What Is Statistical Significance? A Clear Explanation of p-Values, Significance Levels, and the Null Hypothesis
A practical explanation of what “statistically significant” means in research papers and survey analysis, without relying on p-values alone.
When reading statistical analysis results, many people first check whetherthe p-value is below 0.05.However, statistical significance does not itself mean that “the difference is large,” “the study is correct,” or “the finding is clinically meaningful.”
Statistical significance is a criterion used in hypothesis testing to judge whether observed data would be unusually difficult to explain by chance alone. In research papers, undergraduate theses, master’s theses, nursing research, psychological surveys, education research, and marketing studies, it is important to understand this meaning correctly.
Although the p-value is an important index,conclusions should not be based on the p-value alone; effect size, confidence intervals, study design, and sample size should also be considered..
- • What is statistical significance?
- • Understanding the null and alternative hypotheses
- • Relationship between the p-value and significance level
- • Type I and Type II errors also matter
- • Look at confidence intervals and effect sizes, not just p-values
- • Points to consider when reporting statistical significance in a paper
- • Frequently Asked Questions
- • Summary
What is statistical significance?
Statistical significance refers to a state in statistical hypothesis testing in which an observed result is judged difficult to explain by random variation alone. Conventionally, if the significance level is set at 5% and p < 0.05, the result is described as “statistically significant.”
However, this does not mean that “the result is absolutely correct.” It means only that, under the specified hypotheses and assumptions, the observed result would be difficult to explain by chance alone.
Understanding the null and alternative hypotheses
What is the null hypothesis?
The null hypothesis is the initial hypothesis tested, such as “there is no difference,” “there is no association,” or “there is no effect.” For example, when comparing the means of Group A and Group B, the null hypothesis is that “the population means of Group A and Group B do not differ.”
What is the alternative hypothesis?
The alternative hypothesis is the hypothesis opposed to the null hypothesis. In a comparison of means, it would be that “the population means of Group A and Group B differ.” Hypothesis testing examines whether there is sufficient evidence to reject the null hypothesis.
Relationship between the p-value and significance level
The p-value indicates the probability, assuming the null hypothesis is true, of obtaining a result as extreme as or more extreme than the observed data. The smaller the p-value, the less likely the observed result would be under the null hypothesis.
The significance level is the criterion used to reject the null hypothesis. Common levels are 5% or 1%. When the p-value is smaller than the significance level, the null hypothesis is rejected and the result is judged statistically significant.
| p＜0.05 | Often judged statistically significant at the 5% level |
|---|---|
| p＜0.01 | Judged statistically significant at the 1% level and sometimes treated as stronger evidence |
| p≧0.05 | Often described as “not statistically significant,” but this does not prove that there is no effect |
Type I and Type II errors also matter
A Type I error occurs when a difference is concluded to exist even though no true difference exists. Setting the significance level at 5% can also be understood as allowing this type of error at a rate of up to 5% under the testing framework.
A Type II error occurs when no difference is concluded even though a true difference exists. Type II error is more likely to be a concern in studies with a small number of cases or a small sample size.
Look at confidence intervals and effect sizes, not just p-values
In research papers, it is desirable to report not only p-values but also quantities such as mean differences, odds ratios, correlation coefficients, effect sizes, and 95% confidence intervals.
For example, even if the p-value is statistically significant, a very small effect size may have little practical or clinical importance. Conversely, even if the p-value is slightly above 0.05, effect sizes and confidence intervals may still provide important research implications.
Points to consider when reporting statistical significance in a paper
In papers and reports, do not stop at stating that “there was a significant difference” or “there was no significant difference.” Report which statistical test was used, the p-value, and the magnitude of the effect.
Rather than pasting raw output from SPSS, EZR, R, or other software, it is important to write the results in a form that addresses the research objective.
Frequently Asked Questions
Q1. If p < 0.05, does that mean the study was successful?
Not necessarily. Statistical significance is only one piece of evidence and should be evaluated together with the research objective, effect size, confidence interval, sample size, and study design.
Q2. Does p ≥ 0.05 mean the result has no meaning?
Not necessarily. An insufficient sample size, large variability, or the value of the study as exploratory research should also be considered.
Q3. Does “no significant difference” mean there is no difference?
Strictly speaking, it means that the study could not conclude that a difference exists. It does not prove that no difference exists.
Summary | Statistical significance is a starting point for reading research findings
Statistical significance is an important criterion in research and academic papers, but it does not determine the value of a finding based on the p-value alone.
Understanding the null hypothesis, alternative hypothesis, significance level, Type I error, Type II error, confidence intervals, and effect sizes together makes it possible to interpret statistical analysis results more accurately.
