What is Standard Error?

In order to perform effective hypothesis testing, one of the concepts that researchers must be entirely comfortable with is  standard error.

Standard error is often confused with standard deviation, as both metrics are measures of spread or range. The higher the number, the more spread out the data being evaluated is.

While standard error and standard deviation are terms with similar meanings, there is one key difference to keep in mind.

While the standard error relies on statistics from sample data, standard deviations use parameters from population data.

Statistics vs. Parameters

In order to understand standard error fully, it’s best to establish a thorough understanding of the differences between statistics and parameters. 

Afterall, statistics and parameters are very similar concepts.

Statistics and parameters are both used to describe groups. However, a statistic describes a sample, while parameters describe an entire population.

For example, if a group of researchers randomly polls voters for a presidential election, and the researchers find that 35 percent of the population plans to vote for one candidate over another, that is a statistic because the researchers only asked a sample of the population who they are voting for. 

The researchers could then use this statistic to calculate an assumption of what the population is likely to do.

Use this two-step process to tell the difference between a statistic and a parameter:

Step 1: Ask yourself, “Is this a fact describing the entire population of interest?”

With very small populations, you’ll usually be working with a parameter since the groups of interest are small enough to measure.

Step 2: Ask yourself, “Is this clearly a fact about a very large population?”

If the answer is yes, you most likely are working with a statistic.

How to Calculate Standard Error

The method used to find standard error depends on what statistic you need. Use the following table to identify the formula needed to calculate standard error.

Statistic (Sample) Formula for Standard Error
Sample mean = s / sqrt (n)
Sample proportion = sqrt [p (1-p) / n)]
Difference between means sqrt [s21/n1 + s22/n2]
Difference between proportions = sqrt [p1(1-p1)/n1 + p2(1-p2)/n2]