Introduction

Sleep is pivotal in our daily lives. Minor adjustments in sleep habits, including timing, environment, and sleeping positions, can have a profound impact on individuals’ productivity and performance. There is also ongoing research on how taking a nap is associated with health as well as cognitive performance in our daily lives. One research found that daytime naps have advantages on verbal memory for teenagers. The research was conducted on Chinese adolescents who were categorized into a nap group and a non-nap group. Both groups had to perform three specific verbal-related tasks to assess the level of their verbal declarative memory. The result showed that the nap group performed much better than the non-nap group. Not only for teenagers, the cognitive performance of adults is affected by daytime naps. Another research indicated that adults who are habitual nappers experience reduced accuracy in reaction speed during Go/No-go tasks when they lack nap time. This research led to the research question of whether taking a brief daytime nap(15 minutes) can enhance the cognitive performance of college-aged(18-24) students. 15 minutes of daytime nap was determined based on another research that demonstrated that the level of alertness and performance differed by the duration of the nap. It concluded that 5-minute naps didn’t show any benefit compared to no-naps, while 10 minutes showed the most significant improvement; the alertness response was immediate, and benefits lasted the longest. 20 minutes and 30 minutes of nap also showed improvement but less significant than 10 minutes nap. The population parameter of interest in this experiment was the difference in vocabulary memory test scores among two groups(the control group who didn’t take a nap before the test and the experimental group who took a nap before the test). Based on the literature mentioned above, the experimental group was expected to have a higher average test score.

Data Collection Methods

Observational units were each adult in the 18-24 age range in the islands. For the data collection method, first, 40 participants of 18-24 age were non-randomly selected from five cities chosen. It was a non-random selection, since finding the participant who had the age range of 18-24 required visiting every household in the chosen cities. This non-random selection method could have led to a possible non-sampling error where the statistics of the data couldn’t represent the whole population(age 18-24) on the island. Also, a small sample size could have led to possible sampling error. The response rate in the study was 83.3%, as 8 islanders refused to participate in the study, and there was no sampling error occurring from the rejection of these participants.

After selecting the sample, 20 participants were randomly assigned to a control group. The remaining 20 participants were assigned to an experimental group. After participants were randomly assigned to each group, the control group took a vocabulary memory test and the test result was recorded. For the experimental group, participants took a 15 minute nap, followed by taking a vocabulary memory test, and the test result was recorded.

Descriptive Statistics

These are the numerical summaries from the samples. Nappers are the experimental group and the non-nappers are the control group. A significant difference in the average score of the memory test between the two groups was observed. Both groups had a higher value of median than that of mean, which indicates that the distribution was slightly skewed left. Also, the standard deviation was much higher in the control group.

This is the box-plot from the sample statistics. This black dot is the median. There’s a larger variance in the non-napper group. Also, there are three outliers observed as a white dot. It would be further explored in the conclusion but this may be the result of the confounding variables such as the mood of the participants affecting the result of the study.

Analysis of Results

The first parameter of interest was the average vocabulary memory test result(cognitive ability) among all adults (age range from 18 to 24) who took a 15-minute nap right before the test. The assigned symbol was \(\mu_{Nappers}\). The second parameter of interest was the average vocabulary memory test result(cognitive ability) among all adult (age range from 18 to 24) who didn’t take a 15-minute nap right before the test? The assigned symbol was \(\mu_{Non-nappers}\). Using these symbols, the null hypothesis the difference in the two parameters of interest would be zero. The alternative hypothesis would be that there would be a difference between the values of the two parameters. In other words, the null hypothesis indicates no association between taking a nap and the result of the score. The alternative hypothesis would be the other way around.

\[H_0:\mu_{1}-\mu_{2}=0\] \[H_A:\mu_{1}-\mu_{2}\neq0\]

Before conducting the theory-based approach, possible type 1 and type 2 errors were taken into account. Type 1 error would have been that if the theory-based approach was able to make the conclusion that there would be an association between taking a 15-minute nap and the result of the test score, the reality could be that there would be no association between these two variables. For type 2 errors, if the theory-based approach failed to reject the null hypothesis of no association between the two variables, the actual result could be that there would be an association between two variables. Also, there was a concern about representing the samples to the whole population of islanders(age 18-24), since non-random selection was conducted. Moreover, a small sample size can be another factor to prevent the statistics from generalizing to the whole population.

The theory-based approach was conducted after numerical summaries were obtained.The t-statistic was calculated followed by getting the p-value, using the R code. Based on both tests on t-statistic and p-value test, the result of the study was statistically significant.

## difference in sample means is 2.85
## standard error of the difference in sample means is 1.09
## standardized statistic t is 2.62

The value of t-statistic for the theory based aproach(2.62) indicated that the difference statistics from the sample was much far away than 2-standard deviation in t-distribution. Thus, the statistics is at the far end of the t-distribution. This also meant that the difference between two groups are statistically significant.

## the two-sided p-value is 0.01380079

The theory-based p-value of 0.0138 indicates that there was strong evidence against the null hypothesis (0.01<p<0.05). The P-value was small enough to reject the null hypothesis that there would be no association between the two variables. Based on these two tests, the conclusion made was that there would be a strong association between taking 15 minutes of daytime nap and the improvement of the score in vocabulary memory test. Importantly, the validity conditions for the theory-based approach were met. First, both groups(control and experimental) had at least 20 samples. Secondly, there was a slight skewness observed in the sample distribution, the distribution was not strongly skewed.

Lastly, the confidence interval was calculated to not only estimate the possible statistics but also to ensure whether the statistics obtained were statistically significant or not.

The range (0.63,5.07) did not include zero, which meant that a difference of zero between the two means (Nappers and Nonnappers) was not plausible. It also aligned with the rejection of null hypothesis based on theory-based and simulation-based approaches. The interpretation of the interval was that it is 95% confident that the average score of the memory test from Nappers is between 0.63 and 5.07 points higher than the average score of the memory test from Non nappers.

Conclusion

To reiterate, the sample was non-randomly selected from five cities. Since this is not a random selection method, it would be hard to generalize the result to all the islanders whose age is from 18 to 24. Non-random selection could be achieved if the researchers know the number of islanders whose age is from 18 to 24, followed by using a random generator to select the sample from the population. For the random assignment, the sequence of selected 40 participants was mixed up followed by assigning 1-20 as the control group and from 21-40 as the experimental group. Even though random assignment was employed, there still was a possibility that confounding variables could affect the result due to the small sample size. There were three possible confounding variables considered. First, the response variable was not about the improvement of the test score after taking a nap, so the research didn’t focus on comparing the cognitive performance before to after taking a nap. This meant that the default cognitive ability of each individual could be a confounding variable. In the same line, age can also be a confounding variable. However, this variable was recorded for each group and the average age difference between these two groups was not significant. Lastly, some participants were not in a good mood during the study. The mood can also be a confounding variable. Increasing the sample size could have decreased the effects of these confounding variables potentially creating type 1 error. Overall, the confidence to conclude that taking a 15-minute nap causes the enhancement of cognitive performance can be made with an increased sample size. Based on theory-based p-value,t-statistics, and simulation p-value, the final conclusion was that the mean difference in the test scores between the two groups was statistically significant. It was hard to generalize the result to the whole islander population. Lastly, the small sample size can leave a space for confounding variables. Finally, confidence in making a cause-and-effect statement can be increased if the sample size gets larger.

The study reassured that taking a nap can have a significant positive effect on students who are in college to enhance their cognitive ability. Further investigation can be made by making a time interval(10,15,20,25 minutes) as a response variable and the response variable as the test score of students who are in college. Also, the test score was a proxy variable in the study. Combining different kinds of tests can make the explanatory variable closer to the intended variable. Finally, other further investigations can be made by how taking a brief nap time can differently affect the sleep-deprived and non-sleep-deprived group.

Bibliography

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2.Chen, Q., Ru, T., Yang, M. Yan, P., Li, J., Yao, Y., Li, X., Zhou, G., & Dai, X. (2018). Effects of Afternoon Nap Deprivation on Adult Habitual Nappers’ Inhibition Functions,BioMed research international, 2018-01, Vol.2018, p.5702646-9

3.Brooks, A., &Lack, L. A brief afternoon nap following nocturnal sleep restriction: Which nap duration is most recuperative? (2006).Sleep (New York, N.Y.), 2006-06, Vol.29 (6), p.831-840