Introduction to Data Analysis and R: Standard Error of the Mean

The standard error of the mean (SEM) is a measurement that indicates how accurate your estimate of the sample mean is likely to be as compared to the population mean. The larger your sample size, the more accurate your estimation. Another fairly straightforward calculation, it can be expressed as:

where s is the standard deviation of the sample, and n is the total number of observations for the sample.

Confidence limits

Confidence limits are a similar measure that serve the same purpose as the standard error, but which are outside the scope of this module. I mention them here so you are aware of the potential for confusion if you're not careful and explicit when reporting your results. Perhaps because confidence limits and SEM are so similar, they are often reported in the same format ("meansomething", where "something" is either the confidence limits or the SEM). However, confidence limits are obtained by multiplying the SEM by a number called the t-value, which is determined by probability and degrees of freedom. Confidence limits are approximately double the numerical value of the SEM, so unless you explicitly note which one you calculated, you risk miscommunicating your results.

Supplemental Readings

(Don't hesitate to use the player controls to pause, rewind, slow down the video as needed! A thorough understanding of the concepts is vastly preferable to just speeding through.)

You will be using the "weatherData" dataset (linked below) to answer the questions in this quiz.