# Suggestions for summarizing data both visually and statistically

I have a dataset, with two proportions. One is the optimal probabilities of a binary event occuring and the other is the observed proportion of people choosing that binary event.

Participants answered 4 questions with the same 2 options (red or blue).

for example question1: red? answer red or blue
question1: blue? answer red or blue
question2: red? answer red or blue
question2: blue? answer red or blue


The Optimal probabilities show the probability that the answer corresponds to the colour given that the question is red. P(red|question1 red). and blue P(blue | question1 blue)

The other variable Chosing.colour represents the proportion of participants choosing that particular answer on the given question.

So for example:

  optimal<-c(0.59,0.60,0.55,0.55,0.60,0.58,0.67,0.68)
observed<-c(0.16,0.21,0.26,0.53,0.84,0.89,0.84,0.94)


So the Optimal always means:

the probability of the answer being blue when the question is blue and the probability that the answer is red when the question is red


Plotting it is therefore quite tricky, because of the interpretation:

The values corresponding to the RED line are the probability of red given that question is 1red, probability of blue given 1blue, probability of red given 2red, probability of blue given 2blue

Similarly for the blue line on the graph the values mean the proportion of people choosing that particular colour to which the question is referring.

So basically the baseline changes from question to question.

How can I best summarize this to avoid confusion?

Basically I want to see how well Chosing.blue matches the Optimal

UPDATE:

I made the following plot:

But I would somehow like to make it more obvious. Any suggestions? errorbarts etc?

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it is possible to add the images directly to the post, I think you have enough reputation to do that? –  mpiktas Aug 23 '11 at 12:43
@mpiktas I've added it –  Dbr Aug 23 '11 at 12:54
not the first one :) Sorry for nitpicking. –  mpiktas Aug 23 '11 at 13:31
@mpiktas all done! now I deserve some help:) –  Dbr Aug 23 '11 at 13:34