Can I use data taken in a 5-point Likert Scale, and convert it as if it were taken as a 4-point Likert?

Question

I made an error in my qualtrics survey, and used a 5-point Likert scale, when the measure was supposed to use a 4-point scale. I have collected a lot of my data for my dissertation, and am now very nervous. Do I have to go back and collect all of my data again?

Answer 1

In general, from my extensive experience, using a four or a five point response scale is not going to change much the psychometric properties of a typical psychological self-report scale (e.g., reliability and factor loadings). I also imagine that if you were to measure a multi-item scale with a four point version and a five point version that the correlation would be very close to the test-retest correlation you get with the five point scale.

More extreme changes (e.g., using a 2-point instead of a 5-point) or radically altering the response options would eventually start to create issues, but in the 4 to 7 point range, I think the effects would be subtle, especially if you are dealing with a multi-item scale.

The main issue you will have is that you wont be able to compare your descriptive statistics (e.g., means and standard deviations) with other authors who have used the standard 5-point scale. Whether this is an issue, depends on the aims of your analyses. If you are focused on relationships between variables (e.g., correlations, regressions, group differences, SEM, and so on), then whether you use a 4 or a 5-point scale is not going to make much difference. If you want to compare the means of your sample to the means of previous samples, or if there are particular scoring rules that involve the original metrics (e.g., some tests have cut-off scores used for classification), then you have more of a problem.

There are ways to approximate a rescaling. I.e., estimating what the means and SDs would have been had you used the 5-point instead of the 4-point scale.

rescaled_old_score =  (old_score - OLD_MIN) / (OLD_MAX - OLD_MIN) 
new_score = rescaled_old_score * (NEW_MAX - NEW_MIN) + NEW_MIN

Here's what the function looks like in R:

rescale_item <- function(old_score, old_min = 1, old_max = 4, new_min = 1, new_max = 5) {
    rescaled_old_score <-  (old_score - old_min) / (old_max - old_min) 
    rescaled_old_score * (new_max - new_min) + new_min
}

template <- data.frame(original = 1:4)
template$new <- round(rescale_item(template$original, 1, 4, 1, 5), 2)
template

which leads to the following rescaling:

  original  new
1        1 1.00
2        2 2.33
3        3 3.67
4        4 5.00

Of course, this is only an approximation. Better estimates of the mapping values could be obtained by administering the tests using both scales to the same sample.