How can I include Tukey (HSD) result in my boxlpot as "a" and/or "b" indicating whether there is a significant difference or not between the groups?

Dear all,

in the following you can find my script. When I run my script I get two graphics, one graphic shows the result of Tukeys HSD analysis and the other graphic shos the boxplot .

My aim is to include the Tukey result in the boxplot, using letters to indicate significant differences. in this case there should appear the letter "a" above sample 1, and a "b" above the samples 2 and sample 3.

Thanks for any ideas or help!

Test1 = [
    36.4000   40.6000   40.3000
    31.5000   39.7000   41.0000
    25.4000   40.8000   45.7000
    27.5000   35.8000   43.4000
    29.4000   37.0000   40.2000
    30.3000   42.6000   39.5000
    28.8000   41.8000   42.7000
    32.3000   45.4000   39.1000
    22.8000   39.5000   38.8000
    27.6000   46.2000   40.6000
    24.4000   52.4000   41.4000
    19.5000   38.5000   41.9000
    27.7000   42.8000   37.4000
    19.6000   45.5000   32.3000
    28.2000   44.3000   36.1000];

V=Test1;
wt=V(:, 1);
T3=V(:, 2);
T2=V(:, 3);
neuwt=V(:,1)';
neuT3=V(:,2)';
neuT2=V(:,3)';
data(:,1) = neuwt;
data(:,2) = neuT3;
data(:,3) = neuT2;

[p, table, stats] = anova1(data);
[c, a, h, nmn] = multcompare(stats, 'alpha', 0.05, 'ctype','hsd')

boxplot(Test1)

[Abhishek Chakraborty]

Sorry for a very naive question but how did you get to interpret the letters to be "a" and "b" for your samples through the MATLAB results?

[dpb]

That was just an arbitrary naming convention OP wanted to place on the significant versus nonsignificant results. Those that are significantly different are those whose bars are disjoint; by inspection one observes the LH is not overlapping either of the other two while the two RH are. Hence labelling them together and the other differently.

The p-statistic is returned in the c array from multcompare to see the actual probability estimate.

Answer 1

[dpb]

Kinda' a fun one... :)

First, make sure your boxplot is gca, then the following seems to be pretty robust...the one probably unexpected thing is the handles are in reverse order from R to L on the plot in the handles array of lines, hence the flip on the labels index.

hBOX=gca;
hold on
hGbox=hBOX.Children
hUpW=findobj(hGbox.Children,'Tag','Upper Whisker');
labels={'a';'b';'b'};
hTxt=arrayfun(@(h,i) text(h.XData(1),h.YData(2),labels(i), ...
                          'verticalalignment','bottom','HorizontalAlignment','center'), ...
             hUpW,flip([1:numel(hUpW)].');

I just created a labels array by hand, obviously by parsing the returned means and probabilities one could generate the groups and labels programmatically.

It is strange why you built so many intermediary results of the same values, though???

I can see why created a test array for posting question, but if you once have the array V, then

wt=V(:, 1);
T3=V(:, 2);
T2=V(:, 3);
neuwt=V(:,1)';
neuT3=V(:,2)';
neuT2=V(:,3)';
data(:,1) = neuwt;
data(:,2) = neuT3;
data(:,3) = neuT2;

is all just superfluous -- all(V(:)==data(:)) --> 1 (true) so just use V

[p, table, stats] = anova1(V);
[c, a, h, nmn] = multcompare(stats, 'alpha', 0.05, 'ctype','hsd')
boxplot(V)

and generate the same results.

[Valerie]

Dear dpb,

first of all, thank you very much for your support and time! :) "Kinda' a fun one... :)" made me laugh because I am having a really hard time figuring all that stuff out.

I have to admit that I am very new to matlab (which you may have noticed looking at my script which might could have been written way better).

at the moment I have just copied your answer and all the way to "labels={'a';'b';'b'};" the program is fine with your code.

Coming to the next part of the code, i start to struggle. I definitively have to (and will) read a lot about this matter to fully understand.

The part after "labels={'a';'b';'b'};" is where I have to "personalize the settings", i suppose.

I would be glad if you could just shortly comment on the section where I have to fill in my data:

hTxt=arrayfun(@(h,i) text(h.XData(1),h.YData(2),labels(i), ...
                          'verticalalignment','bottom','HorizontalAlignment','center'), ...
             hUpW,[flip(1:numel(hUpW)].'));

E.g. I am unsure what to write down instead of h.YData(2) is it my matrix V=Test1, or should the matrix be subdivided as I have done it (e,g. neuwt instead of h.YData(2)). Also don't know what to fill in for the h.XData(2), since I dont really have a vector defining the x Axis, the vector for the x-axis is just (1 2 3)...? It would be a great help if you could comment on what might could (or should) be written insetad of the "..."

As you can see, there are still a lot of questions ;)

Best regards, Valerie

[dpb]

No, other than creating a labels array to match the number of columns that contains the text you want the labels to be for the given column, you don't do a thing...

The .XData/.YData is retrieving the x- and y- coordinates from the plot to know where to place the text...that's fixed by boxplot() given the data it's given; this just retrieves it for the given plot to use.(*)

Just run the script exactly as given to see what it does for your input....it'll do the same thing for any array passed to boxplot as long as the labels are defined for it.

ADDENDUM:

Oh, I missed seeing the thing about the ellipsis -- "..." is the line continuation indicator for Matlab...just wrapped the line so wouldn't run off the screen. I indented the second line to the level of the parenthesis for the text() as they're continuing arguments for it, the third is then to the level of arrayfun() as the last two arguments of it.

There's nothing to be done but copy the code snippet and run it for your case.

(*) ADDENDUM 2:

hUpW is the array of upper whisker lines which are the vertical lines at the x position of the given column; since it is a vertical line it consists of two data points but the x position is the same--XData(1) is the first of those two. The position of the whisker would be the y value of the horizonatal line or the end of the upper whisker--hence the use of YData(2). Those are the x,y coordinates passed to text of where to place the label...the two '...Alignment' arguments center it over the midpoint and then write the bottom of the text box at that leaving the actual text just a little above the line.

arrayfun is a looping construct, the (h,i) are the dummy arguments to the function, the actual arguments are the arrays hUpW and an index array of 1:numel() which is used to index into the labels array. Each of those arrays' content is passed one element at a time in turn to the anonymous function just as if a loop had been written; just a more succinct way to write it.

[Valerie]

Dear dpd,

sorry for not respoding for such a long time. I've let you wait for a response, because I didnt wanted to bother you without having tried your script, to be precise, I wanted to at least try to solve the error that comes up, when I let your code run.

I tried your code several times, but when I give in the script just as you wrote it down, I do get the following notification:

It took me a while, to find out that the error occured, because there is one round bracket (one too much?), at least I deleted the one round bracket before the semi-colon at the end and it worked just fine. The code I gave in was the following:

hTxt=arrayfun(@(h,i) text(h.XData(1),h.YData(2),labels(i), ...
                          'verticalalignment','bottom','HorizontalAlignment','center'), ...
             hUpW,[flip(1:numel(hUpW))].');

and I now have a graph like that, just like I wanted It to be:

Thank you so much for the explanations, I now do understand what the different parts of the script mean and it works just fine! I really appreciate your support! =)

[dpb]

Huh. Don't know how that [ got misplaced--I'd'a swore I cut 'n pasted from the command line that did work. Sorry about that. What I used and intended to post was

hTxt=arrayfun(@(h,i) text(h.XData(1),h.YData(2),labels(i), ...
                          'verticalalignment','bottom','HorizontalAlignment','center'), ...
             hUpW,flip([1:numel(hUpW)].'));

where the [] were just cosmetic to surround the 1:N vector to transpose it to column. Not really needed.

Like much of ML, once you see something once, it's not nearly as mysterious as seems on first blush! :)

[Valerie]

Yes, indeed! But it can take so much time until that point where it all makes sense (and until it works the way it should :D). Thanks so much for your help!