

For my research project I wanted to determine if there is a relationship between consumption of caffeine and improvement of 100m sprint times. The population parameter is the difference in proportions of students who’s sprint times improved with consumption of caffeine compared to without consumption of caffeine. Before running any tests or looking at data I predict that the proportion of students who consumed caffeine and improved their times will be greater than the proportion who did not consume caffeine and improve their times.

During this project I found three studies to draw inspiration from. The first discusses the effects of acute caffeine supplementation on repeated-sprint ability in healthy young non-athletes. The second one is about the effects of caffeine on athletic agility, and the third demonstrates the effects of caffeine on prolonged intermittent-sprint ability in team-sport athletes. More information about each of these studies is listed below.

Effects of Acute Caffeine Supplementation on Repeated-Sprint Ability in Healthy Young Non-Athletes

This study looked at the effects of 200 mg of caffeine during sprint running. It looked at heart rate (HR), perceived exertion (RPE), blood lactate (BLa) concentration, and sprint time (ST). I thought that this study could be good inspiration for my project because it used the same amount of caffeine, looked at sprint time, and the population for this study is healthy young Non-Athletes. My population is university student islanders which includes both athletes, non athletes, men and women. Many other studies that looked at caffeine and sprinting looked specifically at male athletes, so I was interested in this study because it included people similar to my population.

Belbis, Michael D., et al. “The Effects of Acute Caffeine Supplementation on Repeated-Sprint Ability in Healthy Young Non-Athletes.” International Journal of Exercise Science, vol. 15, no. 2, 2022, pp. 846–60. (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9362885/)

The Effects of Caffeine on Athletic Agility

This study looked to determine whether an acute caffeine dose would enhance agility and anaerobic power. This is good inspiration for my study because the sample is men, aged 21-28 which is similar to the age range of my population of university students. It also makes use of placebo pills which is something I also used for my study.

LORINO, ANDREW J., et al. “THE EFFECTS OF CAFFEINE ON ATHLETIC AGILITY.” Journal of Strength and Conditioning Research, vol. 20, no. 4, 2006, pp. 851–54, (https://doi.org/10.1519/00124278-200611000-00021.)

Effects of Caffeine on Prolonged Intermittent-Sprint Ability in Team-Sport Athletes

This study looked at the effects of acute caffeine ingestion on prolonged intermittent-sprint performance. I thought that this could be good inspiration for my study because it found a very significant correlation between the variables. My study is examining slightly different variables but this was interesting to compare it to because it was similar and found strong correlation.

Schneiker, KT, et al. “Effects of Caffeine on Prolonged Intermittent-Sprint Ability in Team-Sport Athletes.” Medicine and Science in Sports and Exercise, vol. 38, no. 3, 2006, pp. 578–85, (https://doi.org/10.1249/01.mss.0000188449.18968.62.)

Data Collection Methods

Random Sampling and Assignment:

The observational units are student islanders from Hofn university, University Of Arcadia, and Colmar University. I collected my sample by first randomly generating a number between 1-3 to determine which university the person should come from. Each of the universities had 11 departments for students to study so I generated a number between 1-11 to determine which department the person should come from. Finally I counted how many students were studying in that department in that university and randomly generated a corresponding number to pick who was going to be in my study. I then repeated this process 60 times to get a sample of 60. I then generated a number between 1 and 2 for each islander in my sample. If it landed on 2, the islander would receive a placebo pill instead of a caffeine pill and was in the control group. If it generated a student who declined to participate or was already chosen I restarted the sample generation process to get another.

100m without caffeine:

Once I collected my sample I was ready to begin collecting data. At around 6:00pm I had the first 30 islanders run 100m without caffeine or a placebo pill. I then recorded the amount of time it took them to complete it. Another day at around 6:00pm I had the second group of 30 islanders perform the same task.

100m with caffeine / placebo pill:

At around 6:00pm the next day I gave the first 30 islanders in my sample 200mg of caffeine pills or 2 placebo pills then waited 20 minutes before having them run 100m again and recorded the new times. I intentionally waited 24 hours before having them perform the second part of this test to ensure that fatigue from the original run would not affect the caffeinated run. I also intentionally waited 20 minutes after having the islanders take the pills to allow time for the caffeine to properly work. I had the second group of 30 islanders perform this part of the experiment the day after they performed the first part.

My sample:

My sample has 60 students from Hofn university, Colmar University, and University Of Arcadia. There are 32 students in the caffeine group and 28 in the placebo group.

Set backs:

Initially, I had a sample of 30 but did not have enough data to meet the validity conditions for a theory based test. To combat this problem I ran the same procedure again to collect double the amount of data and in doing so was able to meet the conditions.

Descriptive Statistics

The first variable is if the student is caffeinated or not (Explanatory, categorical). This variable is easily measured in the islanders because I had control over giving them caffeine pills or placebo pills. The other variable is if the 100 meter sprint times improved after consuming caffeine (Response, categorical). This variable was slightly more difficult to measure in the islanders because I needed them to do multiple sprinting tests. One test without caffeine or a placebo pill, and the other with caffeine or a placebo pill.

For this study I altered the quantitative sprint times into a categorical variable. I did this by defining the categories as if the time got faster that is a success and if it got slower that is a failure. For this study I did not use a proxy variable. The population parameter is the difference in proportions of students who’s sprint times improved with consumption of caffeine compared to without consumption of caffeine. The two way table shows that the proportion of students who improved with caffeine is 22/32. The proportion of students who improved without caffeine is 14/28. When looking at these proportions it does appear that there might be an association between the variables.

	Caffeinated	Not caffeinated
Sprint time improved	22	14
Sprint time did not improve	10	14
Total	32	28

library(readr)
Caffeine.sprint<- read_csv("~/Islander CSV - Sheet1.csv")
head(Caffeine.sprint, n=2)

mosaicplot(Caffiene~SuccessFail, data = Caffeine.sprint)

Analysis of Results

Population and Parameter: The population is university students from Hofn University, University Of Arcadia, and Colmar University. The population parameter is the difference in proportions of students who’s sprint times improved with consumption of caffeine compared to without consumption of caffeine.

Null and Alternative Hypothesis: The null hypothesis is that the proportion of people whose sprint times improved with caffeine is equal to the proportion of people whose sprint times improved with no caffeine.The alternative hypothesis is that the proportion of people whose sprint times improved with caffeine is greater than the proportion of people whose sprint times improved with no caffeine.

The null hypothesis is \(H_0: \pi_{\text{Caffeine}}- \pi_{\text{No caffeine}} = 0\) The alternative hypothesis is \(H_a:\pi_{\text{caffeine}} - \pi_{\text{No caffeine}} > 0\)

Type I and II errors: A type I error would be if we decided that the proportion of students who’s sprint times improved with the addition of caffeine was not greater than the proportion of people whose sprint time improved with no caffeine, when it actually is greater. A type II error would be if we determine that the proportion of students who’s sprint times improved with the addition of caffeine was greater than the proportion of people whose sprint time improved with no caffeine, when it is actually not greater.

Representative sample: My measurements can reasonably be considered a representative sample because I used a subset of my population that reflects the characteristics of the entire population. Most importantly I used random assignment which helps eliminate confounding variables and helps justify that it is a representative sample.

Theory-Based Approach:

The standardized statistic is 1.520587. The validity conditions are that each group have at least 10 successes and failures. The theory based p-value is 0.0641818. This theory-based p-value represents the probability of observing a z-score as extreme or more extreme than the one calculated, assuming the null hypothesis is true. My conclusion is that the theory based p-value of 0.0641818 is larger than the level of significance of 0.05 meaning that we fail to reject the null hypothesis. The null hypothesis states that the proportion of people whose sprint times improved with caffeine is equal to the proportion of people whose sprint time improved with no caffeine.

round(tally(SuccessFail~Caffiene, data = Caffeine.sprint, format = "prop"),2) # conditional prop

##            Caffiene
## SuccessFail   No  Yes
##      Fail   0.50 0.31
##      Sucess 0.50 0.69

round(-diffprop(SuccessFail~Caffiene, data = Caffeine.sprint),2)

## diffprop 
##     0.19

Did not receive caffeine 14/28 = 0.50 Did receive caffeine 22/32 = 0.69 Statistic of interest: 0.69 - 0.50= 0.19

sd <- sqrt((0.69*(1-0.69))/32 + (0.50 * (1-0.50))/28)
z<-(0.19 - 0)/sd
z

## [1] 1.520587

# Given z-score
z <- (0.19 - 0) / sd

# One-sided p-value for z-score
p_value <- pnorm(z, lower.tail = FALSE)

# Print or use the p-value as needed
print(p_value)

## [1] 0.0641818

Simulation Approach:

The simulation based p-value is 0.067 and the theory based p-value is 0.0641818. Both of these values are above 0.05 which leads us to the same conclusion that we fail to reject the null.

set.seed(4577) 
Caffeine.null <- do(1000) * diffprop(shuffle(SuccessFail)~Caffiene, data = Caffeine.sprint)
head(Caffeine.null, 2)

dotPlot(~ diffprop, data = Caffeine.null, groups = (diffprop >= 0.19), width = 1/15, cex = 5)

prop(~(diffprop >= 0.19), data = Caffeine.null)

## prop_TRUE 
##     0.067

Confidence interval:

The 95% confidence interval for the difference in population proportions has a lower bound of -0.08 and an upper bound of 0.45. We are 95% confident that the true difference in proportions of students whose sprint times improved with the addition of caffeine compared to without caffeine is between -0.08 and 0.45 for university students on the islands. Because 0 is included in this range it further supports the decision that we fail to reject the null.

# given difference in sample proportions
diff <- diffprop(SuccessFail ~ Caffiene, data = Caffeine.sprint)

# simulated standard deviation
SE <- sd(~ diffprop, data = Caffeine.null)

# margin of error for 95% CI
MoE <- 2 * SE
#MoE

LB<-diff - MoE # lower limit of 95% CI
UB<-diff + MoE # upper limit of 95% CI
cat("the 95% confidence interval for the difference in population proportions",round(cbind(LB,UB),2))

## the 95% confidence interval for the difference in population proportions -0.45 0.08

Conclusion

This study looked to see if the addition of caffeine would improve 100m sprint times. The population is university students from Hofn University, Colmar University, and University Of Arcadia. Because I used random assignment we are able to say that it is a representative sample, and we are able to generalize the results of this study to all of the students in those universities.The null hypothesis is that the proportion of students whose sprint times improved with caffeine is equal to the proportion of people whose sprint time improved with no caffeine. The alternative hypothesis is that the proportion of people whose sprint times improved with caffeine is greater than the proportion of people whose sprint time improved with no caffeine. Before examining the results I predicted that the proportion of students who consumed caffeine and improved will be greater than the proportion of students who did not consume caffeine and improved.

Upon examining the results I found a theory based p-value of 0.0641818 and a simulation based p-value of 0.067. Both of these values are above 0.05 which leads us to a conclusion of failing to reject the null. We are 95% confident that the true difference in proportions of students whose sprint times improved with the addition of caffeine compared to without caffeine is between -0.08 and 0.45 for university students on the islands. Because 0 is included in this range it further supports the decision that we fail to reject the null.

My initial prediction that the proportion of students who consumed caffeine and improved will be greater than the proportion of students who did not consume caffeine and improved was incorrect. However, a p-value of 0.0641818 is not very far above the level of significance. With that being said I definitely think further investigation of this topic could be beneficial. If I were to do this study again I might consider changing my population to just university athletes, because that is what is mostly seen in the literature surrounding this topic. I might also consider using a larger sample size because although the validity conditions of having 10 successes and failures in each group were met, there were just barely enough people in each of those groups. Finally, I might also consider using a quantitative variable for the improvement of times section and look at how much each group improves.

Bibliography: references to literature mentioned in the introduction

RPubs (https://rpubs.com/remmertg/1125472)