When psychologists say that their results are statistically significant, they mean that the results: A. have important practical applications. B. have important implications for scientific theory. C. are unlikely to be due to the fluctuations of chance. D. are all of the above.

Statistical significance is a measure used by researchers to help determine if the results of an experiment or study are likely to be due to an actual relationship between the variables being studied and not just due to random chance. In other words, if the results are statistically significant, it means that the probability of obtaining such results by chance alone is very low.

A. have important practical applications: Statistical significance doesn't necessarily indicate that the results have practical importance. It could be a small, significant effect that doesn't have practical implications. B. have important implications for scientific theory: While statistically significant results may support or refute a scientific theory, significance alone doesn't imply that they have a direct theoretical impact. C. are unlikely to be due to the fluctuations of chance: This option correctly describes the concept of statistical significance. If results are statistically significant, it means that the findings are unlikely to be due to random chance. D. are all of the above: As we evaluated each option and determined that only option C is correct, option D is not correct.

Based on our evaluation of each option, the correct answer is option C: "are unlikely to be due to the fluctuations of chance."