What is what does it mean when error bars overlap?

Overlapping error bars are a visual cue in data analysis, particularly in graphical representations like bar charts or scatter plots. They indicate the potential for the underlying populations from which the data were sampled to have similar means or values. However, it's crucial to understand what overlapping error bars do not definitively prove.

Here's a breakdown:

• Potential Similarity, Not Proof: Overlapping error bars suggest that there might not be a statistically significant difference between the means being compared. It doesn't guarantee that the means are truly the same. There could still be a real difference that the analysis wasn't powerful enough to detect. Check out statistical%20significance for more information.

• Depends on Error Bar Type: The interpretation depends on what the error bars represent. Common types include:

  • Standard Deviation (SD): Overlap means there's a substantial amount of overlap in the data distributions themselves. It doesn't directly indicate whether the means are significantly different. Look up standard%20deviation for better understanding.

  • Standard Error of the Mean (SEM): Overlap suggests the true population means could be similar. SEM error bars are smaller than SD error bars. Overlap here indicates a closer probability of no significant difference. Read more on standard%20error%20of%20the%20mean.

  • Confidence Interval (CI): If the confidence intervals overlap, it suggests there is a chance the true means of the two populations are the same. Typically, 95% confidence intervals are used. Note that even with overlap, the means could still be significantly different. To find more about this confidence%20interval.

• Formal Statistical Tests Are Needed: The only way to definitively determine if there's a statistically significant difference between groups is to perform a formal statistical test, such as a t-test, ANOVA, or other appropriate test for your data. These tests consider not only the means and variability but also the sample sizes. Read more about statistical%20tests.

• Overlap is Not a Significance Test: Avoid using overlapping error bars as a substitute for proper hypothesis testing. They are only a visual guide. A lack of overlap, similarly, does not automatically guarantee statistical significance.

• Consider Sample Size: Large sample sizes can lead to smaller error bars, making it easier to detect even small differences as statistically significant. Conversely, small sample sizes can lead to wider error bars, making it harder to detect real differences. To better understand this case, check sample%20size.

In short, overlapping error bars provide a preliminary visual assessment but should always be followed by formal statistical testing to draw reliable conclusions.