Sample Size
Sample size is the number of observations used in an analysis. Larger, appropriately collected samples usually reduce random sampling error; they do not automatically correct biased selection or measurement.
THE IDEA
Sample Size
Sample size is the number of observations used to draw a conclusion. Measuring more people can improve an estimate of a city’s average height, provided the sampling method represents the population of interest. Measuring many people from a single unusual group can still give a biased estimate.
Small samples are more sensitive to random variation. Larger samples generally improve precision, but collecting them costs time and money. Plan the size around the precision or ability to detect an effect that the question requires, rather than collecting data until a significant result appears.
When evaluating a statistic, ask both how many observations it uses and how they were collected. Also check what was measured and which population the result is meant to describe.
When to use it
A medical researcher determining the required number of trial participants to detect a drug's effect with statistical significance while balancing budget constraints.
A business analyst deciding how many customer feedback forms to collect before making strategic changes.
A journalist evaluating the credibility of a political poll by checking the sample size and margin of error.
An investor reviewing comparable startups checks both the number of past ventures and whether the sample omits failures or differs from the new venture.
FROM THEORY TO EVERYDAY LIFE
In practice
Estimating Average Height
You try to estimate the average height of adults in a city by measuring only 5 people you see on a busy street. The small sample size may lead to an estimate far from the true average because your sample isn't representative and random variation is high.
Product Quality Survey
In a hypothetical survey, 10 customers give 8 positive responses, or 80% satisfaction. A later survey of 1000 customers reports 45%. The difference prompts questions about sampling variation, who responded, and whether the surveys measured the same thing. The larger count alone does not settle which estimate is representative.
A MOMENT TO REFLECT
Put it to work.
When you hear a statistic, how do you evaluate the sample size to determine its reliability?
Can you recall a time when you made a decision based on limited data, and how might a larger sample have changed your conclusion?
What are the costs and benefits of increasing sample size in a personal or professional project you're considering?
CONTINUE THE CONVERSATION
Source texts
- The Great Mental Models Volume 3 Systems and Mathematics