7  Reporting Statistical Results

It is of absolute importance to avoid accidentally (or deliberately) providing incomplete information when reporting statistical results. This is because statistics like the mean, proportions, and p-values do not include the information on which they are based, leading to potential misinterpretation by readers of scientific reports (Herzog et al. 2019).

For example, imagine comparing the results of the Term 1 exam for two science classes using percentages. A poorly written report might say:

“75% of students in Class A achieved a mark above 50%, whereas only 60% of students in Class B achieved a mark above 50%.”

It sounds like Class A did better than Class B. However, would you still think the Class A result is more impressive if you found out that it was a small class with only 8 students, compared with Class B that was a large class with 30 students? If only one less student in Class A achieved above 50%, the Class A percentage would drop to 62.5%, almost the same as Class B. Informed assessment of the reported results cannot be made without the full information. So, to avoid the issue of incomplete information,

always include the full information when reporting statistical results.

Here is an example from Navarro, “12.1.9 report the results of the test”, (Navarro 2019) that demonstrates how to report the results of a statistical test with full information.

“Of the 200 participants in the experiment, 64 selected hearts for their first choice, 51 selected diamonds, 50 selected spades, and 35 selected clubs. A chi-square goodness of fit test was conducted to test whether the choice probabilities were identical for all four suits. The results were significant (χ2(3)=8.44,p<.05), suggesting that people did not select suits purely at random.”

Note that,