Statistical test can often result in a lot of different numbers, but should also result in clear decisions and messages. To facilitate communication, there are sets of guidelines regarding what to report. In this course, we are using the APA (American Psychological Association) guidelines, which are also commonly used in journals in psychology and beyond.
When reporting inferential statistical tests, always make sure to:
t.test()
-output. If equal variances are assumed, it is the sample size - 1; otherwise, typically a bit less. In any case, it describes which t-distribution was used to find the p-value.simulate.p.values
, R does not report it because it does not use a fixed $\chi^2$-distribution to look up the p-values; you should report it nonetheless as it also gives an indication for the complexity of your hypothesis.Examples can be found all over the internet; this set of notes contains detailed instructions for most statistical tests.
$\alpha$
You can use the same approach to show sums, fractions etc., though you would generally not need that in this course. The easiest way to get special characters like Greek letters into Word documents is to Google and copy-paste them.It is important to round numbers consistently, partly because too many decimal places might convey a false impression of accuracy, but also because numbers that do not convey relevant information can quickly clutter up papers and presentations - or does it help if I report that I spend 2.978536776 hours working on this book today?
In general, test statistics and most descriptive statistics should be rounded to two decimal places (i.e. places after the decimal point) and p-values to three decimal places. If that leads to descriptive statistics or regression coefficients to be rounded down to 0.00, that is a strong indication that you should consider changing the scale of the variables (e.g., from hours to minutes). p-values by definition can never be equal to 0, so here you need to pay attention to report small p-values as < .001 rather than = .000
How to round? (With one change to what you learned in school) Cross out all numbers after the last decimal place you want to keep. If the first number you crossed out is less than 5, then you are done. If it more than 5, then increase the last number you keep by 1. If it is 5 and any later number if more than 0, then also increase the last number you keep by one. If it is exactly 5 with only 0s following, then keep the last number unchanged if it is even, and increase it by 1 if it is odd. Some examples:
Why not just round up 5 like we all learned in school? If we always did that, we would introduce a small but consistent bias into our numbers. Therefore, this would better be randomised. The rule set out here goes towards randomisation without being too complicated, and is therefore what the APA guidelines recommend.
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