Lets say you do a T test for difference in means with alpha at .05. If the p value is .08 and you want to report this in words to laymen, non-statisticians

would you say:

The difference in means are not statistically significant at a 5% significance level

or would you say something about the 95% confidence intervals used to determine significance? if so - in what way?

has to be 1 sentence IN WORDS not numbers

  • $\begingroup$ Is this for a homework or self-study problem? If so please tag the question accordingly. $\endgroup$
    – AdamO
    Aug 17, 2016 at 20:10

1 Answer 1


I would prefer to report the mean difference and 95% confidence interval. "We estimated a mean difference of X.X (95% CI X.X - X.X) which was not statistically significant at the 0.05 level.".

This is conventional reporting technique for findings. A verbal description of exactly what a confidence interval and/or p-value are is not what you asked for. Nonetheless an interpretation of a confidence interval is "an interval in which findings would be expected to fall if the present study was replicated independently an infinite number of times." Similarly a $p$-value is interpreted as "a frequency with which infinite, independent replications of the present study would produce findings as inconsistent or more inconsistent with the null hypothesis than the present study if the null hypothesis were true."

Your interpretation is wrong because it is not the means that are statistically significant, but their difference. So you can say, "The mean difference was not statistically significant at the 0.05 level".

  • $\begingroup$ Adam it has to be in words so you say " the mean difference was not statistically significant at the 5% level" but non-statistisiancs will struggle with significance level so I'm thinking somehow mentioning 95% confidence.... $\endgroup$ Aug 17, 2016 at 20:19
  • 1
    $\begingroup$ @user3022875 Your description was unclear as the interpretation of frequentist results is a different question than the one you asked, hence I added a section to address this, reconciling how statisticians usually report findings in a single sentence with the deeper meaning of that sentence, bearing in mind, this "1 sentence" nonsense shows a lack of understanding of English: you can make 1 sentence about as long as you'd like it to be. $\endgroup$
    – AdamO
    Aug 22, 2016 at 16:34

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