I have read other posts before raising this question. I understood the mechanics behind Anova but I have not fully grasped its essence in logical terms. What I mean is that if I calculate the mean difference between two treatments I fully understand the concept and can visually see it in a plot.

What remains not fully understood is the concept of confidence intervals (lwr and upr in aov function using R). If for instance I have a dataset of 5382 observations of 2 treatments or variables I will obviously have 1 as degree of freedom within and 5380 in residuals.
Are the upper/lower confidence telling me the min/max value the mean difference between these 2 groups can vary assuming those degree of freedom and a p-val (say) of 5%?
Or should we also take in consideration the sum/mean of squares and F-value to get to that conclusion?

My question is what in essence lower and upper confidence intervals are telling us (possibly without falling in the standard definition of min and max values of the difference of mean within treatments)?

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    $\begingroup$ Post the output of your aov model and the CI's. $\endgroup$ – user2974951 Oct 5 '18 at 9:49
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    $\begingroup$ I don't think aov produces output with confidence intervals. It might be helpful if you include what output you are looking at. $\endgroup$ – Sal Mangiafico Oct 5 '18 at 18:30

I am not so sure about this but, why the confidence interval in ANOVA will be different from the other techniques. The lower and upper bound is the bound the refer to the confidence of our hypothesis and if it exceeds that bound, it means that we collected the extreme case data based on our hypothesis which is extremely to be true. So it just a confidence interval of testing the significant of what we interest in.

  • $\begingroup$ Thanks EconBoy, it seems your answer is aligned with my conclusion of possible variance in mean difference provided those specified degree of freedoms: although the difference (diff) is the obvious result of the difference between those 2 groups, that same difference can vary due to the different values the observations can assume giving those degree of freedoms. Therefore we have those min/max extremes telling us by how much the mean difference can vary.. Am I right in interpreting it this way? Or am I missing anything? If someone could please contribute? Thanks $\endgroup$ – AlGrasso Oct 5 '18 at 8:51
  • $\begingroup$ When you talking about the F-test are you talking about a significant test for every group or between 2 groups which seem likely to be the latter. $\endgroup$ – EconBoy Oct 5 '18 at 9:02
  • $\begingroup$ If it is the diffence in the mean between 2 groups, when you get their confiedence interval if they are both negative mean that the most of the data said that it is negative and have a slightly likely chance for it to be positive. Also interpret the same as positive case. Hope this help. Confidence interval is a different way to say a probability of data. $\endgroup$ – EconBoy Oct 5 '18 at 9:04

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