## What is Sample Size?

Sample size is the number of observations or data points collected in a study. It is a crucial element in any statistical analysis because it is the foundation for drawing inferences and conclusions about a larger population.

When delving into the world of statistics, the phrase “sample size” often pops up, carrying with it the weight of your study’s credibility and the clarity of your findings. But why should you care about sample size?

Imagine you’re tasting a new brand of cookies. Sampling just one cookie might not give you a true sense of the overall flavor—what if you picked the only burnt one? Similarly, in statistical analysis, the sample size determines how well your study represents the larger group. A larger sample size can mean the difference between a snapshot and a panorama, providing a clearer, more accurate picture of the reality you’re studying.

In this blog post, learn why adequate sample sizes are not just a statistical nicety but a fundamental component of trustworthy research. However, large sample sizes can’t fix all problems. By understanding the impact of sample size on your results, you can make informed decisions about your research design and have more confidence in your findings.

## Benefits of a Large Sample Size

A large sample size can significantly enhance the reliability and validity of study results. We’re primarily looking at how well representative samples reflect the populations from which the researchers drew them. Here are several key benefits.

### Increased Precision

Larger samples tend to yield more precise estimates of the population parameters. Larger samples reduce the effect of random fluctuations in the data, narrowing the margin of error around the estimated values.

Estimate precision refers to how closely the results obtained from a sample align with the actual population values. A larger sample size tends to yield more precise estimates because it reduces the effect of random variability within the sample. The more data points you have, the smaller the margin of error and the closer you are to capturing the correct value of the population parameter.

For example, estimating the average height of adults using a larger sample tends to give an estimate closer to the actual average than using a smaller sample.

Learn more about Statistics vs. Parameters, Margin of Error, and Confidence Intervals.

### Greater Statistical Power

The power of a statistical test is its capability to detect an effect if there is one, such as a difference between groups or a correlation between variables. Larger samples increase the likelihood of detecting actual effects.

Statistical power is the probability that a study will detect an effect when one exists. The sample size directly influences it; a larger sample size increases statistical power. Studies with more data are more likely to detect existing differences or relationships.

For instance, in testing whether a new drug is more effective than an existing one, a larger sample can more reliably detect small but real improvements in efficacy.

### Better Generalizability

With a larger sample, there is a higher chance that the sample adequately represents the diversity of the population, improving the generalizability of the findings to the population.

Consider a national survey gauging public opinion on a policy. A larger sample captures a broader range of demographic groups and opinions.

Learn more about Representative Samples.

### Reduced Impact of Outliers

In a large sample, outliers have less impact on the overall results because many observations dilute their influence. The numerous data points stabilize the averages and other statistical estimates, making them more representative of the general population.

If measuring income levels within a region, a few very high incomes will distort the average less in a larger sample than in a smaller one.

Learn more about 5 Ways to Identify Outliers.

## The Limits of Larger Sample Sizes: A Cautionary Note

While larger sample sizes offer numerous advantages, such as increased precision and statistical power, it’s important to understand their limitations. They are not a panacea for all research challenges. Crucially, larger sample sizes do not automatically correct for biases in sampling methods, other forms of bias, or fundamental errors in study design. Ignoring these issues can lead to misleading conclusions, regardless of how many data points are collected.

### Sampling Bias

Even a large sample is misleading if it’s not representative of the population. For instance, if a study on employee satisfaction only includes responses from headquarters staff but not remote workers, increasing the number of respondents won’t address the inherent bias in missing a significant segment of the workforce.

Learn more about Sampling Bias: Definition & Examples.

### Other Forms of Bias

Biases related to data collection methods, survey question phrasing, or data analyst subjectivity can still skew results. If the underlying issues are not addressed, a larger sample size might magnify these biases instead of mitigating them.

### Errors in Study Design

Simply adding more data points will not overcome a flawed experimental design. For example, increasing the sample size will not clarify the causal relationships if the design doesn’t control a confounding variable.

### Large Sample Sizes are Expensive!

Additionally, it is possible to have too large a sample size. Larger sizes come with their own challenges, such as higher costs and logistical complexities. You get to a point of diminishing returns where you have a very large sample that will detect such small effects that they’re meaningless in a practical sense.

The takeaway here is that researchers must exercise caution and not rely solely on a large sample size to safeguard the reliability and validity of their results. An adequate amount of data must be paired with an appropriate sampling method, a robust study design, and meticulous execution to truly understand and accurately represent the phenomena being studied.

## Sample Size Calculation

Statisticians have devised quantitative ways to find a good sample size. You want a large enough sample to have a reasonable chance of detecting a meaningful effect when it exists but not too large to be overly expensive.

In general, these methods focus on using the population’s variability. More variable populations require larger samples to assess them. Let’s go back to the cookie example to see why.

If all cookies in a population are identical (zero variability), you only need to sample one cookie to know what the average cookie is like for the entire population. However, suppose there’s a little variability because some cookies are cooked perfectly while others are overcooked. You’ll need a larger sample size to understand the ratio of the perfect to overcooked cookies.

Now, instead of just those two types, you have an entire range of how much they are over and undercooked. And some use sweeter chocolate chips than others. You’ll need an even larger sample to understand the increased variability and know what an average cookie is really like.

Hmm. Lots of cookie tasting!

Power and sample size analysis quantifies the population’s variability. Hence, you’ll often need a variability estimate to perform this type of analysis. These calculations also frequently factor in the smallest practically meaningful effect size you want to detect, so you’ll use a manageable sample size.

To learn more about determining how to find a sample size, read my following articles:

## Sample Size Summary

Understanding the implications of sample size is fundamental to conducting robust statistical analysis. While larger samples provide more reliable and precise estimates, smaller samples can compromise the validity of statistical inferences.

Always remember that the breadth of your sample profoundly influences the strength of your conclusions. So, whether conducting a simple survey or a complex experimental study, consider your sample size carefully. Your research’s integrity depends on it.

Consequently, the effort to achieve an adequate sample size is a worthwhile investment in the precision and credibility of your research.

Alvaro says

Hi Jim, thanks for your post.

It’s clear that a small sample size could take to a type 2 error. But Could it put my study in risk to make a type 1 error? I mean, compared to a correct sample size based on proper calculations?

Jim Frost says

Hi Alvaro,

That’s a great question! The surprising answer is that increasing or decreasing the sample size actually does not affect the type 1 error rate! The reason why is because as you increase or decrease the sample size, the detectable effect size changes to maintain an error rate that equals your significance level. Controlling the false positives is built right into the equations and process.

So, if you’re studying a certain subject and you have a sample size of 10 or 1000, your false positive error rate is constant. However, as you mention, the type 2, false negative error will decrease as sample size increases.

John Holmes says

A problem which ought to be considered when running an opinion poll: Is the group of people who consent to answer strictly comparable to the group who do not consent?. If not, then there may be systematic bias

Jesse says

When I used survey data, we had a clear, conscious sampling method and the distinction made sense. However, with other types of data such as performance or sales data, I’m confused about the distinction. We have all the data of everyone who did the work, so by that understanding, we aren’t doing any sampling. However, is there a ‘hidden’ population of everyone who could potentially do that work? If we take a point in time, such as just first quarter performance, is that a sample or something else? I regularly see people just go ahead and apply the same statistics to both, suggesting that this is a ‘sample’, but I’m not sure what it’s a sample of or how!