Part 1
Introduction
The survey will analyze the relationship between the level of physical activity and the duration of concentration in class. The level of physical activity is determined by the number of hours spent exercising in a day, whereas the duration of concentration in class is measured in minutes. Empirical and cross-sectional studies have suggested that students who participate in games and fitness activities are often more alert in class (Apriana, Sofiyya, Julia, Huriyati, 2016). These studies point out that alertness and concentration are influenced by a person’s level of activity and physical fitness. According to Han (2018), the relationship between these two variables is important as it explains a possible reason why some students perform better than others do.
Population
The survey will aim evaluating the exercise and concentration duration of the students in learning institutions within the state. The representative sample will be students selected at random from the school. The ethical issue of concern in the survey is the possibility of students lying about their participation in physical activities and exercise. This concern will be mitigated by keeping the survey anonymous. Anonymity will limit the need for the students to falsify their responses because they will have no fear of publicization of their information.
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Materials
The student participants in the survey will be selected at random in the different colleges and schools. The students will then be asked questions regarding their physical activity and duration of alertness in class. Further information to validate the survey responses and curtail cheating will be obtained by analyzing the students’ GPA scores, observing the students both in and out of class, and consulting their respective team captains where applicable. The survey questions are:
On average, how long would you say your concentration in class lasts?
On average, how many hours do you exercise in a week?
Part 2
The first step to this project is to describe the appropriate sampling technique to use in data collection. In the sampling method, every subject involved must have an equal chance of being selected. The next step will be the data collection process. At this step, there will be a clear description of how the unique data set used in the analysis section was collected. The third step will be the data analysis part. At this step, various statistical analysis methods will be employed to ensure that the research question is well answered. The two variables – physical activity and duration of concentration in class – will be measured. Finally, there would be the discussion part where the results obtained will be evaluated and the limitations of the method used to collect data.
Sampling method
To ensure that the data collected was unbiased; all the names of the learning institutions were written in small identical pieces of papers and rubbed similarly. They were then put in an opaque closed bag. A person who was not available during this whole process was asked to pick randomly one piece of paper from the pack. Then the name of the institution contained in that piece of paper was the one its students were used in the survey. While in the institution, all the students were asked to gather at one place so that 20 of them can be chosen randomly. The students were asked how many minutes they play and also approximated the minutes they concentrate in class in a week, and their corresponding scores were extracted from the school records.
Data Collection
The survey questions were set, which allowed the students to the only answer with a numerical answer. The survey questions set are;
On average, how long would you say your concentration in class lasts?
On average, how many hours do you exercise in a week?
The following table displayed the results of the survey. Physical activity was measured in minutes per day a student plays, and the duration of concentration in class was measured in minutes per 50 minutes class.
Table 1: Results of the data collection process
| Physical activity (minutes/day) | Duration of concentration in class (minutes/lesson) |
| 40 | 38 |
| 23 | 37 |
| 11 | 24 |
| 37 | 46 |
| 20 | 33 |
| 50 | 28 |
| 15 | 31 |
| 29 | 42 |
| 21 | 44 |
| 48 | 37 |
| 25 | 38 |
| 8 | 18 |
| 21 | 42 |
| 0 | 15 |
| 17 | 20 |
| 39 | 35 |
| 28 | 38 |
| 44 | 34 |
| 30 | 40 |
Descriptive Statistics for Physical Activity
Physical activity was measured as the number of minutes the student plays in a day. The descriptive statistics were performed, and the following is the output found.
| Descriptive statistics | |
| Mean | 26.63157895 |
| Median | 25 |
| Mode | 21 |
| Standard Deviation | 13.7728014 |
| Sample Variance | 189.6900585 |
| Skewness | 0.020529125 |
| Range | 50 |
| Minimum | 0 |
| Maximum | 50 |
| Sum | 506 |
| First quartile | 18.5 |
| Third quartile | 38 |
| Count | 19 |
The five-number summary will be written as: minimum, first quartile, median, third quartile, and maximum. Therefore, the five-number summary can be written as
0, 18.5, 25, 38, 50
Also, the interquartile range will be determined by;
The histogram of variable physical activity was drawn using the frequency table below;
| Class (Range of physical activity in minutes) | Frequency |
| 0 – 9 | 2 |
| 10 – 19 | 3 |
| 20 – 29 | 7 |
| 30 – 39 | 3 |
| 40 – 49 | 3 |
| 50 – 59 | 1 |
Chart 1: A histogram for variable physical activity
Chart 2: The boxplot of variable physical activity
As can be noted from the above charts, the data in variable physical activity is positively skewed because there is a long tail towards the positive side. Also, at the boxplot, the whisker tail is longer at the top than the bottom rear; implying that the data is positively skewed. But when considering the interquartile range, the distribution is 21.5 around the mean which is more accurate than of the standard deviation. The IQR is correct than the standard deviation because the data collected is skewed. The median is the precise measure of central tendency because the data involved is skewed.
Descriptive Statistics for the Variable Duration of Concentration in Class
Duration of concentration in class was measured in minutes, and the maximum class duration was taken to be 50 minutes. The descriptive statistics was done, and the following output was determined.
| Column1 | |
| Summary output | |
| Mean | 33.68421053 |
| Standard Error | 2.046324092 |
| Median | 37 |
| Mode | 38 |
| Standard Deviation | 8.919719923 |
| Sample Variance | 79.56140351 |
| Kurtosis | -0.212550196 |
| Skewness | -0.819877903 |
| Range | 31 |
| Minimum | 15 |
| Maximum | 46 |
| Sum | 640 |
| Count | 19 |
| First quartile | 29.5 |
| Third Quartile | 39 |
Therefore the five-number summary becomes;
15, 29.5, 37, 39, 46
The interquartile range is given by
The histogram for this variable was created using the frequency table below
| Class (Duration of concentration in minutes) | Frequency |
| 15-19 | 2 |
| 20-24 | 2 |
| 25-29 | 1 |
| 30-34 | 3 |
| 35-39 | 6 |
| 40-44 | 4 |
| 45-49 | 1 |
Chart 3: Histogram of variable duration of concentration in class
The box-plot was created using the five-number summary and the following output was determined.
Chart 4: The boxplot for a variable duration of concentration in class
From graph 3 above, it can be noted that the data is negatively skewed because it has a longer tail towards the negative than to the positive. From chart 4 it can also be pointed out that the box-plot has a longer tail at the bottom than at the top, implying that the data of variable concentration duration is negatively skewed. Since the data is skewed, the median is the most effective measure of central tendency than the mean (Peter and Erich, 2012).
Part 3
Z-scores and Regression Analysis
Z Scores and Outliers
Physical Activity
Concentration in Class
According to the second definition, an outlier is a point that lies more than 2 standard deviations from the mean. The z-score for the duration of physical activity is -1.93, while that for the duration of concentration in class is -2.09. Therefore, the point on the duration of concentration is considered an outlier because it lies more than 2 SD from the mean.
Linear Regression and Correlation
In the survey, the duration of physical activity is the explanatory (independent) variable, while the duration of concentration in class is the response (dependent) variable. This is because the rate and duration of physical activity explain the changes in the duration in physical activity. Students who are more physically active are likely to concentrate longer in class, unlike their colleagues who less engage in physical activities.
Chat 5: Scatter plot for duration of physical activity(x) and concentration in class(y)
The scatter plot was created using the graphs feature of MS Word. From the Insert tab, graphs were selected, then the type of graph, i.e., scatter plot selected. The values for the x and y variables were then inputted into two columns on MS Excel. The columns were labeled as x values depicting the duration of physical activity and y values depicting the duration of concentration in class.
The scatterplot shows a linear, positive, and moderately strong association between the duration of physical activity and the concentration in class. There are suspected outliers on the plot, a notable outlier being the first point on the plot. There are however no clusters on the plot.
Linear Regression Equation: y = 0.3447x + 22.506
Correlation coefficient: R = 0.5321
The linear regression equation and the correlation coefficient was determined from the MS word, and Excel scatter plot. The two functions were obtained by right-clicking on the trendline and then the format trendline option from the dialogue box. The display equation on chart box was then selected. The correlation coefficient confirms the observations from the scatter plot. The strength and linearity of association increases from 0 to 1. A positive correlation coefficient indicates a positive direction of the trendline (Koo & Li, 2016). Thus, a correlation factor of 0.5321 is interpreted as linear, positive, and moderately strong association.
Discussion
The results from the linear regression and correlation analysis confirm the survey hypothesis that the rate of physical activity affects the student’s duration of concentration in class. This hypothesis is supported by research that has focused on how physical exercises affects academic performance and mental health. According to a study by Han (2018), aerobic exercise and physical performance have been linked to the development of new neurons. The connections between neurons have also been enhanced by physical exercises, becoming denser, and more diverse. This has an effect of improved brain performance and mental health. Memory, alertness, cognitive functions, and concentration are the primary functions of the brain ( Apriana, Sofiyya, Julia, & Huriyati, 2016). Improved brain function and mental health, thereby directly translates to improved concentration in class and better academic performance.
The accuracy of the findings might have been affected by the sampling and data collection procedures. Although stringent measures were taken in ensuring that bias in sampling did not occur, there might have been a slight chance of the selection being interfered with, thus skewing the results in favor of a particular student of the institution. Also, data collection was based on self-reporting and self-determination by the students. In this case, the students might have intentionally provided inaccurate responses to the two survey questions. The lack of external quality control and evaluation for the survey could weaken the findings and conclusion of the survey.
The primary evaluation of the data indicated that there were outliers in both variables. However, from the z-scores, there was an outlier in only one variable (duration of concentration), while there was no outlier in the duration of physical activity. The possibility of the existence of outliers as is observed on the scatter plot shows that there might be students who do not conform to the study findings and conclusions. This group, however, represents a very small proportion of the student population as most people have similar physiologic characteristics. The regression analysis and scatter plot indicated that the association between the duration of physical exercise and the rate of concentration in class was positive, linear, and moderately strong. This observation thus supports the survey hypothesis.
The survey findings can be generalized to the larger population because they depict the trends from a sample student population. Given the finding from other scientific studies and research, this is probably a common population characteristic. The possibility of bias in selection and falsified responses will not significantly affect the population trend.
References
Apriana, W., Sofiyya, I., Julia, M., & Huriyati, E. (2016). Relationship Between Physical Activity and Concentration of Study of Teenagers in Yogyakarta, Indonesia. Pakistan Journal of Nutrition , 15 (3), 211.
Han G. S. (2018). The relationship between physical fitness and academic achievement among adolescent in South Korea. Journal of physical therapy science , 30 (4), 605–608. doi:10.1589/jpts.30.605
Koo, T. K., & Li, M. Y. (2016). A guideline of selecting and reporting intraclass correlation coefficients for reliability research. Journal of chiropractic medicine , 15 (2), 155-163.
Bickel Peter J., & Lehmann Erich. (2012). Descriptive statistics: Dispersion. Selected Works of EL Lehmann , 499-518.
Palinkas, Lawrence A., Sarah M., & Carla Green. (2015). Perposeful Sampling for Quantitative data. Administration and policy in mental health services research , 533-544.
S., M. (2011). Measure of central tendency: Median and mode. Journal of phamacology and pharmacotherapeutics , 214.
