The Use of Asterisks in Data Analysis and Research

Introduction

Asterisks (*, **, ***) are commonly used in statistical tables to communicate the statistical significance of research findings. They provide a quick way for readers to identify results that meet specified significance levels without having to examine every p-value individually.

Asterisks are particularly common in tables reporting correlation analysis, regression analysis, t-tests, ANOVA, and other statistical procedures. Statistical software packages such as SPSS, Stata, R, and many academic reporting systems use or support asterisk notation.

However, the meaning of an asterisk is not universal. Researchers must always provide a table note or explanation showing what each asterisk represents.

What Does an Asterisk Mean in Data Analysis?

An asterisk next to a statistical result usually indicates that the result is statistically significant at a specified significance level.

A commonly used convention is:

For example, a table might report:

The table note could state:

**Note: *p < 0.05, **p < 0.01, *p < 0.001.

The asterisks therefore allow readers to identify statistically significant results quickly.

Asterisks in Correlation Analysis

Asterisks are frequently used when presenting Pearson correlation coefficients.

For example:

If the table note states:

**Note: p < 0.01 (2-tailed).

the two asterisks indicate that the correlation between study hours and academic performance is statistically significant at the 1% level.

The asterisks do not indicate the strength of the correlation. The coefficient itself—0.642 in this example—indicates the direction and magnitude of the association.

Thus:

• 0.642** = the correlation coefficient is 0.642
• ** = the associated p-value meets the specified significance criterion

These are two different pieces of information.

Asterisks in Regression Analysis

Asterisks are also commonly used in regression tables.

Consider the following hypothetical results:

A table note might state:

**Note: *p < 0.05, **p < 0.01, *p < 0.001.

This means the coefficients for education and training meet the specified statistical significance thresholds, while the coefficient for experience does not.

However, researchers should not interpret the number of asterisks as the size or importance of an effect. For example, a coefficient marked *** is not necessarily more practically important than a coefficient marked *.

Asterisks and P-Values

The asterisk system is essentially a shorthand for p-values.

Suppose a study produces the following results:

• p = 0.032
• p = 0.007
• p = 0.0004
• p = 0.284

Using the convention above:

The system makes large statistical tables easier to read.

What Does “Statistically Significant” Mean?

A statistically significant result generally means that, under the statistical model and null hypothesis being tested, the observed result would be relatively unlikely if the null hypothesis were true.

For example, if a study reports:

r = 0.58, p = 0.003

and uses the conventional 5% significance level, the result is statistically significant because:

0.003 < 0.05

The researcher may therefore reject the null hypothesis of no linear correlation under the assumptions of the test.

However, statistical significance should not automatically be interpreted as practical significance, substantive importance, or causation.

Asterisks Do Not Measure Effect Size

This is one of the most important points in interpreting statistical tables.

Consider two hypothetical findings:

• Finding A: r = 0.12, p < 0.001
• Finding B: r = 0.65, p = 0.04

Finding A could have more asterisks despite having a much smaller correlation coefficient.

This can happen because statistical significance is influenced by factors such as sample size, variability, and the magnitude of the effect.

Therefore, researchers should report and interpret the actual effect size or coefficient rather than relying solely on asterisks.

Asterisks in SPSS Output

SPSS commonly uses asterisks in correlation matrices.

For example:

SPSS commonly provides a note such as:

Correlation is significant at the 0.01 level (2-tailed).

The researcher can then reproduce the appropriate table note when transferring the results into a thesis, dissertation, journal article, or research report.

Asterisks in Stata

Stata is also commonly used to present regression results with significance stars.

A regression table may appear conceptually as:

A corresponding note might be:

Standard errors in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001.

The exact significance-star convention can vary depending on the command or table-generation method used.

Asterisks and Hypothesis Testing

Asterisks are particularly useful when researchers are testing hypotheses.

Suppose a researcher proposes:

H₀: There is no significant relationship between teacher support and student academic performance.

H₁: There is a significant relationship between teacher support and student academic performance.

Suppose the analysis produces:

r = 0.481, p = 0.002

Under a 5% significance criterion:

p = 0.002 < 0.05

The relationship is statistically significant.

In a table, the researcher might present:

Teacher Support = 0.481**

with the table note explaining the meaning of the two asterisks.

The researcher should still consider the direction, magnitude, confidence interval, sample size, study design, and theoretical context when interpreting the finding.

One Asterisk Does Not Mean “Important”

A common mistake among students and inexperienced researchers is to assume that:

*** = very important
** = moderately important
* = slightly important

That interpretation is incorrect.

The asterisks normally indicate different statistical significance thresholds, not levels of practical importance.

For example:

• * generally means p < 0.05
• ** generally means p < 0.01
• *** generally means p < 0.001

They do not tell the reader whether an effect is large or small.

Asterisks and Confidence Intervals

Modern research reporting should not rely exclusively on significance stars. Where appropriate, researchers should also report confidence intervals.

For example:

B = 0.452, 95% CI [0.210, 0.694], p = 0.001

This provides considerably more information than:

B = 0.452*.

The coefficient describes the estimated effect, the confidence interval communicates uncertainty around the estimate, and the p-value provides information about compatibility with the null hypothesis under the specified statistical model.

Asterisks and Multiple Comparisons

Researchers should also be careful when conducting many statistical tests.

Suppose a researcher tests 30 different relationships and applies a 5% significance threshold to every test. Some statistically significant findings may occur by chance alone.

Therefore, when many hypotheses are tested, researchers may need to consider procedures such as:

• Bonferroni adjustment
• Holm adjustment
• False discovery rate procedures

The use of asterisks does not solve the problem of multiple testing. The underlying statistical analysis must be appropriate.

Asterisks in Academic Tables

When preparing a thesis or journal article, researchers should clearly explain their notation.

A typical table note could be:

Note: *p < 0.05, **p < 0.01, ***p < 0.001.

Alternatively, researchers can report exact p-values where appropriate.

For example:

This approach provides more precise information than relying entirely on stars.

Common Mistakes When Using Asterisks

1. Failing to explain the notation

A table containing *, **, or *** should include a note explaining what they mean.

2. Treating stars as effect size

Asterisks indicate significance thresholds, not the strength of an association or the magnitude of an effect.

3. Claiming causation

A statistically significant correlation marked with *** does not establish that one variable causes another.

4. Ignoring the actual p-value

Where precision is important, researchers should consider reporting the actual p-value rather than only significance stars.

5. Assuming all software uses exactly the same convention

Different software packages, commands, journals, and researchers may use different thresholds. The table note should therefore always define the convention being used.

Best Practices for Using Asterisks

Researchers should follow several principles when using significance stars:

1. Define the asterisks clearly.
2. Report the coefficient or effect size, not just the stars.
3. Report exact p-values where useful.
4. Consider confidence intervals.
5. Distinguish statistical significance from practical significance.
6. Avoid interpreting stars as evidence of causation.
7. Consider multiple-testing issues when many hypotheses are examined.
8. Follow the reporting requirements of the target journal, university, or research institution.

Conclusion

Asterisks provide a convenient method for communicating statistical significance in research tables. The commonly used notation—*, **, and ***—allows readers to quickly identify results meeting specified p-value thresholds.

However, asterisks should be treated as supplementary notation rather than a substitute for proper statistical reporting. A good research report should provide the relevant coefficient or effect size, p-value, and, where appropriate, confidence interval and sample size.

Most importantly, researchers should remember that statistical significance is not the same as practical significance, and neither establishes causation by itself. Proper interpretation requires consideration of the research question, study design, effect size, uncertainty, assumptions, and substantive context.