Histogram for bins with different numbers of elements..

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MiauMiau 2015-5-5

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评论： Walter Roberson 2015-5-6

Hi

I have the following problem:

I have data which I want to plot - but not every bin has the same number of datapoints. An example:

The values on the x-axis: 300 350 400 450 450 450 500 550 600 600

each of this values corresponds to a binary value: 0 0 0 1 1 0 0 0 1 1

Now careful - a zero means that the person has seen the stimuli with the intensity as defined on the x axis, but has not correctly recognized it - it does not mean that the value has not been sampled (or did not occur).

Hence the idea is the following, if I use linspace(min(speed),max(speed),3), each bin contains another number of stimuli shown, if I have 6 values in the first bin and 2 thereof are 1, this would mean that the subject could detect 2/6 of the stimuli, whereas if for the second bin 4 stimuli were shown and 2 answers correspond to a 1, here 50% of the stimuli were correctly detected - hence I need basically a percentage plotted per bin (not absolute numbers since as said the number of stimuli shown per bin varies).

How can I do that best - is there any standard way?

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Answer 1

Chad Greene 2015-5-5

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编辑：Chad Greene 2015-5-5

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Perhaps I'm misunderstanding your question, but why not compare two separate histograms--one histogram for distribution of intensities for recognized stimuli, and one histogram for unrecognized stimuli.

I have an old version of Matlab, so I'm using histf (available on File Exchange) to format the histograms and legalpha to support he semitransparent objects:

intensity = [300 350 400 450 450 450 500 550 600 600]; 
recognized = logical([0 0 0 1 1 0 0 0 1 1]); 
xbins = 200:50:700; 
histf(intensity(recognized),xbins,'facecolor','b','facealpha',.5); 
hold on
histf(intensity(~recognized),xbins,'facecolor','r','facealpha',.5); 
box off
legalpha('recognized','unrecognized','location','northwest')
legend boxoff
xlabel('stimulus intensity')

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MiauMiau 2015-5-6

But the problem is that the recognized stimuli are only a proportion of stimuli shown in a certain bin - and the number of stimuli shown in the two different cases are different. Hence comparing absolute numbers does not make any sense.

Chad Greene 2015-5-6

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What about normalizing your data? I can think of two ways. In one way, you could multiply the number of tests to get the same numbers of recognized vs unrecognized data. You have 4 recognized signals and 6 recognized signals, so you could multiply to get 24 of each:

intensity = [300 350 400 450 450 450 500 550 600 600]; 
recognized = logical([0 0 0 1 1 0 0 0 1 1]); 
% intensities recognized vs unrecognized: 
int_rec = intensity(recognized); 
int_unr = intensity(~recognized); 
% normalize data by multiplying number of trials:
norm_int_rec = repmat(int_rec,1,length(int_unr)); 
norm_int_unr = repmat(int_unr,1,length(int_rec)); 
xbins = 200:50:700; 
histf(norm_int_rec,xbins,'facecolor','b','facealpha',.5); 
hold on
histf(norm_int_unr,xbins,'facecolor','r','facealpha',.5); 
box off
legalpha('recognized','unrecognized','location','northwest')
legend boxoff
xlabel('stimulus intensity')

But that approach is a bit strange. Can you forget the histogram entirely and simply plot the percent of respondents who recognize a signal as a function of stimulus intensity?

intensity = [300 350 400 450 450 450 500 550 600 600]; 
recognized = logical([0 0 0 1 1 0 0 0 1 1]); 
xbins = unique(intensity); 
pct_recognized = NaN(size(xbins)); 
for k = 1:length(xbins) 
    pct_recognized(k) = 100*sum(intensity(recognized)==xbins(k))/sum(intensity==xbins(k));
end
plot(xbins,pct_recognized,'bo-')
box off
xlabel 'stimulus intensity'
ylabel 'percent of respondents recognizing stimulus'

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Answer 2

Walter Roberson 2015-5-6

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binlocs = [300 350 400 450 450 450 500 550 600 600];
stimulus_locs = [.....];   %the time for each stimulus
was_recognized = [1 0 0 0 1 1 1....];   %recognized?
totalcounts = histc(stimulus_locs, binlocs);
recognizedcounts = histc( stimulus_locs(was_recognized>0), binlocs );
adjusted_totals = max(1, totalcounts);
recognized_fraction = recognizedcounts ./ adjusted_totals;

The adjusted_totals is there to handle the case that some bin has no entries, to avoid doing a 0 (recognized) divided by 0 (total)

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MiauMiau 2015-5-6

the last line of your code throws an error:

Subscript indices must either be real positive integers or logicals.

Error in testPlot (line 12) recognizedcounts = histc(stim_durations(was_recognized), binlocs);

So, the number of bins I would chose with edges = linspace(min(speed),max(speed),3), inputing edges then to histc. But I would need to have basically a percentage (recognized over total number of stimuli) for each of the bins defined by edges.

Walter Roberson 2015-5-6

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recognizedcounts = histc(stim_durations(was_recognized)>0, binlocs);
adjusted_totals = max(1, totalcounts);
recognized_fraction = recognizedcounts ./ adjusted_totals;
recognized_percent = recognized_fraction * 100;

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