The concept of reaction time has always intrigued me, from the seductive rhythm of a basketball game to the greater rhythms that dictate our daily interactions. As an athlete and also young, curious and motivated student, I am intrigued by this subject, which crosses the boundaries between sportsmanship and science. A deeply personal connection that follows the passage of time and the modifications it forms into our skills arises as I watch people that belong to different age groups catch a ball. When I think about this relationship, I remember basketball highlights from my father's twenties, which stand in vividly strong contrast to the skills he possesses now. When I saw videos of him playing basketball 40 years ago, I felt the need to discover how much aging process effected his movement and skills. Additionally, the idea of human reaction time has emerged as an intriguing story thread in a society saturated with tales that brilliantly blend the worlds of fantasy and reality. The colourful story told in the 2018 film "Uncle Drew" (Allen, 29 C.E.) sparked this passion for me recently. The thought that would lead me on my investigation came to me as I watched the main character's lively moves on the basketball court. I started thinking whether people could exhibit movements as good as these in the later years or not. My fascination with the influence of age on human reaction time has been inspired by these discoveries, which have their origins in the simple task of catching a basketball.

The duration between the introduction of a stimulus and the start of an acceptable response is captured by reaction time, a key indicator of human performance (MerriamWebster, 2019). It serves as a crucial indicator of how quickly our sensory and cognitive processes digest information and put it to use. This vital parameter provides a window into our cognitive capacity in addition to being essential to sports and daily activities. The first stage of reaction time involves the detection of a stimulus by our sensory organs, such as the eyes in this process, after which the stimulus is then transmitted to the relevant sensory areas in the brain for processing. This includes the thalamus, sensory cortex, and association areas. However, according to National Institutes of Health, the thalamus decreases in volume with age, with a linear course of change (1-3), that is associated with diminished cognitive speed (4) (Mather & Nga, 2013). Also, vision tends to decline. As you age, the sharpness of your vision, known as visual acuity, gradually declines. The most common problem is difficulty focusing the eyes on close-up objects Emmett, S. D. (2021). In sports, rapid reflexes frequently make the difference between a reception that is safe, a pass that is precisely timed, and an interception that could change the outcome. Also, this type of experiment has very little place for thinking and planning, as the fastest possible reaction is needed. Reaction time has little to do with how long the "planning" period lasts, and a lot to do with the trajectory of the neural activity in the brain. The concept is fairly simple: the closer the neurons that fire during planning are to the neurons that must fire to initiate execution, the shorter the reaction time (Valenti, 2011). Rapid sensory processing and coordinated motor actions are essential for athletes to succeed in their particular sports. As people move through the stages of life, the complex interaction between aging and human function is more and more obvious. Reaction times can be impacted by a variety of basic aging-related changes that can influence elements like vision, neurological processing, muscle strength, and cognitive function. For instance, a new study indicates that some aspects of peoples' cognitive skills begin a slow decline at the age of 27 ("Cognitive Decline Begins in Late 20s, Study Suggests," 2009). By testing people from different age groups, I am looking to discover to what extent does reaction time decrease over time.

My hypothesis null ho states that the difference in reaction time between people from 2 age groups is significant. My alternative hypothesis one \(h_{1}\) states that the difference in reaction time between people from 2 age groups isn't significant.

Dependent variable: Reaction time at which participants catch a ball
Independent variable: Age of all 30 participants
Control of variables:

I found 30 participants, 15 from the age of 17 to 19 (referred to as the "Teenage Group"), and 15 from the age of 40 to 60 (referred to as the "Adult Group"), with the aim to test their ability to catch a ball. My aim was to include diverse range of participants, from men who used to play basketball to women who didn't have any basketball experience. The influence of gender on reaction time wasn't tested. Participants younger than 18 years of age were informed about the nature of experiment and verbally asked whether they'd like to participate, and accepted to be filmed for the purpose of obtaining results important for my investigation. None of the participants had any visual or motor problems that would have slowed down their ability to react quickly or catch the ball. Line was crossed at the height of 1.80 m from which ball was being tossed constantly throughout the experiment. Rules were clear, everybody was obliged to hold their arms beneath their body and to sit still until the ball was thrown. Participants were told not to consume caffeine or energy drinks, to sleep well in order to prevent some difficulties (Ryan, 1998). Reaction time was measured as the interval between the release of the ball and moment when the participant caught the ball. All participants were recorded 3 times and the best result of 3 attempts from every candidate was taken into consideration. All the results were taken, measured with stopwatch and then statistically processed by t-test. Mean reaction times were calculated for both the younger and older groups. A t-test was conducted to compare the mean reaction times between the two groups and determine the statistical significance of any observed differences.

In order to conduct the experiment, I needed to get the signature of acceptance from participants. So, here is the example of survey that was given to them before the start of experiment:

Raw data

The numbers in this table are important because represent the exact reaction times of both groups.

Values on the x-axis of the graph (18-60) represent years.

In order to statistically process all measured results, I decided to conduct t-test (Glen, 2020), where I obtained mean1 and mean2 values, variance1 and variance2 values, standard error, t-statistic, degrees of freedom for significance level 0.05 (5%).

Firstly, I calculated mean of each group.
Mean \(_1=\sum\) of all reaction times in "teenage group"/ n1 (number of teenagers, 15)
Mean \(_2=\sum\) of all reaction times in "adult group"/ n2 (number of adults,15)

Table with results of all deviations:

Variance \(_1=\sum(\) deviation \(_1^2)/n\); deviation for each result is calculated by subtracting mean 1 from the reaction time of participant (e.g. 1. 0,236-0,2538), after which every result is squared. Therefore, deviation of the first member of teenage group would be \((0,236-0,2538)^2=0,00031684\). By summing all squared deviations and then dividing them with the numbers of participants (15), variance \(_1\) is obtained.

Variance \(_2=\sum(\) deviation \(_2^2)/n\); the same principle was used but reaction times from "adult group" were taken into consideration.

\(SE=\sqrt{(\frac{\text{var}1}{n1})+(\frac{\text{var}2}{n2})}\)

\(SE=\sqrt{(\frac{0.000545563}{15})+(\frac{0.00471963}{15})}\)

\(SE=\sqrt{(0.00036371)+(0.00031464)}\)

\(SE=\sqrt{(0.00067835)}\)

\(SE \approx 0.02605\); This represents the standard error of the difference between the means of the two groups with variances 0.00545563 and 0.00471963, and sample sizes 15 each.

When employing the t-test, the t-statistic is an essential part of hypothesis testing (Frost, 2022). It is calculated to determine whether differences between groups in a sample that are observed are statistically significant or if they are likely to be the result of chance. The t-statistic offers an identical measurement of the variance within the sample by accounting for the difference between sample means. If the absolute value of the t-statistic is bigger than the critical value, it shows that the result is statistically significant. So simply:

• If \(|t\)-statistic \(|>\) Critical value: This shows that calculated t-statistic is far from the expected value under the null hypothesis. In this case, the null hypothesis would be rejected and it would be concluded that the difference in reaction times between the two age groups is statistically significant.
• If \(|t\)-statistic \(|\leq\) Critical value: This shows that calculated t-statistic is not significantly different from the expected value under the null hypothesis. If this is the case, the null hypothesis wouldn't be rejected and it would be concluded that there is not a significant difference in reaction times between the two age groups.

T-statistic formula is:
t-statistic \(=(\) mean \(_1-\) mean \(_2)/\) SE

- t-statistic=-8.19; the fact that the value is negative that mean 2 is greater than mean 1

In order to find a critical value, it's needed to calculate degrees of freedom for my significance level (\(\alpha=0.05\)) first.

Principle by which degrees of freedom is calculated is:
Degrees of freedom \((\mathrm{df})=\mathrm{n}_1+\mathrm{n}_2-2\)
- Degrees of freedom \(=15+15-2=28\)

Critical value is found into t-distribution table ("T-Distribution Table (One Tail and TwoTails)," n.d.). But to understand which value I chose, it is needed to clarify difference between one-tailed and two-tailed test because critical values of these two types of test differ. In a two-tailed test, emphasis is put on determining if there is a significant difference between groups in either direction. In my case, the reaction times of participants from two age groups are compared. I want to know if there's a significant difference in catching speed between the two groups, whether it's faster or slower. It's important to say that l'm not making a specific hypothesis about whether one group would be faster or slower. If that was the case, my experiment would fall into one-tailed test group. Therefore, my investigation belongs to the two-tailed test group, which influences the choice of critical value. Simply:

• Critical value for significance value of \(\alpha=0.05\) and df= 28 for one-tailed test is 1.701
• Critical value for significance value of \(\alpha=0.05\) and df=28 for two-tailed test is 2.048

As we concluded that it is a two-tailed test, critical value I took into consideration is \(\underline{2.048}\).

The absolute value of t-statistic (-8.19) is much larger than the critical value (2.048), so I reject my null hypothesis at 0.05 significance level. In a hypothesis test, if the calculated t-statistic is far beyond the critical value, it suggests that the observed difference is highly unlikely to have occurred due to random chance alone. Therefore, there is a statistically significant difference in reaction rates between two age groups compared.