How can I count errors?

EDIT: Although the Workaround is still valid (despite being long-winded), 'The Large Problem' as described below is incorrect - use getEmbeddedData instead of just setting a variable - see other responses in this thread.

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Really good question - worth creating a feature request due to the larger problem described below. I don't think it's possible (due to the larger problem) to achieve this as perfectly as possible, but I've suggested a workaround below.

THE LARGER PROBLEM

Really good question - worth creating a feature request out of it as getting/setting embedded data when a page refreshes does NOT work as expected. Specifically, if I have defined an embedded data variable and then decide to bring it in JS and then re-set its value within the onLoad fucntion, a page refresh or a validation error does not overwrite the embedded data variable. For example, if you have define a variable n = 0 to count the times a page is refreshed, then the following code (when set on any question within a page) does NOT work:

var n = parseInt("${e://Field/n}")
Qualtrics.SurveyEngine.setEmbeddedData("n", n+1)

While this code should take n the first time when it's 0, then set its value to 1; if a page is refreshed/validation error occurs, then it should take n as 1 and set its value to 2 and so on. Instead what happens is that n is set to 1 every time (i.e. it's initialized to 0 every time).

WORKAROUND

Instead of validation, I've taken advantage of display logic. Specifically, if the user selects the wrong choice of the validation question (or whatever criteria you want to specify), then they progress on the next page which increments the embedded data variable n. Once the variable is incremented, then they immediately go to the previous page to complete the validation question again. A descriptive text question contains an error message and is updated if the validation is unsuccessful. Importantly, the back button needs to be enabled from the Survey Options (hide it on all other pages if you don't need it).

There is a lot of room for customization.

Working version attached - see JS code on Q1, Q2 and note again that the Back Button is enabled via the Survey Options.

Snap! Silly me... My previous elaboration of 'the larger problem' is dead wrong.

Starting from your great insight to actually use the getEmbeddedData function, I've improved it ever so slightly to capture validation errors specifically and to also be question-specific. Insert this code to any question whose validation errors you want to capture (after creating an embedded data variable errors_q_1 before the page):

var question = $(this.questionId)
$(question).select('.ValidationError').each(function(error) {
if (error.innerHTML != '') {
var errors = parseInt(Qualtrics.SurveyEngine.getEmbeddedData("errors_q_1"))
errors++;
Qualtrics.SurveyEngine.setEmbeddedData("errors_q_1", errors);
}
})

You can even customize it if you have multiple validation errors (e.g. force response and numbers only)

var question = $(this.questionId)
$(question).select('.ValidationError').each(function(error) {
if (error.innerHTML == 'error message 1 goes here') {
var errors = parseInt(Qualtrics.SurveyEngine.getEmbeddedData("errors_q_1_v1"))
errors++;
Qualtrics.SurveyEngine.setEmbeddedData("errors_q_1_v1", errors);
}
if (error.innerHTML == 'error message 2 goes here') {
var errors2 = parseInt(Qualtrics.SurveyEngine.getEmbeddedData("errors_q_1_v2"))
errors2++;
Qualtrics.SurveyEngine.setEmbeddedData("errors_q_1_v2", errors2);
}
})