Author: Roshan Ambavale
Introduction:
Messi: Widely regarded as one of the greatest football players of all time, Lionel Messi is known for his incredible dribbling, playmaking, and goal-scoring abilities. He has won numerous awards, including multiple Ballon d’Or titles, and spent the majority of his career with FC Barcelona before joining Paris Saint-Germain.
Ronaldo: Cristiano Ronaldo is a global football icon, famous for his extraordinary athleticism, goal-scoring prowess, and versatility. He has played for top clubs like Manchester United, Real Madrid, and Juventus, winning several prestigious titles, including five Ballon d’Or awards.
Neymar: Neymar da Silva Santos Júnior, known simply as Neymar, is a Brazilian forward recognized for his exceptional skill, speed, and creativity on the field. He has played for top clubs such as Barcelona and Paris Saint-Germain, and is known for his significant contributions to the Brazil national team.
Suarez: Luis Suarez is a prolific Uruguayan striker, renowned for his clinical finishing and aggressive style of play. He has been a key player for clubs like Liverpool, Barcelona, and Atletico Madrid, and has earned numerous individual and team honors throughout his career.
Objective: Find out whether all Football Players are the same or not.
Data Collection: Primary data was collected in a classroom setting, with 28 students participating. The students provided ratings on a scale of 1 to 10. The collected data was subsequently analyzed, and an ANOVA table was generated for further statistical interpretation.
Data Analysis:
The results of an ANOVA (Analysis of Variance) test comparing the performance metrics of four football players: Messi, Ronaldo, Neymar, and Suarez.
Data Analysis
1. Hypotheses:
– Null Hypothesis (H₀): All football players have the same mean performance.
– Alternative Hypothesis (H₁): At least one player’s performance is different.
2. Summary Table:
– Messi: Average = 7.93, Variance = 1.92
– Ronaldo: Average = 5.93, Variance = 9.48
– Neymar: Average = 7.43, Variance = 3.59
– Suarez: Average = 8.18, Variance = 3.12
– The averages show some differences, with Ronaldo having the lowest average and Suarez the highest.
3. ANOVA Table:
– SS (Sum of Squares):
– Between Groups = 85.3125 (measuring the variance between the players)
– Within Groups = 488.6786 (measuring the variance within each player’s performance)
– Degrees of Freedom (df):
– Between Groups = 3
– Within Groups = 108
– MS (Mean Square):
– Between Groups = 28.4375
– Within Groups = 4.5248
– F-statistic (F): 6.284806
– P-value: 0.000569
– F critical (F crit): 2.688691
Conclusion:
– Since the P-value (0.000569) is much smaller than the standard significance level (0.05), we reject the null hypothesis (H₀).
– The F-statistic (6.284806)is greater than the critical value F crit (2.688691)**, which also indicates that the null hypothesis should be rejected.
– This means that there is statistically significant evidence that at least one football player has a different mean performance from the others.
In conclusion, the performance of the players is not the same; at least one player’s performance standso ut as significantly different from the others.