What to Do When the Means Differ but ANOVA or T-Test Shows No Statistical Significance

This situation often confuses and frustrates many researchers — especially when the data clearly show that “The means of each group are different, yet the ANOVA or T-Test results show no statistical significance (p > .05).”

Why does this happen, even when the averages appear visibly different in the tables?Let’s explore the possible reasons and how you can address them effectively.

What to Do When the Means Differ but ANOVA or T-Test Shows No Statistical Significance

Possible Reasons Why the Means Differ but the Test Is Not Significant

1. High Within-Group Variance

Even if the means differ between groups, if there is a high variation within each group (for example, high Standard Deviation), the statistical test may show no significant difference — because the variation is mainly due to within-group fluctuations, not the actual difference between groups.

Solution:Check the Standard Deviation (SD) for each group.

If the variability differs widely, consider:

• Increasing the sample size to stabilize the variance, or

• Using statistical methods that handle unequal variances, such as Welch’s ANOVA or Welch’s t-test.

2. Small Sample Size (Low Statistical Power)

When sample sizes are small, the statistical test often lacks sufficient power to detect real differences. As a result, even visible differences in means may not reach statistical significance.

Solution:

• Increase the number of participants in each group.

• Alternatively, use non-parametric tests such as Mann-Whitney U Test or Kruskal-Wallis Test, which are suitable for small or non-normally distributed samples.

3. Non-Normal Distribution of Data

Both ANOVA and T-Test assume that the data are normally distributed. If the data are skewed or contain extreme values (outliers), the assumptions are violated, and the p-value may not be reliable.

Solution:

• Test the normality of the data using the Shapiro-Wilk Test or Kolmogorov-Smirnov Test.

• If the data are not normal, switch to non-parametric analysis instead.

4. The Difference in Means May Not Be Practically Significant

Sometimes, the numeric difference between means (e.g., 3.40 vs. 3.46) may look different but is too small to be statistically meaningful, especially when data variation is large or sample sizes are uneven.

Solution:Evaluate both the effect size and the p-value to determine whether the observed difference has practical (real-world) significance, not just statistical.

5. Presence of Outliers or Extreme Values

Outliers can heavily influence the mean and distort statistical results.If these are not checked or managed properly, ANOVA or T-Test outcomes may not represent the true pattern of the data.

Solution:

• Use Boxplots to identify outliers.

• Consider using the median instead of the mean or applying data transformation (e.g., log or z-score) to normalize the data before reanalysis.

  
  

Why You Should Use Data Investigator

Interpreting non-significant ANOVA or T-Test results — even when means differ — requires both theoretical understanding and practical experience in statistical analysis.

With over 15 years of expertise, Data Investigator provides complete support for students, researchers, and organizations, including:

• Reviewing data accuracy and verifying statistical assumptions

• Conducting analyses using SPSS

• Providing detailed interpretation and explanation of statistical findings

• Issuing a Certificate of Statistical Analysis for official submission

• Guiding you in writing clear, professional Chapter 4 and 5 reports that meet academic standards

Whether you are a graduate student, medical researcher, or government agency,Data Investigator ensures your statistical analysis is accurate, credible, and publication-ready.

For more information:

E-mail: info@datainvestigatorth.com

Line: @datainvestigator