Introduction

How does Running Affect Attention?

    The population interest are adults (18+ years old) who reside on Providence Island in The Islands simulation. The population parameters of interest are the mean levels of attention for residents after running a 5k indoors and the mean level of attention for residents that did not run a 5k indoors. Attention was measured using a code transmission test, a test often used as a part of a series of tests to determine everyday attention in children. On the test, you could range between 0 correct and 50 correct based on pressing the correct key when a image is shown on the screen, and the score recorded would be the number of correct inputs from the user. The goal of this analysis is to determine whether running a 5k indoors (moderate to intense level of cardiovascular activity) increases acute attention when compared to individuals who did not run. Many studies show that long term affects of running long distance and everyday cardiovascular activity have significant neurological effects such as increase of executive functioning, neuro-plasticity, and attention. One study also indicated that there are similar acute affects from running or intense cardiovascular activity. My initial conjecture for the parameter value is that the mean level of attention for residents who ran would be higher than the mean level of attention for residents who didn’t run, indicating that running has acute effects on average attention when compared to no running.

Data Collection Methods

My Sampling Process
My Sampling Process


    The observational units were people from the island of Providence. Subjects were selected using random number generators, first to obtain which village to select from (1-9: 1 correlating to Hayarano, 2 - Akkeski, 3- Biruwa, 4- Shinobi, 5- Takazaki, 6- Reading, 7- Nelson, 8- Arcadia, and 9- Kiyobico). Then to determine which house to select, another random number generator was run with all of the houses in each specific village that was selected. Finally, in the house, there was a random chance for each person in the house to be selected and were selected using a random number generator for the individuals in the house. Once I had by pool of individuals, I randomly assigned each to either the test group or the control group. 10 out of 53 people questioned did not want to participate giving a response rate of 43/53 = 0.81.

    The variables were recorded by applying the explanatory variable (5k indoor run) to all of the participants in the test group, and to none of the participants in the control group. Then the response variable attention was measured using a code transmission test, recording only the final score on the test which could range between 0 and 50.

    Some sampling errors that could occur with this process are as follows: 1) Smaller towns have a larger chance for individuals to be selected as the towns were selected by just 1-9 random number rather that adjusting for the size of the town. 2) Individuals living alone or with one other person have a higher chance of being selected as when their house is chosen, they are more likely to be selected to participate than in larger homes/families.

Descriptive Statistics

library(readr)
install.packages("devtools")
Running <- read_csv("~/Downloads/Mini Project 3 Data - Sheet3.csv")
boxplot(Score~Group,data=Running,
   xlab="Treatment Group", ylab="Score on Code Transmission Test")

favstats(~Score, data = Running, groups = Group)

    By looking at the bar chart, we can see a slight association with running and a decreased score on the code transmission test. For each group it could be slightly towards the lower scores, but not too significantly. Additionally, we also see a difference in variability between the two groups, with the running group having a significantly higher standard deviation of 11.1 vs the control group deviation of about 7. This is important to account for when we are doing our t test.

Analysis of Results

    The residents of Providence is our population and our parameter of interest is the difference between average attention in the running group and the control group.

Null Hypothesis: There is no difference in average attention after running a 5k indoors. \[H_0: \mu_{Running} - \mu_{Control} = 0\]

Alternative Hypothesis: Running a 5k indoors will increase the average attention compared to no running. \[H_a: \mu_{Running} - \mu_{Control} > 0\]

    A type 1 error would mean rejecting a true null hypothesis, or in this case, the true difference in means of the running group vs control group would be 0. Due to our sample, however, a type 1 error would be strong evidence against the null, leading us to reject the true null hypothesis that there is in fact no difference. The negative effects this could have is it could encourage people to start running to increase attention, when in reality it will not.

    A type 2 error would mean failing to reject a false null hypothesis. In this case, the true difference in means of the running group vs control group is greater than 0, but our sample does not provide strong enough evidence against the null hypothesis. This would lead to the error to fail to reject the null hypothesis, indicating that there is no difference in average attention between people who run a 5k before a attention test and those who do not. The negative effects this could have is it could dissuade people from running for a increased attention.

Despite the potential for minor representative bias from our random selection process, the sampling is random enough to be considered a fairly representative sample of the Island of Providence.

t.test(Score ~ Group, data = Running, var.equal = FALSE,alternative = "less")
## 
##  Welch Two Sample t-test
## 
## data:  Score by Group
## t = 2.5644, df = 30.694, p-value = 0.9923
## alternative hypothesis: true difference in means between group control and group running is less than 0
## 95 percent confidence interval:
##    -Inf 12.225
## sample estimates:
## mean in group control mean in group running 
##              32.20833              24.85000


    The standardized statistic found by our t test is -2.56. The validity conditions are met as there are 20 or greater individuals in each group, the data doesn’t show any significant level of skew, and we are using different variability to calculate the two sample t test, as the standard deviations of the running group is significantly higher than that of the control group.

Students t Distribution. with df = 42
Students t Distribution. with df = 42


    The p value is 0.9923, indicating that if null hypothesis is true, there is a 0.9923 chance of observing a result as extreme or greater than the one that we received. In my case, a more extreme result would be further in the left tail, as I used a one tailed t test rather than a two tailed t test. A p value this high provides no evidence against the null hypothesis, thus I fail to reject the null hypothesis with a p value of 0.9923, as this is no evidence against the null hypothesis, indicating that average attention after running is no different than average attention after no running.

confint(t.test(Score ~ Group, data = Running, var.equal = FALSE,alternative = "less"))


    The interval given by the t test is (-infinity,12.225). I am 95% confident that the true difference in means between running group minus no running group is between negative infinity to 12.225, which provides no evidence against the null hypothesis, indicating that the two groups could have the same mean as zero is included in the interval.


Conclusion

My study aimed to answer the following question: Does Running Increase Attention?

    Statistical analyses of the data collected revealed that there is not sufficient evidence to reject the null hypothesis that the difference in mean levels of attention (as scored on a code transmission test) for residents who ran before taking the test vs those who did not run before the test is zero. This conclusion is supported by the theory based p value of 0.992, and the 95% confidence interval of (-infinity, 12.225) both of which do not provide any evidence against the null hypothesis. A reasonable explanation for the observed difference in average levels of attention are due to random chance, or potentially the converse of what we predicted, that running could have decreased the attention of individuals but we did not test for that, so no conclusions can be made about the converse effects. The study results did not suggest that running is associated with a higher average level of attention. This result can be generalized to the population of Providence as a whole.

    The data did not behave as I expected. Despite previous research and anecdotes supporting a higher level of attention after running, all descriptive statistics for the running group were less than the control group. The box plot also showed a greater variability in the running group than the control group, which was slightly unexpected, as I predicted similar standard deviations between the groups. In general I predicted that the running group would have a higher score on average on the code transmission test than the control group, but this was not revealed by the data. Instead, the null hypothesis was left as a potential explanation for

    Next time, I would test participants on multiple different attention tests, rather than just one. In psychological research, the code transmission test is used as a small part of a larger more comprehensive attention test that could be interesting to see if the measurement the variable could have been flawed. Additionally, to build on my results, I would suggest to do a two tailed test, so that we can determine if the difference in averages is different, rather than if the running group average is greater. Other variables to test could be outdoor running, or just spending time outdoors and study the affects on attention.

Bibliography: Literature Mentioned in the Introduction