Critical Analysis of Statistical Operation - Case Study Example

Statistical Operation Introduction: It is easier to have a logical comment but harder to prove the same statistically. The statistical proof of any incident involves a few step that have to be followed sequentially with great rigor and care. Before resorting to any statistical operation it is necessary to mention and explain these steps; as they would be appearing during the operation. Research Design – Process Understanding the problem in concern: The process starts with a clear understanding of the concerned phenomenon; any vague idea about the same would be catastrophic for further proceeding and eventually would yield a flawed result. Discussing with other team members and senior researchers would help the researcher in better understanding. Preparing theoretical framework: After having a clear understanding of the phenomenon, one has to frame a theoretical framework. A theoretical framework would provide the base for further actions. Theoretical framework might be framed following a literature review on the phenomenon in concern or through the application of existing theories on practical problems. While opting for literature review the selected literatures should come from scholarly journals and written by apex academicians in the concerned field (Antara, 2006). Preparing mathematical and statistical framework: The theoretical framework is followed by the mathematical and statistical framework. At this stage the researcher narrows down the problem for further statistical application. The most important aspect of this stage is to ascertain necessary variables and defining them as precisely as possible. The variables might not be always in one to one correspondence with the problem in concern and might require modification and relating to the problem (Hurley, Denegal and Hertel, 2010). Data Collection: Once the variables are determined and defined (also the nature of association between variables and what the researcher set out to prove through those association and how; should also be clarified at this stage.) the next step is to collecting the data through survey. The researcher might be the surveyor as well and that reduces the chance of human error or might hire additional surveyor to save time, however hiring surveyors is a costly affair and at times result in higher level of human error. Statistical operation: Once the data is collected then they need to be tabulated under exact variables for further statistical actions. After the collection and tabulation of data the researcher should set out to prove the concerned problem statistically either manually or through the use of software. It is worth mentioning that with the advent of software that are capable of undertaking statistical operations; manual operations of statistical methods have become obsolete. Interpreting the result: After the statistical operation on the collected and tabulated data using statistical software; the outcome or the results needs to be interpreted so as to determine the outcome regarding the concerned problem. Remaining alert during the entire process and checking and rechecking each step would help to reduce human error and provide a much correct result. Description of the problem: For the present paper the concerned problem has been chosen as impact of time spend in the park and watching television on the result in the exam. Considering the fact that time in a day is constant at 24 hours and result in exam is subject to hard work; it is expected that higher number of hours spend in watching television and park would result in poor grade following less number of hours left for study. Again for the development of the children spending time in playing and socializing is also necessary. The present day television telecast many programs that are education oriented and typifying television as evil to study might not be a good idea at present day. Since logical interpretation is yielding ambiguous ideas hence statistical verification of the same might be beneficial to reach a decision. Hypothesis: Watching television and spending time at the park have a negative impact on student’s grade. Theoretical Framework – Literature Review According to the study of Sharif and Sargent (2006) school performance of students decreased with increasing exposure to weekday television and movie channel access and grades improved with parental constraint on their children’s watching of television. However, interestingly, weekend exposure to the visual media was not associated with school grades. These results were based on a cross-sectional survey of middle school students falling in the grades of 5-8 in Northeastern America. Keith et al (1986) observed the impct of TV time, on high school students’ accomplishment with a sample of 28,051 students. Results predict that time spent on watching TV time had a small negative effect on performance. Results suggested excessive weekday TV viewing. A study by Eric (2010) incorporating interviews of four students and their friends and families show that involvement of students in sports led to success in academics as they helped in building confidence and develop an optimistic attitude towards future goals. Participation in school sports helped in promoting success in performance. Statistical framework of the mentioned problem: Time spent in park has been measured in hours and so as the watching television. Grade of the students has been quantified following a five point Likert scale as excellent (1), good (2), average (3), poor (4), fail (5). The grade of the students have been considered as the dependent variable and time spent in park and time spent in watching television have been considered as the independent variable. The objective of the concerned study is to determine the impact of the independent variables on the dependent variable. Through mathematical equation the problem might be depicted as: G = p*P + t*T …………………. (1) In the above equation G depicts the grade of the students, p is the coefficient of time spent in park and P is the time spent in park. t is the coefficient of time spent in park and T is the time spent in park. The above equation in statistical terms stands as: G = p*P + t*T + µ ………………… (1a) In the above equation µ stands for the error term owing to random disturbances. The objective of the statistical operation is to determine the central tendency and the dispersion of the data collected and finally run a regression having the grade in exam as dependent and time spent in park and watching television as independent variable; this would help to reach a conclusion on the impact of the determined independent variables on the dependent variable. This would be a multiple regression analysis. t statistics for the independent variables after running the regression analysis using excel would help to comment on the statistical significance of the results. Data Collection: Data collection for the concerned analysis has been done following strict ethical consideration. Fifty students with age varying from seven to eleven years have been chosen through non-random sampling with ten respondents each belonging to a particular age. The respondents have been surveyed following a structured questionnaire.Considering the juvenile nature of the respondents, their parents have been briefed before the interview about the nature of the same. Often interview has been conducted at the presence of the parents or at least one of them. Under no circumstances respondents have been forced to initiate an answer or guided to the expected outcome. In case respondents are reluctant to give an answer they were accepted that way. The questionnaire: Name of the respondent: Age of the respondent: Class of the respondent: Grade obtained in the exam: excellent (1), good (2), average (3), poor (4), fail (5). [Put a √] The complete data set has been provided in the appendix at the end of the paper. Statistical operation and interpretation of the result: It is assumed that the data gathered through the questionnaire on the selected variables strictly adheres to the assumption of correlational analysis. The assumptions are stated as follows – Assumption 1: The two of the three variables under consideration are measured from a bivariate normal distributed population. Assumption 2: The two of the three variables under consideration are linearly associated. Assumption 3: Data under consideration are not heteroscedastic. Assumption 4: Data under consideration does not have any outliers. Descriptive Statistics Watching TV (hours per day) For time spent in Park Result in Exam Mean 2.9 Mean 2.9 Mean 2.9 Standard Error 0.20 Standard Error 0.20 Standard Error 0.20 Median 3 Median 3 Median 3 Mode 3 Mode 3 Mode 3 Standard Deviation 1.45 Standard Deviation 1.45 Standard Deviation 1.45 Sample Variance 2.09 Sample Variance 2.09 Sample Variance 2.09 Kurtosis -1.24 Kurtosis -1.24 Kurtosis -1.24 Skewness 0.18 Skewness 0.18 Skewness 0.18 Range 4 Range 4 Range 4 Minimum 1 Minimum 1 Minimum 1 Maximum 5 Maximum 5 Maximum 5 Sum 145 Sum 145 Sum 145 Count 50 Count 50 Count 50 The three measures of central tendency namely mean, median and mode for all the variables under consideration have yielded similar number 2.9, 3 and 3 respectively. The numbers received that way depicts that on an average students watch television for 2.9 to 3 hours a day and spend time at park for 2.9 hours to 3 hours per day. Their average grade at examination is 2.9 to 3 that is average. Again the data received has a tendency to deviate from the mean by 1.45 following the standard deviation and 2.9 following the variance. Hence the data lies within 1.45 of the mean. If the data of student’s grade and number of hours spent in park and watching television are plotted in two separate bivariate graphs, the nature of movement of one variable with respect to other can be understood. The positive association between student’s grade and time spent in park can be understood from the above graph through their same direction movement. The negative association between student’s grade and time spent watching television can be understood from the above graph following their opposite direction movement. However the main problem with the graph is that it cannot specify the magnitude of impact and cannot highlight on the fact that whether the results are statistically significant. For that a multiple regression analysis needs to be carried. The result of the multiple regression analysis is as follows - SUMMARY OUTPUT Regression Statistics Multiple R 0.76 R Square 0.58 Adjusted R Square 0.56 Standard Error 0.88 Observations 50 ANOVA   Df SS MS F Significance F Regression 2 49.35 24.67 32.18 1.57E-09 Residual 47 36.03 0.77 Total 49 85.38         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.89 0.52 1.72 0.092 -0.15305 1.93877 -0.15305 1.93877 times spent in park (hours per day) 0.69 0.096 7.13 5.11E-09 0.492269 0.878901 0.492269 0.878901 watching TV (hours per day) -0.0192 0.099 -0.19 0.847995 -0.2196 0.181202 -0.2196 0.181202 Inference Considering the adjusted R square value the independent variables considered are capable of explaining 56 percent of the impact on the dependent variable. The model as a whole stands owing to the high value of F statistics. Following the values of the regression coefficient watching television imparts a negative impact on the grade of a student but according to the associated t statistics the result obtained is statistically insignificant. On the other hand spending time at the park leaves a positive impact on the student’s grade and this is statistically significant as well following the t statistics. It reveals that socialization and physical activities positively effects student’s grade while idly watching television imparts a negative impact (though this result cannot be accepted owing to statistical insignificance) References Antara, V. (2006), Theoretical Frameworks in Qualitative Research, SAGE Hurley, W. Denegal, C and J. Hertel (2010), Research Methods, Wolters Kluwer Sharif, I. and J.D. Sargent (2006), Association Between Television, Movie, and Video Game Exposure and School Performance, Pediatrics, 118(4), 2005-2854 Keith et al (1986), Parental involvement, homework, and TV time: Direct and indirect effects on high school achievement. Journal of Educational Psychology, 78(5), 373-80 DeMeulenaere, E. (2010), Playing the Game: Sports as a force for promoting improved academic performance for Urban Youth, Journal of Cultural Diversity, 17(4), 127-35 , Appendix: The complete and tabulated data set Number of observation Age of the respondent Class of the respondent Time spend in the park (hours, P) Watching TV (hours, T) Result in the exam (G) 1 7 2 1 5 2 2 7 2 1 5 1 3 7 2 3 2 4 4 7 2 3 2 3 5 7 2 2 1 1 6 7 2 1 1 1 7 7 2 5 3 4 8 7 2 3 2 2 9 7 2 4 3 3 10 7 2 3 4 3 11 8 3 1 4 2 12 8 3 1 4 2 13 8 3 1 5 1 14 8 3 1 5 2 15 8 3 4 1 2 16 8 3 5 3 4 17 8 3 5 1 5 18 8 3 3 5 4 19 8 3 3 4 3 20 8 3 1 5 2 21 8 3 5 5 4 22 9 4 2 3 3 23 9 4 2 4 2 24 9 4 2 4 1 25 9 4 3 2 4 26 9 4 3 2 3 27 9 4 3 2 2 28 9 4 3 3 3 29 9 4 4 1 5 30 9 4 3 2 4 31 9 4 2 3 3 32 10 5 2 2 2 33 10 5 3 4 4 34 10 5 3 4 4 35 10 5 2 4 1 36 10 5 4 3 5 37 10 5 5 2 5 38 10 5 5 3 3 39 10 5 1 5 2 40 10 5 2 4 1 41 10 5 1 5 1 42 11 6 5 3 3 43 11 6 2 5 1 44 11 6 5 2 4 45 11 6 5 5 5 46 11 6 5 3 3 47 11 6 2 2 2 48 11 6 1 5 1 49 11 6 4 1 5 50 11 6 5 1 4 Read More