Simple Random Sample (SRS)
A simple random sample is a sample drawn uniformly at random without replacement.
- “Uniformly” means every individual has the same chance of being selected.
- “Without replacement” means we won’t pick the same individual more than once.
To perform an SRS from a List or Array options, we use np.random.choice(options, n, replace=False).
staff = ['Oren Ciolli', 'Nate Del Rosario', 'Jack Determan', 'Sophia Fang', 'Charlie Gillet',
'Ashley Ho', 'Henry Ho', 'Vanessa Hu', 'Leena Kang', 'Norah Kerendian', 'Anthony Li', 'Weiyue Li',
'Jasmine Lo', 'Arjun Malleswaran', 'Mert Ozer', 'Baby Panda', 'Arya Rahnama', 'Aaron Rasin', 'Chandiner Rishi', 'Gina Roberg',
'Harshi Saha', 'Keenan Serrao', 'Abel Seyoum', 'Suhani Sharma', 'Yutian Shi', 'Ester Tsai',
'Bill Wang', 'Ylesia Wu', 'Jason Xu', 'Diego Zavalza', 'Ciro Zhang']
# Simple random sample of 4 course staff members.
np.random.choice(staff, 4, replace=False)
# array(['Yutian Shi', 'Oren Ciolli', 'Ylesia Wu', 'Sophia Fang'],
# dtype='<U17') If we use replace=True, then we’re sampling uniformly at random with replacement – there’s no simpler term for this.
If we want to sample rows from a DataFrame, we can use the .sample method on a DataFrame. That is,
df.sample(n) returns a random subset of n rows of df, drawn without replacement (i.e. the default is replace=False, unlike np.random.choice).
The effect of sample size
- The law of large numbers states that when we repeat a chance experiment more and more times, the empirical distribution will look more and more like the true probability distribution.
- Similarly, if we take a large simple random sample, then the sample distribution is likely to be a good approximation of the true population distribution.
- In general, statistics computed on larger samples tend to be better estimates of the Population parameters than statistics computed on smaller samples.