Statistical Annotations in Figures
By Dr. Zubair Khalid, DVM, MS, PhD ·
Quick Answer
- Statistical annotations in figures use asterisks, letters, and brackets to show whether observed differences are likely due to chance or reflect a real effect.
- Read the figure legend first to identify which annotation system the authors used, then match symbols to the stated significance threshold before interpreting any comparison.
- Annotations only describe statistical significance, not practical importance, so a small p-value does not prove that a finding matters in real-world terms.
What Statistical Annotations Mean in Published Figures
Scientific figures compress large amounts of data into visual form. The asterisks, brackets, letters, and symbols that appear above bars, points, or box plots are a shorthand system for reporting statistical significance. These annotations tell the reader whether the difference between two groups, the relationship between two variables, or the effect of a treatment is statistically meaningful or could plausibly be explained by random variation.
Statistical significance is a probability statement. When a figure shows an asterisk above a comparison, the authors are reporting that the probability of observing a difference at least this large if no true difference existed falls below a chosen threshold. The most common threshold in biomedical research is 0.05, meaning there is less than a 5 percent chance the result occurred by random variation alone. Other thresholds include 0.01 and 0.001, which represent stricter standards of evidence.
The annotation system is a convention, not a universal law. Different journals, disciplines, and software programs use different symbols. A figure from a psychology journal may use one asterisk for p less than 0.05, while a figure from a genetics paper may use letters or a different symbol set. The only reliable way to interpret any figure is to read the legend and the methods section that accompany it.
Why Readers Misinterpret Annotations
Readers commonly make three errors when interpreting statistical annotations. The first error is assuming that all asterisks mean the same thing. A single asterisk in one figure may indicate a p value below 0.05, while in another figure it may indicate a p value below 0.01. The threshold is set by the authors and reported in the figure legend or the methods section.
The second error is treating significance as a measure of effect size. A statistically significant result can be tiny in practical terms. A drug that lowers blood pressure by one millimeter of mercury can be statistically significant in a large study but clinically irrelevant. The annotation only tells the reader that the result is unlikely to be due to chance. It does not tell the reader how large the effect is or whether the effect matters.
The third error is ignoring the difference between tests. An annotation may indicate a comparison between two groups, a comparison among several groups, or a correlation between two continuous variables. The statistical test used determines what the annotation means. A figure that compares three treatment groups may use a different annotation system than a figure that compares two groups.
At a Glance
| Symbol or Pattern | Common Meaning | Typical Threshold | What to Check |
|---|---|---|---|
| Single asterisk | Statistically significant | p less than 0.05 | Confirm the threshold in the figure legend |
| Double asterisk | More stringent significance | p less than 0.01 | Confirm the threshold in the figure legend |
| Triple asterisk | Highly stringent significance | p less than 0.001 | Confirm the threshold in the figure legend |
| Lowercase letters above bars | Pairwise comparison groups | Varies by journal | Match letters to the comparison table |
| Brackets with asterisks | Specific group comparison | Varies by test | Identify which groups are being compared |
| ns or NS | Not significant | p greater than the chosen threshold | Check whether the threshold is stated |
How to Read a Figure with Annotations
Step 1: Read the Figure Legend
The figure legend is the first place to look. It should state which statistical test was used, what the symbols mean, and what thresholds were chosen. A well-written legend will say something like "Data are shown as mean plus or minus standard deviation. Asterisks indicate p values from a two-tailed Student t-test. Single asterisk p less than 0.05, double asterisk p less than 0.01." If the legend does not provide this information, the figure is incomplete and the reader should treat the annotations with caution.
Step 2: Identify the Comparison Structure
Look at the brackets or lines above the data. A bracket that spans two bars indicates a direct comparison between those two groups. A bracket that spans three bars may indicate an overall comparison or a set of pairwise comparisons. The legend should clarify which comparisons were tested and which test was used.
Step 3: Match Symbols to Thresholds
Once the legend has been read, match each symbol to its threshold. A single asterisk may mean p less than 0.05, a double asterisk p less than 0.01, and a triple asterisk p less than 0.001. Some figures use letters instead of asterisks. In a letter system, bars that share the same letter are not significantly different from each other, while bars with different letters are significantly different. This system is common in agricultural and ecological research.
Step 4: Consider the Test Type
The type of statistical test affects the meaning of the annotation. A t-test compares two groups. An analysis of variance, or ANOVA, compares three or more groups and requires a post-hoc test to identify which specific groups differ. A figure that reports ANOVA results may show an overall p-value in the legend and then use letters or asterisks to indicate pairwise comparisons. The reader should know which test was used to interpret the annotation correctly.
Step 5: Check the Sample Size
The sample size affects the reliability of the significance test. A small sample can produce a significant result by chance, and a large sample can produce a significant result for a trivial difference. The figure legend or the methods section should state the sample size for each group. If the sample size is not reported, the reader cannot fully assess the reliability of the annotation.
Common Annotation Systems
Asterisk System
The asterisk system is the most common in biomedical and life-science figures. One asterisk indicates p less than 0.05, two asterisks indicate p less than 0.01, and three asterisks indicate p less than 0.001. Some figures use four asterisks for p less than 0.0001, but this is less common. The system is simple and widely recognized, but the thresholds are not universal. Always confirm the threshold in the legend.
Letter System
The letter system is common in agricultural, ecological, and animal science research. Bars that share a letter are not significantly different. Bars with different letters are significantly different. This system is useful for figures with many groups because it avoids the clutter of multiple brackets and asterisks. The reader must match letters carefully, especially when the figure has many bars.
Bracket System
The bracket system uses horizontal lines with vertical ticks that span the groups being compared. An asterisk above the bracket indicates the significance of that specific comparison. This system is useful for figures that show only a few comparisons among many groups. The reader must identify which groups are spanned by each bracket.
Symbol System
Some figures use symbols such as daggers, double daggers, or section marks to indicate significance. These symbols are less common and are usually defined in the legend. The reader should not assume that a symbol means the same thing in a different figure.
How to Interpret Significance in Context
Statistical Significance versus Practical Importance
A statistically significant result is not necessarily important. The p-value tells the reader the probability of the result occurring by chance, but it does not tell the reader the size of the effect or whether the effect is meaningful in practice. A large study can detect a tiny difference as significant, and a small study may fail to detect a large difference. The reader should look at the magnitude of the difference and the confidence interval to assess practical importance.
Confidence Intervals and Annotations
Confidence intervals provide more information than a p-value alone. A confidence interval shows the range of plausible values for the true effect. If the confidence interval excludes zero, the result is statistically significant. If the interval is wide, the estimate is imprecise. Figures that show confidence intervals as error bars allow the reader to assess both significance and precision. An annotation that indicates significance should be consistent with the confidence interval. If the annotation says significant but the confidence interval includes zero, the figure is inconsistent and should be examined carefully.
Multiple Comparisons and the Risk of False Positives
When a figure shows many comparisons, the risk of false positives increases. If a researcher performs 20 comparisons and uses a threshold of p less than 0.05, the expected number of false positives is one. Some figures adjust for multiple comparisons, and some do not. The legend should state whether the p-values were adjusted. If the legend does not mention adjustment, the reader should be cautious about interpreting individual asterisks.
How to Create Figures with Clear Annotations
Choose a Consistent System
When creating a figure, choose one annotation system and use it consistently. The asterisk system is the most widely recognized and is a safe choice for most audiences. The letter system is useful for figures with many groups. The bracket system is useful for figures with a few specific comparisons. The chosen system should be defined in the legend.
Define the Thresholds in the Legend
The legend must state the thresholds for each symbol. A legend that says "asterisks indicate significance" is incomplete. The legend should say "p less than 0.05" or "p less than 0.01" for each symbol. This allows the reader to interpret the figure without guessing.
Report the Test Used
The legend should state the statistical test used for each comparison. A t-test, an ANOVA, a chi-square test, or a regression all produce p-values, but the meaning of the p-value depends on the test. The legend should also state whether the p-values were adjusted for multiple comparisons.
Show the Sample Size
The figure or the legend should state the sample size for each group. This information is essential for assessing the reliability of the significance. A figure that does not report sample sizes is incomplete.
Use Error Bars That Match the Test
The error bars should match the statistical test. Standard deviation bars show the spread of the data. Standard error bars show the precision of the mean. Confidence intervals show the range of the true effect. The legend should state which type of error bar is used. A reader cannot interpret the significance from the error bars alone, but the error bars provide context for the annotation.
Common Failure Patterns in Figure Annotation
Missing Legends
A figure without a legend is incomplete. The reader cannot interpret the asterisks or brackets without knowing the thresholds and the test. This is a common failure in drafts and in some published figures. The reader should treat the annotations as uninterpretable and request the missing information.
Inconsistent Thresholds
A figure that uses one asterisk for p less than 0.05 in one panel and p less than 0.01 in another panel is misleading. The thresholds should be consistent within a figure and within a paper. The reader should check the legend for each panel.
Unadjusted Multiple Comparisons
A figure that shows many comparisons without adjusting the p-values can mislead the reader. The probability of a false positive increases with the number of comparisons. The legend should state whether the p-values were adjusted. If the legend does not mention adjustment, the reader should be cautious.
Confusing Error Bars
A figure that uses standard error bars but labels them as confidence intervals is misleading. The reader should check the legend to see which type of error bars is used. The error bars should match the test statistic and the significance annotation.
Missing Sample Sizes
A figure that does not report the sample size cannot be fully interpreted. The significance of a result depends on the sample size. The reader should look for the sample size in the legend or the methods section.
How to Use Annotations in Your Own Work
For Students and Researchers
When you read a figure, always read the legend first. Identify the test, the threshold, and the error bar type. Then look at the annotations and interpret them in context. When you create a figure, follow the same standards. Define the thresholds, report the test, and show the sample size. This practice makes your figures transparent and interpretable.
For Laboratory Staff
When you present data, use a consistent annotation system. The asterisk system is the most widely recognized. Define the thresholds in the legend. Show the sample size. If you use multiple comparisons, state whether the p-values were adjusted. This practice helps your audience interpret your results correctly.
For Animal Owners and Life-Science Professionals
When you read a figure in a product label, a research summary, or a veterinary report, look for the legend. The annotation tells you whether the result is likely due to chance. It does not tell you whether the result is important. Consider the size of the effect and the context of the study before making a decision.
The Role of Reporting Guidelines
Reporting guidelines help authors present their research clearly and completely. The EQUATOR Network provides a collection of reporting guidelines for different study types. These guidelines often specify how statistical results should be reported, including the use of annotations in figures. When you read a paper, you can check whether the authors followed the relevant reporting guideline. When you write a paper, you can use the guideline to ensure your figures are complete and interpretable. The EQUATOR Network is a useful starting point for selecting the appropriate guideline for your study type.
The Role of Data Management in Reproducible Figures
The reliability of a figure depends on the data behind it. The National Institutes of Health data management and sharing policy describes expectations for planning and managing research data. A figure that is based on well-managed data is more likely to be reproducible and accurate. When you read a figure, you can consider whether the data are available for verification. When you create a figure, you should ensure that your data is organized and documented so that the figure can be reproduced.
The Role of Researcher Identity in Figure Interpretation
The identity of the researcher who created the figure matters for accountability. ORCID provides a persistent identifier for researchers, which links them to their publications and data. When you read a figure, you can identify the researcher who created it and check their other work. When you create a figure, you can use your ORCID to link your work to your identity. This practice supports accountability and transparency in research.
The Role of Publication Ethics in Figure Reporting
Publication ethics govern how research is reported. The Committee on Publication Ethics core practices cover authorship, peer review, data, conflicts of interest, and misconduct. A figure that is misleading or that misrepresents the data is a violation of publication ethics. When you read a figure, you can assess whether the annotation is consistent with the data. When you create a figure, you should ensure that the annotation accurately represents the statistical analysis.
The Role of Funding and Grants in Research Quality
The quality of research is often affected by the funding and review process. The National Institutes of Health grants and funding pages describe the application and review process. The review process is designed to ensure that funded research is rigorous and well-designed. When you read a figure, you can consider whether the research was funded and reviewed. When you apply for funding, you can use the NIH resources to understand the review criteria.
The Role of Research Methods in Figure Interpretation
The research methods used to collect the data affect the meaning of the figure. The National Library of Medicine books provide a gateway to authoritative biomedical references on research methods. A figure that is based on a well-designed study is more reliable than a figure that is based on a flawed study. When you read a figure, you should consider the study design and the methods used to collect the data.
How to Assess the Reliability of a Figure
Check the Source
The source of the figure affects its reliability. A figure from a peer-reviewed journal is more reliable than a figure from an unverified website. The journal should have a peer review process that checks the statistical analysis and the figure presentation.
Check the Legend
The legend should provide the test, the threshold, and the sample size. If the legend is incomplete, the figure is less reliable. The reader should look for the legend before interpreting the annotations.
Check the Data
The data behind the figure should be available for verification. The data management policy may require the data to be shared. If the data is not available, the figure is less reliable.
Check the Consistency
The annotation should be consistent with the data. If the annotation says significant but the confidence interval includes zero, the figure is an error. The reader should check the consistency of the annotation with the data.
Common Failure Patterns in Figure Creation
Failure to Define the Threshold
A figure that uses asterisks without defining the threshold is incomplete. The reader cannot interpret the annotation. The author should define the threshold in the legend.
Failure to Report the Test
A figure that does not report the statistical test is incomplete. The reader cannot interpret the annotation. The author should report the test in the legend.
Failure to Show the Sample Size
A figure that does not show the sample size is incomplete. The reader cannot assess the reliability of the significance. The author should show the sample size in the legend.
Failure to Adjust for Multiple Comparisons
A figure that does not adjust for multiple comparisons can mislead the reader. The author should state whether the p-values were adjusted.
Failure to Use Consistent Symbols
A figure that uses different symbols for the same threshold is confusing. The author should use a consistent symbol system.
Limitations of Statistical Annotations
Annotations Do Not Show Effect Size
The annotation shows the significance, not the size of the effect. A significant result can be small. The reader should look at the effect size and the confidence interval to assess the importance.
Annotations Do Not Show the Direction of the Effect
The annotation shows that the result is significant, but it does not show the direction of the effect. The reader should look at the data to see whether the effect is positive or negative.
Annotations Do Not Show the Clinical or Practical Importance
The annotation shows the statistical significance, but it does not show the practical importance. The reader should consider the context of the study and the size of the effect.
Annotations Are Only as Reliable as the Data
The annotation is only as reliable as the data behind it. If the data is flawed, the annotation is flawed. The reader should consider the study design and the data quality.
When to Escalate a Concern
If you are reading a figure and you notice a problem, you should consider whether to escalate the concern. The following situations warrant escalation:
Inconsistent Annotations
If the annotation is inconsistent with the data, you should ask the author for clarification. If the author cannot explain the inconsistency, you should consider whether the figure is reliable.
Missing Information
If the legend is missing the threshold, the test, or the sample size, you should ask the author for the missing information. If the author cannot provide the information, you should consider whether the figure is reliable.
Suspicious Data
If the data appears to be fabricated or manipulated, you should report the concern to the journal or the institution. The Committee on Publication Ethics core practices describe the process for handling misconduct.
Unclear Methods
If the methods are unclear, you should ask the author for the methods. If the methods are not available, you should consider whether the figure is reliable.
How to Apply This to Your Own Reading
When you read a figure, you should follow a consistent process. First, read the legend. Second, identify the test and the threshold. Third, identify the comparison groups. Fourth, interpret the annotation. Fifth, assess the effect size and the confidence interval. Sixth, consider the sample size and the study design. This process will help you interpret the figure correctly.
How to Apply This to Your Own Writing
When you write a figure, you should follow a consistent process. First, choose an annotation system. Second, define the thresholds in the legend. Third, report the test. Fourth, show the sample size. Fifth, adjust for multiple comparisons. Sixth, check the consistency of the annotation with the data. This process will help you create a clear and interpretable figure.
Frequently Asked Questions
What does an asterisk mean in a figure?
An asterisk in a figure indicates that the result is statistically significant. The specific threshold is defined in the figure legend. A single asterisk usually indicates a p value less than 0.05, but the threshold can vary. Always read the legend to confirm the threshold.
What does "ns" mean in a figure?
The abbreviation "ns" stands for "not significant." It indicates that the result is not statistically significant at the chosen threshold. The threshold is defined in the legend. The result may still be important, but the statistical test did not find a significant difference.
How do I know which threshold the asterisk refers to?
The threshold is defined in the figure legend. The legend should state the p value for each symbol. If the legend does not state the threshold, the figure is incomplete and the annotation cannot be interpreted.
What is the difference between a p value and an asterisk?
A p value is the probability of the result occurring by chance. An asterisk is a symbol that indicates the p value is below a threshold. The asterisk is a shorthand for the p value. The p value provides more information than the asterisk.
What is the difference between a significant and a non-significant result?
A significant result is a result that is unlikely to have occurred by chance. A non-significant result is a result that could have occurred by chance. The threshold for significance is defined by the researcher. The significance does not indicate the importance of the result.
How do I interpret a figure with letters instead of asterisks?
A figure with letters uses a letter system. Bars that share the same letter are not significantly different. Bars with different letters are significantly different. The legend should define the letter system.
What is the difference between a standard error and a standard deviation?
The standard deviation shows the spread of the data. The standard error shows the precision of the mean. The legend should state which type of error bar is used. The error bar type affects the interpretation of the significance.
How do I know if a figure is reliable?
A figure is reliable if the legend is complete, the test is reported, the sample size is shown, and the annotation is consistent with the data. The source of the figure should be a peer-reviewed journal. The data should be available for verification.
Using the Evidence
| Source | Best use in this topic | Important limitation |
|---|---|---|
| Research Methods Resources | official guidance | Check the linked page for current local requirements |
| EQUATOR Network | official guidance | Check the linked page for current local requirements |
| Core Practices | official guidance | Check the linked page for current local requirements |
Related Articles
- Statistical Significance
- Data Visualization for Biological Research: Choosing Figures That Preserve Meaning
- Multiple Comparisons: Controlling the Family-Wise Error Rate
- Inferential Statistical
- Statistical Analysis
References and Further Reading
- Research Methods Resources. National Library of Medicine.
- EQUATOR Network. EQUATOR Network.
- Core Practices. Committee on Publication Ethics.
- NIH Grants and Funding. National Institutes of Health.
- ORCID for Researchers. ORCID.
- Data Management and Sharing Policy. National Institutes of Health.
- NCBI Literature Resources. National Center for Biotechnology Information.
- PubMed. National Library of Medicine.
This article is educational and does not replace institutional policy, professional advice, or applicable safety and regulatory requirements.