Statistical Correlation Between Height And Arm Span Essay.

The height and the arm span of an individual are thought to be statistically correlated. The height of individual measures is believed to be directly proportional to the arm span of such an individual. Scientists and other researchers have concluded that the height of a particular student is directly proportional to their arm span. The arm span can be used to predict the height of an individual. How tall an individual depends on their arm span. The statistical test has drawn much attention, and I decided to carry out an experiment t to verify the truth of the above guess. Initially, it was my understanding that the height of an individual is itself an independent variable. An individual is born and his or her height depends on hereditary and genetic factors (Matsumoto et al., 2021). The height of an individual relied on the height s of the initial family members. However, following the fact, the scientists state that an individual's arm span can be used to determine their respective height. The experiment below tries to answer the question that an individual's arm span and height are statistically correlated. One can be used to predict the other r and vice versa. 

Height is the dependent variable. The height is the variable that will receive the changes made to the arm span. We shall measure the different arm span and predict the height of that particular individual. Assume a scenario whereby at the school gate of entering an institution, scientists would like to determine if they measure the arm span of the students as they enter the university gate whether at the end of the day they shall come up with the appropriate measures of a given students height.

The arm span will be used as the independent variable in the experiment. We shall measure the different arm spans of the student at the university gate main entrance and later on use the measurement collected To predict the height of the particular student.

Gender will be the controlled variable. We can decide to ignore at all]l costs the Gender of a particular student and carry out the experiment assuming that the height and the arm span of the student are correlated despite the fact the height was obtained from a  male or a female; e student. At all costs, we pick the height and the arm span without considering the Gender. We shall have the two variables correlated. 

The null hypothesis: H₀:e=0 (Meaning that the height and the arm span are not correlated. There is no particular relationship between the height and the arm span of an individual.

The alternative hypothesis: H₀:e≠0 (meaning the correlation coefficient between the height and the arm span of an individual is not equal to 0. The correlation coefficient between the dependent and the independent variable is not 0). If we increase an individual's arm span, we shall expect an increase in the height of that particular individual.  

µ1 represents the Average Height of the male students

Hypothesis

µ2 represents the c=average arm span of the female students

Null hypothesis:  µ1= µ2 (The average height of the male students is equal to the average height of the female students

The alternative hypothesis: µ1 > µ2 (The average height of the male students is greater than the average height of the female students. If we measure the arm span, and use it to predict the height of a given student, then if it results out that we obtain a considerable measure for the height, that particular student shall be a male student. 

 The experiment took place at one of the universe's laboratories. We set our experiment at an edge near the university's main gate. We had the tent stationed at the particular border. All the measurement tools were already staged at the venue several days before the actual experiment was done. The target population was the students at the university. The group of the students who agreed for their credentials to be taken was composed of the population of the students. 

The photos were taken during the experiment

Picture 1

Picture 2

Picture 3

Procedures

The procedure for the above experiment was as follows:

The first step involved staging a place where we shall obtain the different measures of the student's arm span. We set as tend close to the universities' main gate, whereby as the students are done with their classes on that particular day, we would measure their respective arm span. We decided to experiment immediately after the course at the students early in the morning are always rushing to their classes. Most of them might not be willing to provide their credentials. Therefore doing it in the afternoon session would be the most suitable time. To make sure that we came up with a good number of observations, we decided to give incentives to the student who agreed for us to measure their arm span (Stagi et al., 2021). We decided that soda and a small piece of cake would be a better reward for the students who took part in the experiment. This is done to ensure that we come up with such a voluminous number of observations to mention the claims stated above at the end of the day. 

The second step involved selecting a team to create public awareness of the same matter. We decided to create posters and spread them around all the university relaxing sites and the university's website with permission from the dean of the students. Then we set aside an entertainment team to entertain the student as the process continues. This is made to ensure that our guests have the best time they need possible. 

The tent was divided into three stages. The first stage involved recording the Gender of the student. As the student enters the tent, the first question involves having them state their Gender. They proceed to stage two. In the second stage, the student's arm span is measured. The student Is required to stretch their two hands then a tape measure was used to measure the arm span of that particular student. The team in charge of taking the measurements will be forced to be as keen as possible to ensure that the correct measurements are taken for the male students who might have a broader chest capacity and the female students whose ability may trigger the measures.

Experiment Setup

Immediately after this stage, the students proceed to stage three, where their respective height is recorded. The student must stand in an upright position to ensure that the precise measurement is taken. Additionally, the team responsible for measuring the height is well set and fits the unit to make sure that it is possible to measure the students who might be abnormally tall. In some rare cases, some individuals are so tall compared to the rest of the students. 

Once the correct measurements had been taken, we had another that assisted us with data collection. We gathered all the Data data we obtained from the tents and composed it into an extensive composite data. To make precise calculations and tabulation and the keying of the data collected, we use the following statistical packages.

1. We used excel to enter what was collected from the field. Excel has good data entry options since it can place the data into respective rows and columns. In excel, we divided the data into four columns. In the first column, we recorded the student's name, and in the second column, we recorded the Gender of that particular student. In the following two columns, we had students' arm span recorded and height recorded, respectively, and we saved the document in a comma-delimited file.
2. R Programming Language. Since I am proficient with R statistical package, I decided to carry out my data analysis using an R programming language. I imported the data to R statistical package, then began my computations.  

The process of data was relatively smooth. After importing the data To R statistical package, we had to carry out a few steps to make sure that our data was ideal. We at first had to clean the data. We had to make sure that the data was free of any missing variables and that there were no instances of having data keyed in wrongly. R statistical packages come with such tools for checking for any lost data. Afterward, we had to create a scatter diagram that helps to show the relationship between the two variables of interest: the dependent variable, height, and the independent variable, arm span. After creating a scatter plot for visualizing the relationship, we created a correlation matrix that shows the relationship between all the numeric variables used in the experiment. We further calculate the correlation coefficient between the two variables of interest (Träuble et al., 2021). Afterward, to verify that the average height of the male students is more enormous than that of female students, we calculated the summary statistics of our data. We then requested R to carry out hypothesis testing and check out whether the average height of the males is larger than the average height of the females. Before this, we were forced to group the data for the male students separately from the data of the female students. 

Fig 1

The Graph above shows the Graphed Relationship between the students' Arm span on the x-axis and the Height of the particular student on the y axis. From the Graph, it is clear that a student's height and their arm span are related correlated. Two happen to have a remarkably intact linear Relationship with each other. The alignment of the plotted line shows this.  

Fig 2

All the plotted points align close to the line of best fit marked by a blue line between the points. The points align very closely with the blue line, which is the line of best fit, then we deduce that students' height and the student arm span are closely related. Also, it is evident that as the arm span increases, the height of the student increases and vice versa. Therefore the height and the arm span of a student picked at random have a linear relationship (Saville et al., 2021). 

Procedures

The correlation of the Height and Arm span of the males.  

Fig 3

The Graph below also reveals that male students' height and arm span have a linear relationship. One of the variables can be used to predict the other variable.

The correlation coefficient between the two variables amongst the males’ data was also significant and positive. Hence, the height and arm span of male students picked at random exhibit a linear relationship. 

The correlation of the Height and Arm span of the females.   

Fig 4

A linear relationship exists as well in the female data—the height of any female student exhibit a linear relation with the arm span of the student. 

When two statistical objects portray a linear relationship, it is always possible to predict the outcome of the other variable given one of the variables. The Result of fitting a linear Regression Line between the two plotted points was as follows:

The slope and the intercept value are; 4.2797 and 0.9244, respectively. The regression line forecasting the height of a student given his arm span is

The height= 4.27972  + 0.92436(The arm Span )

We can use this equation each time we would like to determine the height of a given student given the measurements of their arm span.

The  R – squared coefficient used to evaluate model fitness is 92.49. Therefore, the model is fit for prediction.

The correlation matrix above involves only two variables: the dependent variable is height, and the independent variable is Arm span. Therefore the correlation matrix, which 0only takes numerical variables, may not be as comprehensive as it might be thought. The correlation coefficient is positive(Fuchs et al., 2021 ). Which implies that two variables have a strong positive linear association with each other? Moreover, the correlation coefficient one is when a variable is compared against itself, but the coefficient is 0.9871703 when compared to aging, the opposite variable. This clearly shows that the height and arm span, as the scientists and researchers suggest, have an influential linear association. A single change in the independent variable will lead to an increase in a dependent variable. This further indicates that the longer the student, the longer the arm span and vice versa.  

The output above summaries on the descriptive statistics. The student who had a minimum height had a height of 40.50 units, while the student who had the maximum height had a height of 76.50 units, and the students were Scott and Hellen Respectively. The mean height of all the students who took part in the experiment was 59.49 (Berriel et al., 2021). The student who recorded the minimum arm span recode a span of 37.50 units, while the student who recorded the highest arm span had an arm span of 76.50, and the student was Hellen and Scott. This further shows that the student who recorded the highest arm span also had the highest, which shows that arm span and height share a very close linear association. 

Males students data

The male student's mean Height and arm span are 62.57 and 62.86, respectively. The shortest male student was Jeremy and mark, and the two had a size of 50.0 units but had the shortest arm span of 48.75.  

Female students Data

The mean Height of the female student was 54.10, and the mean arm span was 54.09. The tallest female student was Irene, with a height of 63.0 units, while the shortest student was Hellen, with a size of 43.50 units. Charity had the longest arm span, and Hellen still had the shortest arm span.  

Conclusion

The results of hypothesis testing depicted that, indeed, the mean of x variable, which is the mean of the male student's height, is greater than the mean height of the female students. The critical region had been set at Reject H₀: µ1 =µ2 if the calculated t value is greater than the tabulated t value of t_tab = 2.068658.

With the calculated t value, t_calc=2.1415, we reject the H₀: µ1 =µ2 and conclude that the mean height of the male students is greater than the mean height of the female students. 

Faulty gadgets- we had some of the devices used in the experiment failing us at the last moment, and this forced us to use them defective, which could have triggered errors.

The unwillingness of the students to take part in the experiment- most of the students preferred to have their information kept private. Some of them did not want their height and weight measured. Also, some of the students were in much hurry; therefore, we did not have much time to take their measurements precisely. 

The measuring skill of science

I measured several students and therefore made use of the measuring skill outlined by science.

There was no need to ask a student which gender group they belonged to during the experiment. I could use my science observing skills to tell which Gender a given student belongs to. However, in rare observations, some of the students seemed to belong to both genders, which involved keen observation in ensuring that the correct Gender was indeed the one recorded for each student.

After doing several measurements, I was able to predict a student's heigh after measuring their arm span. Most of the students had a height equal s to their arm span. Therefore it was pretty easy for me to predict the height of such students after measuring their arm span, although some of the students had their arm span differing so much from their height.   

The experiment above has helped me understand that a particular individual's height and arm span are directly correlated. The arm span can predict how tall or short an individual is if one knows their arm span. Moreover, I have also noted that the scientific claims made by researchers and scientists are really of great help in teaching the new generation how science plays a significant role in todays and upcoming lifestyles. Experimenting in science helps us reject or reinforce the claims made by the researcher or other scientists.  

List of References

Berriel, G. P., Schons, P., Costa, R. R., Oses, V. H. S., Fischer, G., Pantoja, P. D., ... & Peyré-Tartaruga, L. A. (2021). Correlations between jump performance in block and attack and the performance in official games, squat jumps, and countermovement jumps of professional volleyball players. The Journal of Strength & Conditioning Research, 35, S64-S69.

Träuble, F., Creager, E., Kilbertus, N., Locatello, F., Dittadi, A., Goyal, A., ... & Bauer, S. (2021, July). On disentangled representations learned from correlated data. In International Conference on Machine Learning (pp. 10401-10412). PMLR.Matsumoto, H., Marciano, G., Redding, G., Ha, J., Luhmann, S., Garg, S., ... & White, K. (2021). Association between health-related quality of life outcomes and pulmonary function testing. Spine deformity, 9(1), 99-104.

Stagi, S., Ibáñez-Zamacona, M. E., Jelenkovic, A., Marini, E., & Rebato, E. (2021). Association between self-perceived body image and body composition between the sexes and different age classes. Nutrition, 82, 111030.

Fuchs, P. X., Mitteregger, J., Hoelbling, D., Menzel, H. J. K., Bell, J. W., von Duvillard, S. P., & Wagner, H. (2021). Relationship between broad jump types and spike jump performance in elite female and male volleyball players. Applied Sciences, 11(3), 1105.

Saville, N. M., Cortina-Borja, M., De Stavola, B. L., Pomeroy, E., Marphatia, A., Reid, A., ... & Wells, J. C. (2021). Comprehensive analysis of the association of seasonal variability with maternal and neonatal nutrition in lowland Nepal. Public Health Nutrition, 1-16.