Introduction

I am interested in looking into how sugar intake affects a person’s athletic ability. The variables I am choosing to work with are sugar intake and a person’s athletic ability. For half of the people in the study they will perform the athletic test (5km indoor run) and then take a sugar tablet and perform the athletic test again. For the other half they will take the sugar tablet second. Individuals will be randomly assigned into these groups following randomization protocols. There will be a full 24 hours in between each run to ensure that participants are not overly tired. Sugar intake is a binary categorical variable, it is whether the subject consumed a sugar tablet before the run or not. A 5km indoor run will be a quantitative variable, it will be the minutes it takes to complete the run. I chose these variables because I am a tennis player and someone who in general enjoys exercising. I also enjoy eating sugar and I want to know if it benefits athletic ability in any significant way. I know that sugar gives you energy and it is important to eat some type of carbohydrate before exercising. I was curious if a sugar tablet that is straight sucrose and does not contain any protein or fat will increase athletic ability. I chose the 5km indoor run because I thought it was the best option for athletic performance testing. A 5 km run is not too long or strenuous that the majority of people will be able to do it. It is also long enough to see if the sugar tablet had a lasting and significant effect. The papers I read all pointed to sugar having a greater effect on long-period endurance sports. Unfortunately “The Islands” do not have an option of a longer timed physical activity. I chose the indoor run so that there would be fewer distractions and variability in weather and road conditions. The amount of sugar in the sugar tablet is unstated but since all of the participants will be taking the same tablet it will be standardized.

Research Question: Does sugar intake (sugar tablet) increases athletic performance (the time it takes to run 5km indoors)?

The population parameter is \[\mu_{sugar} - \mu_{nosugar}\] The population parameter of interest is the difference in mean run times when the individual consumed a sugar tablet and when the individual did not consume sugar before the run. I expect that the run times when an individual consumed the sugar tablet before running will be faster (lower) than that of not taking a sugar tablet.The consumption of sugar will make the individuals faster.

When conducting this research question there were several studies I looked at for information and learning more about the topic. The first study I looked at was on sugar and exercise, it showed the importance of sugar for athletes (Peinado et al. 2023). This study stated that sucrose (commonly known as table sugar) is essential for athletes as it maintains and increases their muscle glycogen storage (Peinado et al. 2023 p.48). Glycogen is sucrose stored in muscle and is the main energy source when performing an athletic endeavor. Having large amounts of glycogen in the muscle is needed for endurance and to perform at a high athletic level (Peinado et al. 2023, p.49). This study found that consuming sugar right before an endurance sport like a marathon is an effective way to improve endurance (Peinado et al. 2023, p. 52). A 5km run is nowhere close to a marathon length, but it will be interesting to see if eating sugar right before the run improves the time. Another paper I looked at was titled “The Metabolism of Sugars and Physical Performance”. This paper, similar to the first paper I read, discussed the importance of sugar for fuel and the need to have a large storage of muscle glycogen (Sherman, 1995.) This paper stated that fat and protein are not readily metabolized for exercise like carbohydrates (what sugar is). So for athletes to train and compete, ingesting a carbohydrate like sugar is needed to maintain peak performance. This paper also stated that inadequate carbohydrates will cause fatigue and decrease physical performance. The last paper I looked at that gave me inspiration for my research question was on dietary sugars and exercise. This paper stated that sugar is needed for athletes competing in an athletic endeavor and should be consumed during or after exercise. This paper also found that consuming sugar after a workout or athletic event reduced recovery time and that eating fructose (a type of carbohydrate monomer) accelerated recovery time (Gonzalez and Betts, 2019, p.246). This paper stated that exercise increases energy expenditure which increases the metabolic rate of carbohydrates (sugar) (Gonzalez and Betts, 2019, p.247). Having a large store of carbohydrates before a workout will help maintain endurance and increase exercise capacity(Gonzalez and Betts, 2019, p.250).

I Initially thought that sugar would increase athletic performance. The runners who took a sugar tablet before the run would have a faster running time. I suspected the actual parameter might not yield much of a difference between taking a sugar tablet before the first run versus taking one before the second run.

Data Collection Methods

The observational units are the individual islanders who are performing the two running trials. The observational units are the islanders who I have recruited to be a part of my study. The response variable of running a indoor 5km was measured in minutes. It was the time in minutes it took each individual to run the 5km. The explanatory variable is if the islander consumed sugar on the first or second run was measured by if they ate the sugar tablet or not. During the course of the study there was not many complications it ran smoothly and as predicted. I met islanders by going one of the many islands,randomly choosing a village then house. I would then ask the islanders who lived in the house if they would consent to participate in my study. I was able to get twenty islanders to be in my study, I asked lots more but many denied to give me consent. All of the twenty islanders I met and sampled were able to run a 5km and everyone completed the two running trials. I waited a full 24 hours before doing the second 5km trial run. I did this to ensure the participants would not be tired. My response rate was 100% for the twenty people I tested all of them completed the full two trials. One difficultly I had in this study was finding enough people. I made three different repeats visits to the island to get enough individuals for this study, some people did not consent to my study so I had to ask significantly over twenty people. One of the errors I had in sampling was not setting a age limit I think that this effected my data and may have skewed. Since there was no age limit elderly people and young adults were running a 5km. This vast age range most likely caused variation in my data that was not due to the effects of sugar alone, because younger people will most likely run much faster compared to elderly people. I think setting a age limit would produced data that I could be more generalize to a larger population.

Descriptive Statistics

library(readr)
rundata <- read_csv("~/Math 247/Mini Project 3 - Sheet3 (1).csv")

# View the first few rows of the data
head(rundata)
rundata <- rbind(
do(27.4) * data.frame(sugar = "Y", person = "P1"),
do(26.4) * data.frame(sugar = "N", person = "P1"),
do(19.0) * data.frame(sugar = "Y", person = "P2"),
do(17.4) * data.frame(sugar = "N", person = "P2"),
do(19.4) * data.frame(sugar = "Y", person = "P3"),
do(19.0) * data.frame(sugar = "N", person = "P3"),
do(16.6) * data.frame(sugar = "Y", person = "P4"),
do(13.8) * data.frame(sugar = "N", person = "P4"),
do(18.6) * data.frame(sugar = "Y", person = "P5"),
do(18.6) * data.frame(sugar = "N", person = "P5"),
do(29.9) * data.frame(sugar = "Y", person = "P6"),
do(30.8) * data.frame(sugar = "N", person = "P6"),
do(13.4) * data.frame(sugar = "Y", person = "P7"),
do(13.6) * data.frame(sugar = "N", person = "P7"),
do(17.9) * data.frame(sugar = "Y", person = "P8"),
do(18.9) * data.frame(sugar = "N", person = "P8"),
do(15.7) * data.frame(sugar = "Y", person = "P9"),
do(15.4) * data.frame(sugar = "N", person = "P9"),
do(18.9) * data.frame(sugar = "Y", person = "P10"),
do(18.6) * data.frame(sugar = "N", person = "P10"),
do(17.6) * data.frame(sugar = "Y", person = "P11"),
do(18.1) * data.frame(sugar = "N", person = "P11"),
do(13.6) * data.frame(sugar = "Y", person = "P12"),
do(13.4) * data.frame(sugar = "N", person = "P12"),
do(21.0) * data.frame(sugar = "Y", person = "P13"),
do(20.3) * data.frame(sugar = "N", person = "P13"),
do(18.8) * data.frame(sugar = "Y", person = "P14"),
do(19.6) * data.frame(sugar = "N", person = "P14"),
do(28.1) * data.frame(sugar = "Y", person = "P15"),
do(27.6) * data.frame(sugar = "N", person = "P15"),
do(15.4) * data.frame(sugar = "Y", person = "P16"),
do(14.7) * data.frame(sugar = "N", person = "P16"),
do(28.9) * data.frame(sugar = "Y", person = "P17"),
do(28.3) * data.frame(sugar = "N", person = "P17"),
do(19.8) * data.frame(sugar = "Y", person = "P18"), 
do(18.3) * data.frame(sugar = "N", person = "P18"),
do(16.4) * data.frame(sugar = "Y", person = "P19"),
do(17.0) * data.frame(sugar = "N", person = "P19"),
do(13.8) * data.frame(sugar = "Y", person = "P20"),
do(13.0) * data.frame(sugar = "N", person = "P20")

)
rundata<-rundata %>% 
  mutate(proportion=.row/ n()) %>% # creating a new variable called proportion
  select(sugar,person,proportion)

head(rundata,n=3)
round(tally(sugar~person, data = rundata, format = "count"),2) 
##      person
## sugar P1 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P2 P20 P3 P4 P5 P6 P7 P8 P9
##     N 26  18  18  13  20  19  27  14  28  18  17 17  13 19 13 18 30 13 18 15
##     Y 27  18  17  13  21  18  28  15  28  19  16 19  13 19 16 18 29 13 17 15
tally(sugar~person, data = rundata, format = "prop")
##      person
## sugar        P1       P10       P11       P12       P13       P14       P15
##     N 0.4905660 0.5000000 0.5142857 0.5000000 0.4878049 0.5135135 0.4909091
##     Y 0.5094340 0.5000000 0.4857143 0.5000000 0.5121951 0.4864865 0.5090909
##      person
## sugar       P16       P17       P18       P19        P2       P20        P3
##     N 0.4827586 0.5000000 0.4864865 0.5151515 0.4722222 0.5000000 0.5000000
##     Y 0.5172414 0.5000000 0.5135135 0.4848485 0.5277778 0.5000000 0.5000000
##      person
## sugar        P4        P5        P6        P7        P8        P9
##     N 0.4482759 0.5000000 0.5084746 0.5000000 0.5142857 0.5000000
##     Y 0.5517241 0.5000000 0.4915254 0.5000000 0.4857143 0.5000000
rodata <- c(27.4,19,19.4,16.6,18.6,29.9,13.4,17.9,15.7,18.9,17.6,13.6,21,18.8,28.1,15.4,28.9,19.8,16.4,13.8)

sudata <- c(26.4,17.4,19,13.8,18.6,30.8,13.6,18.9,15.4,18.6,18.1,13.4,20.3,19.6,27.6,14.7,28.3,18.3,17,13)
# Create side-by-side boxplot
boxplot(rodata, sudata, horizontal = TRUE, col = c("blue", "green"), names = c("Run with sugar","Run"))

Sugar intake is the binary categorical variable, it is whether the subject consumed a sugar tablet before the run or not. A 5km indoor run is the quantitative response variable, it will be the minutes it takes to complete the run. Looking at the the box plot, the two samples have similar run times the run without sugar has more variation. While the run with sugar has less variation. The means are similar with the run without sugar having a smaller mean. There appears to be some association that a run with sugar will result in a faster run time as there were less outliers in that data set.

Analysis of Results

The populations are all of the subjects who took the sugar tablet and ran a 5km. The parameter of interest is the difference in mean run times between running a 5km without a sugar tablet and running the 5km with a sugar tablet. The parameter of interest is the mean difference between an individuals two run times.

\(H_0\): The null hypothesis is that there is no difference in 5km running times between the two groups. The group who consumed sugar will not run faster than the group who did not consume sugar and vice versa.

\[H_0:\mu_{sugar first}-\mu_{no sugar }=0\] \[H_a:\mu_{sugar first} > \mu_{no sugar}\]

\(H_a\): There will be a difference in 5km running times between the the two groups. The group who consumed sugar will run faster than the group who did not consume sugar.

A Type I error would occur I incorrectly reject the null hypothesis when it is actually true. It would mean concluding that there is a significant difference in the run times between those who consumed a sugar tablet first and those who consumed it second. When there is no true difference in run times. This could lead to the false belief that sugar intake has an effect on run times when it actually doesn’t. A Type II error would occur if I fail to reject the null hypothesis when it is actually false. It would mean failing to detect a significant difference in run times between those who consumed a sugar tablet fist and those consumed it second. When there is actually a true difference. This could lead to the false belief that sugar intake has no effect on run times when it actually does.

My measurements can reasonably be considered a representative sample from the population of intrest for a few reasons. One being due to the sample method, I used a random sampling method which makes it more representative and means there will be less bias. Another is the sample size, the sample size is ten for each population which means it is fairly representative. There is also a large demographic in the population, with different ages, genders and fitness levels making it representative. Lastly the measurements were taken accurately and are valid.

I did a paired t-test. I used this because the data was paired and not independent, as each person ran twice and there scores were checked to see if they ran faster with sugar. I used this approach because the data had at least 20 pairs. Also the distribution of the sample differences was not strongly skewed. The T-test came out to -0.22624. Which means there is a difference of -0.22624 between two means for the run with sugar and the run without sugar. This shows that there is a difference between the means of the runs, with the run with sugar being slightly faster. The mean run time with sugar is 19.51 and the mean run without sugar is 19.14.

# Assuming you have two vectors named rodata and sudata
paired_t_test_result <- t.test(sudata, rodata, Paired = TRUE)
print(paired_t_test_result)
## 
##  Welch Two Sample t-test
## 
## data:  sudata and rodata
## t = -0.22624, df = 37.982, p-value = 0.8222
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.680882  2.940882
## sample estimates:
## mean of x mean of y 
##     19.14     19.51

The p-value is 0.822. A p-value of 0.822 means there is 82.2% probability of observing the data assuming that the null hypothesis is true.

The p-value is 0.822 is very high. This p-value suggests that the data is not significant and the p-value is not statistically significant. This would lead to the null hypothesis being rejected.

To conclude, the null hypothesis that there will be no difference in 5km running times based on if the person consumed sugar or not can be accepted. The data shows that the alternative hypothesis can not be accepted and that there is not a statistically significant difference in running times based on sugar consumption. I did not run a stimulation based approach on this data to get the stimulation p-value because I did not believe it was needed. The sample size is not too small and the distribution of the population is known. The standard deviation are very similar showing that the two data sets had similar variance, the means were also very similar.

The confidence interval for the mean difference between run times with ans without sugar is between -0.067 and 0.807.

#The mean runtime for people who consumed sugar 
rodata <- c(27.4,19,19.4,16.6,18.6,29.9,13.4,17.9,15.7,18.9,17.6,13.6,21,18.8,28.1,15.4,28.9,19.8,16.4,13.8)

# Calculate the mean
mean_value <- mean(rodata)

# Print the mean
print(mean_value)
## [1] 19.51
# Calculate the standard deviation
standard_deviation <- sd(rodata)

# Print the standard deviation
print(standard_deviation)
## [1] 5.114983
#The mean runtime for people who did notconsumed sugar 
sudata <- c(26.4,17.4,19,13.8,18.6,30.8,13.6,18.9,15.4,18.6,18.1,13.4,20.3,19.6,27.6,14.7,28.3,18.3,17,13)

# Calculate the mean
mean_value <- mean(sudata)

# Print the mean
print(mean_value)
## [1] 19.14
# Calculate the stan dard deviation
standard_deviation <- sd(sudata)

# Print the standard deviation
print(standard_deviation)
## [1] 5.228002
# Perform t-test and compute confidence intervals
result_sudata <- t.test(sudata)
result_rodata <- t.test(rodata)

# Print confidence intervals
print(result_rodata$conf.int) # Confidence interval for data1
## [1] 17.11611 21.90389
## attr(,"conf.level")
## [1] 0.95
print(result_sudata$conf.int) # Confidence interval 
## [1] 16.69322 21.58678
## attr(,"conf.level")
## [1] 0.95
# Perform t-test and compute confidence interval for the difference in means
result <- t.test(sudata, rodata, paired = TRUE)

# Print confidence interval
print(result$conf.int) #
## [1] -0.80774789  0.06774789
## attr(,"conf.level")
## [1] 0.95

The confidence interval goes from -0.06774789 to 0.80774789. This means that I am 95% confidence that the true mean difference between the 5km run with sugar and without sugar falls within the range of -0.06774789 to 0.80774789. Therefore I can conclude that the population mean 5km run with and without sugar differences is likely to be in this range. Zero is included in this confidence interval which means that there is a possibility that the true differences between the means is zero. Having a zero in the interval supports the previous conclusion to accept the null hypothesis. The Zero would imply that there is a possibility that the true difference between the means of the two paired samples is zero, which would strengthen the evidence for accepting the null hypothesis.

Conclusion

To conclude the p-value suggests that the null hypothesis should be accepted. The p-value is 0.822, which means there is a not any significance and the alternative hypothesis can not be accepted. The t-statistic is a small number at -0.22624 which means the two data sets are similar, showing that the null hypothesis can not be rejected. The confidence interval contains zero which means that there is a possibility that the null hypothesis is true. The confidence interval is between -0.067 and 0.807 which shows that the difference between the run with sugar and the run without sugar could be zero and there could be no difference. The data did not behave as expected I thought there would be a large difference in running times but both were very close. There was also not much difference in mean running times within the two groups.The run with sugar had a mean run time of 19.51 and the run without had a mean run time of 19.14, these are very close means. The standard deviations of both these data sets were very similar, with the run with sugar having a SD of 5.11 and the run without had a SD of 5.22. This means that the two data sets have very similar variance showing that there was really not a large difference between the two. I do believe that this data could be generalized to a larger population as was done through random sampling and contains a diverse group of individuals, but it would be a population of islanders not humans. I think that the data would have behaved differently if humans were being tested instead of islanders. If I were to do this project again I would get a much larger sample size of islanders and make a age cutoff. I would do a age cutoff because I do not think it is fair to compare run times of young adults with elderly individuals. I think that may have actually skewed my data. I would do a sample of individuals who did two runs without any sugar to have a control group. To see if there was a difference when the subjects did two runs with no sugar. Someone could investigate the relationship between running time and a sugary food, like candy or a fruit. This study could also be done on a different form of exercise or a task, to determine if the type of exercise changes the results.

Bibliography: references to literature mentioned in the introduction

  1. Gonzalez, J. T., & Betts, J. A. Dietary sugars, exercise and hepatic carbohydrate metabolism. Proceedings of the Nutrition Society, Volume 78 no. 2, 2019, Pages 246–256. doi:10.1017/S0029665118002604

  2. Peinado, A. B., Rojo-Tirado, M. A., Benito, P. J. El azúcar y el ejercicio físico: su importancia en los deportistas [Sugar and exercise: its importance in athletes]. Nutrición hospitalaria, Volume 28 Suppl 4, 2013, Pages48–56. https://doi.org/10.3305/nh.2013.28.sup4.6796

  3. Sherman, W. M. Metabolism of Sugars and Physical Performance. The American Journal of Clinical Nutrition Volume 62, no. 1, 1995, Pages 228S-241S. https://doi.org/10.1093/ajcn/62.1.228S.

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