With the aid of examples briefly explain the difference between fixed effect and random effects models in experimental design.

Survival Analysis: An observational study is conducted to compare the survival experience of individuals with brain cancer following treatment. Participants undergo treatment and are followed until the time of recurrence, until they are lost to follow-up or up to 40 weeks, whichever comes first. The following table details the experiences of participants undergoing radiotherapy alone or radiotherapy and surgery. The data below are week to recurrence or week of last contact. Using the Kaplan-Meier approach, what is the Survival Probability at the end of 34 weeks for surgery/radiotherapy? (Hi nt: set up a table for Surgery/radiotherapy including columns for time (week), Nt, Dt, Ct, and St+1) Radiotherapy Alone Weeks to Surgery/Radiotherapy Weeks to Week of Last Contact (no recurrence) Week of Last Contact (no Irecurrence recurrence recurrence) 10 3 2 2. 4 6 14 10 21 5 23 29 8 32 34

Survival Analysis: An observational study is conducted to compare the survival experience of individuals with brain cancer following treatment. Participants undergo treatment and are followed until the time of recurrence, until they are lost to follow-up or up to 40 weeks, whichever comes first. The following table details the experiences of participants undergoing radiotherapy alone or radiotherapy and surgery. The data below are week to recurrence or week of last contact. Using the Kaplan-Meier approach, what is the Survival Probability at the end of 8 weeks for radiotherapy alone? (Hint: set up a table for radiotherapy including columns for time (week), Nt, Dt, Ct, and St+1) Radiotherapy Alone Weeks to Surgery/Radiotherapy Weeks to Week of Last Contact (no recurrence) Week of Last Contact (no recurrence recurrence recurrence) 3 2 10 2. 4. 14 2 5 10 21 5 23 29 8 32 34

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use a = 0.05. Factor A is method of loading and unloading; Factor B is the type of ride. Type of Ride Roller Coaster Screaming Demon Long Flume Method 1 49 50 47 51 42 43 Method 2 48 46 47 50 42 43 Set up the ANOVA table (to whole number, but p-value to 4 decimals and F value to 2 decimal, if necessary). Do not round intermediate calculations. Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Factor A Factor B Interaction Error Total The p-value…