1-Way Random Effects Model 2016/2017 NBA Points Per Game by Player

Population Description NBA Players playing at least 4.8 minutes (10% of game time) for at least 20 games in 2016/2017 Regular Season (390 players) Response: Points per 36 minutes (36*Points/Minutes) For each player, obtain “population” mean across all games playing 4.8 minutes or more Population mean across players: Simple mean of players’ means Player effect: Difference between player mean and population mean Random Error: Difference Between Player individual game Between player variance: Variance of Player effects Error (Residual) Variance: Average of Players’ Variance of Random Errors

Population Parameters / Statistical Model Among the 390 Players, average of player mean is m = 14.43 The variance of the player effects is sa2 = 22.63 The variance of the random errors is se2 = 54.18 Note that for this example, the distributions of the player means {mi} and effects {ai} are skewed, while the within player random errors {eij} appear to be more “mound-shaped (see next slide)

Sampling Procedure Select the number of random samples to take: 10000 Select the number of players (treatments) to be sampled in a given random sample: r = 10 Select the number of games (replicates) to be sampled for a given player in a given random sample: n=5 For each sample, obtain and save the sample means and variances for each player and the Among player Mean Square (other quantities will be obtained after obtaining all samples)

Computations Based on Saved Results (r=10, n=5)