<p>Understanding the effect of heterogeneity is fundamental to numerous fields. In community ecology, classical theory postulates that habitat heterogeneity determines niche dimensionality and drives biodiversity. However, disparate heterogeneity-diversity relationships have been empirically observed, generating increasingly complex theoretical developments. Here we show that spurious heterogeneity-diversity relationships and subsequent theories arise as artifacts of heterogeneity measures that are mean-biased for bounded continuous variables. To solve this, we derive an alternative mean-independent measure of heterogeneity for beta and gamma distributed variables that disentangles statistical dispersion from mean. Using the mean-independent measure of heterogeneity, true monotonic positive heterogeneity-diversity relationships, consistent with classical theory, are revealed in data previously presented as evidence for both hump-shaped heterogeneity-diversity relationships and theories of an area-heterogeneity trade-off for biodiversity. This work sheds light on the source of conflicting results that have hindered understanding of heterogeneity relationships in broader ecology and numerous other fields. The mean-independent measure of heterogeneity is provided as a solution, essential for understanding true mean-independent heterogeneity relationships in wider research.</p>