Overview
This lecture explains Standard Error of the Mean (SEM), how to calculate it, how it's used in AP Biology, and how to interpret data significance using error bars.
Understanding Bar Graphs and Data Variation
- Bar graphs often only show averages, not the full data set or variability.
- Individual data points provide more information about the spread of data than averages alone.
- Error bars on graphs visually represent data variability and help indicate the reliability of averages.
Standard Error of the Mean (SEM)
- SEM measures how well a sample mean estimates the true population mean.
- It is calculated by dividing the standard deviation by the square root of the sample size (n).
Interpreting Error Bars
- Error bars show the range within which the actual mean could fall if the experiment was repeated.
- If error bars between two groups overlap, the difference is not statistically significant.
- If error bars do not overlap, the difference is considered statistically significant.
Graphing Error Bars in AP Biology
- Use "two standard errors of the mean" (2 SEM) above and below the sample mean to create error bars.
- 2 SEM provides a 95% confidence interval for the data—a common standard in biology.
Significance of Error Bar Size
- Smaller error bars: greater significance, usually due to larger sample size or less variation.
- Larger error bars: less significance, usually due to small sample size or high variation.
Calculating and Graphing SEM
- SEM = standard deviation ÷ √n.
- For the given example: standard deviation = 1.58, n = 5, SEM = 0.7.
- When graphing, plot two SEM (+1.4 and -1.4) from the mean to show the error range.
- Each dataset will have its own SEM based on its unique data.
Key Terms & Definitions
- Standard Error of the Mean (SEM) — A measure of how accurately a sample mean estimates the population mean.
- Error Bars — Graphical lines that represent data variability and uncertainty around the mean.
- Confidence Interval — The probability range (95% in AP Bio) that a population parameter lies within the error bars.
Action Items / Next Steps
- Practice calculating SEM and graphing error bars for sample datasets.
- Review the difference between standard deviation and standard error.