# Correlation Formula for Ordinal Variables

Six Sigma – iSixSigma Forums General Forums Methodology Correlation Formula for Ordinal Variables

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• #56101

Barbie Jayne Abaiz
Participant

I am having a thesis right now and I would like to know what kind of statistical analysis or method to use in correlating 3 or more ordinal dependent variables? The scaling is from Not At All (1) to To the Highest Extent (5).

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#203065

Robert Butler
Participant

There are two schools of thought concerning ordinal variables – one says you can’t use standard statistical techniques to analyze them and the other says you can. To the best of my knowledge neither school has been proved to be either right or wrong.

As written it sounds like you have 3 or more ordinal responses and you want to test their correlation with some group independent variables. The usual methods of regression analysis will work.

One thing to bear in mind, if you are running a regression analysis with an ordinal as a dependent your residual plots will have a banded structure to them. This is to be expected and it is not a problem.

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#203069

Barbie Jayne Abaiz
Participant

Hello, Robert! Thank you for your response.
My groupmates are thinking to use Spearman but we’re still confused.
We are using Likert-Scale (1 – Not at all to 5 – To a Very High Extent) as responses to our respondents. Is it correct to use Spearman? Or should we use Pearson?
We’re planning to correlate 2 questions with such responses.

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#203070

Robert Butler
Participant

There are a number of answers to your question. Before trying to offer anything more could you provide more information on what it is that you are trying to do. For example – you say you are trying to look for a correlation between the answers to two questions- does this mean you want to see if one predicts the other, or is it a case of looking for internal consistency, or is it a case of looking for agreement, or something else. Each one of the above objectives will result in a different answer.

At the moment, my personal guess with respect to what you are trying to do is assess agreement. In that case you would want to look at things like a Kappa statistic and not an assessment of correlation.

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#203071

Barbie Jayne Abaiz
Participant

We just wanted to know the relationship of competency and employability among graduates of our department.

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#203073

Robert Butler
Participant

If that is what you want to do then I wouldn’t recommend using either one. If you want to know the relationship between the two then you should look at a regression along with the 95% confidence intervals for individuals. This will give you an estimate of the change in employment status as a function of change in competency.

Based on what you have said employment would be the response and competency would be the predictor. The other thing you really should do is get a plotting routine that will allow you to jitter the plotted points. This will give you an excellent visual understanding of the relationship between the two. If you don’t jitter the data points you will just have a graph with a bunch of single data points corresponding the the 1-5 combinations of the two rating scales. If you can’t jitter then you should at least be able to annotate the graph so you can indicate the number of data points at each of the 1-5 combinations.

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