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In scientific papers there are asterisks representing the significance. Do these asterisks represent the significance level of the performed test or do they represent the obtained p-values? For example if you perform a t-test with a significance level of 0.05 and you get a p-value of 0.003. Then you have to reject the null-hypothesis. But can you put one asterisk (p<0.05) or two asterisks (p<0.01) above the graph if you make one?

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    $\begingroup$ I don't understand the question: what do you mean by "make one"? $\endgroup$ – whuber Apr 1 '16 at 17:20
  • $\begingroup$ @whuber "if you make one" refers to the "the graph", i.e. "when one is making a figure, what are the rules for deciding on the asterisk". $\endgroup$ – amoeba Apr 1 '16 at 21:25
  • $\begingroup$ @amoeba That interpretation occurred to me, but I gave it a low probability of being correct because asterisks are usually applied to tables, not graphs. I haven't any definite idea what kind of "graph" is being referred to here, either. It seems one has to make a lot of assumptions in order to follow this question, which is why I have specifically requested clarification. $\endgroup$ – whuber Apr 1 '16 at 21:34
  • $\begingroup$ @whuber Oh, it is very very common in some fields to use asterisks in figures. Look at this: google.com/search?q=figure+asterisk+significance&tbm=isch. $\endgroup$ – amoeba Apr 1 '16 at 21:35
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There's not a single convention for asterisks. Sometimes they are for 10, 5 and 1% significance, or 5, 1 and 0.1% significance. Other times they could be in standard deviations and so on. You always have to read the table captions to see what they represent.

For instance, a table caption may say that the significance levels are given by stars: * - 10%, ** - 5% and *** - 1%. In this case a coefficient with ** would mean that the p-value was under 0.05. It's like Michelin rating - more stars, better. At least, that's what I see in papers.

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  • $\begingroup$ (+1) But do they indicate achieving a prespecified significance level - so that if you were conducting all tests at a significance level of 5% you'd give one star only to all p-values under 5%, say, and no stars to all p-values over 5%? Or does one star indicate an observed p-value between 5% & 1%, say, & two stars indicate ones between 1% & 0.1%, &c.? I think that was part of the question. (And I don't recall having seen or heard of the former convention.) $\endgroup$ – Scortchi Apr 1 '16 at 21:16
  • $\begingroup$ Conventions for how many asterisks corresponds to what number may differ, but asterisks always refer to the actual p-values, I agree with @Scortchi. $\endgroup$ – amoeba Apr 1 '16 at 21:28
  • $\begingroup$ Giving one star to $p=0.1$ is weird. What fields are using this convention? $\endgroup$ – amoeba Apr 1 '16 at 21:33
  • $\begingroup$ @amoeba, I do it in economic forecasting :) when you have 50 observations, it's a gift to get $\alpha=0.05$. The point is that it's not a convention. I put the mapping in the table caption, so the reader knows what's it about. My table captions tend to be long, so you don't have to read the text to browse the tables and plots. $\endgroup$ – Aksakal Apr 1 '16 at 21:37

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