Two way Anova Hypothesis Testing

Question

I am looking to perform Two way Anova on the following dataset :

 YEAR       TOURNAMENT          WINNER           RUNNER-UP 
 2023  Australian Open  Novak Djokovic  Stefanos Tsitsipas   
 2022        U.S. Open  Carlos Alcaraz         Casper Rudd   
 2022        Wimbledon  Novak Djokovic        Nick Kyrgios   
 2022      French Open    Rafael Nadal         Casper Rudd   
 2022  Australian Open    Rafael Nadal     Daniil Medvedev 

WINNER_NATIONALITY  WINNER_ATP_RANKING  RUNNER-UP_ATP_RANKING  
Serbian                 1.0                    3.0   
Spanish                 2.0                    5.0   
Serbian                 NaN                   25.0   
Spanish                 5.0                    8.0   
Spanish                 5.0                    2.0 


WINNER_LEFT_OR_RIGHT_HANDED   TOURNAMENT_SURFACE       WINNER_PRIZE  
right                          Plexicushion Prestige   2050000.0  
right                          DecoTurf - outdoors     2600000.0  
right                          Grass / Outdoor         2507460.0  
left                           Clay                    1870000.0  
left                           Plexicushion Prestige   4400000.0  

I will be testing the following hypothesis

1. Do Right hand players have advantage over left hand players
2. Playing on type of surface has benefited a player to win?

The independent variables WINNER_LEFT_OR_RIGHT_HANDED have an effect on the dependent variable a WINNER

The independent variables WINNER have an effect on the dependent variable a TOURNAMENT_SURFACE

What other possible Hypothesis can be performed on the given dataset and are the hypothesis i am trying to answer are valid, are their other possible sources of variation in the data that i can take into account.?

Answer 1

ANOVA is done to test whether there is a difference between groups, there isn't necessarily a direction. That is, you will not be testing if there is an advantage of right hand players over left hand players; you will be testing if their performance differs significantly. Same can be said for the surface as well.

As for your other questions, you can choose other explanatory variables upon your choice. Note that if you utilize more than 2 variables you will formulate a different experimental design, which gets further complicated depending on the model you formulate.