Hi,

The first thing to clarify is your research question. You describe *items* which constitute *scales*. Do you want to know how *items* correlate or how the *scales* correlate?

Assuming you want to know how the items intercorrelate (all 9*10 =90 correlations), there are different options for computing correlations between pairs of ordinal variables. Cramer's V is one. Kendall's tau is another. Spearman's rho is a third.

But if instead what you want to know is the correlation between the *scales* of agreeableness and emotional intelligence, then you have to create the scales first. There are usually rules offered by the scale developer explaining how the scales are to be created. See the original publication for the measure or the test manual. Often it is the mean of a respondent's scores on all nine (or ten) items, but sometimes it's a sum, or even a weighted mean. Once the scale scores are created, many researchers will treat the scale scores as continuous variables and use continuous variable methods for computing the correlation between them such as the Pearson product moment correlation coefficient.

Hope this helps,

Scot

Hello Shereen,

I support what Scot has written. Unless you are doing anything unusual with these two scales, I recommend that you use Pearson's product-moment correlation coefficient on their composite totals. Although the individual items should probably be regarded as ordinal, by the time you combine them to obtain totals for each scale, most statisticians would say that it's safe to use a parametric test such as Pearson's correlation. There's no need to use a nonparametric correlation (i.e., Spearman's rank-order correlation coefficient).

As said above, there are two related possibilities, whether you are looking to see how the items on set A are related to those on Set B, or whether some summary measure for these sets are associated.

If items. If you are worried about the ordinal nature of the items, an ordinal version of canonical correlation should be of use. OVERALS is part of different versions of SPSS, is available in R packages, and there are probably stand alone packages for it.

If scales. Figure out how to create aggregate measures. If there is not a manual this can be a tricky step. If there is a manual, you still might want to question if their method applies to your situation. Once you have those measures, do a scatter plot. Then you can start thinking about measures of association.

Oh, and remove the word "prove"

Dear Shereen

First of all I want say that individual item of each construct is not an ordinal scale data as you have measured using a five-point Likert scale. Data gathered by 5/7 Likert scale are considered as interval scale data and hence treated as metric data.

Since your variables are metric in nature, you can calculate simple correlation coefficient (Pearson) to identify the nature of association (positive or negative) and strength of association between these two variables. But how you can do it?

1) You can see the relationship among the items of the two variables. But it doesn't make sense.

2) You can aggregate or average the score of all items of the construct (e.g. agreeableness) individually and then run the Pearson correlation in SPSS or any supporting software.

3) You can use SEM technique. This one is important to justify whether the items of each construct reliavle and valid or not. Besides, you can check the factor loading of all the items of each construct. Then you can also check the correlation as well discriminant validity of these constructs through Fornell & Larker criterion.

Hopefully, you will decide first and then go for analysis.

Thank you so much for your replies!

Am I meant to calculate the mean or average to examine the relationship between two ordinal variables?

Daniel Wright Mirza Mohammad Didarul Alam Robert Trevethan

Your question is a bit difficult to answer, Shereen, because first up it seems you might think that the mean and the average are different things. They're not.

Second, as several of us have indicated up above, essentially, by the time you combine all items to get a total score, the result does not need to be regarded as ordinal. Without going into details, a total score comprising a number of separate scale items can be regarded as equal interval for statistical purposes.

Rather than calculating a total for each scale, many people calculate a mean for each scale under your circumstances. Either way, you might need to be mindful of missing data.

There are more issues in the kind of research you are doing, including what to do with missing data if you have any, but this should get you on your way.

Treating ordinal Likert type items as interval scale is a topic of debate in applied psychology literature. However, simulation studies show that treating ordinal Likert type items as interval when the number of response categories five or more as in your case generally not problematic and suggested in literature.

Thus you can use Pearson correlation analyses either item level or as using total score (sum of scores of emotional intelligence and sum of scores of Agreeableness ). I prefer to use total scores in your case as total scores may be more reliable indicator of construct of interest rather than individual items. If you use total scores you can also use simple linear regression analysis.

Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354.

Finney, S. J., & DiStefano, C. (2013). Non-normal and categorical data in structural equation modeling. In Structural equation modeling: A second course (2nd ed., pp. 439–492). Greenwich, CT: Information Age Publishing.

I have a different opinion about Ertugrul Sahin stand about the data nature generated from Likert scale. The debate is true for ordinal type Likert scale (e.g. from lowest to highest or vice versa). but it the scale format is balanced with a neutral point then it is clearly interval (metric) data.

However, if anyone have ordinal type of data, it is not allowed to measure mean and standard deviation. In this case non-parametric analysis of association (Spearman's Phi coefficient) can be followed.

Shereen Zalloum. Shereen, after providing some advice up above, it occurred to me that the agreeableness scale you are using probably has some negatively worded as well as positively worded items. Please be aware that you will need to reverse code one of those sets of items (probably the negatively worded ones would be best) so that they are all "swimming in the same direction" before you calculate a composite total score - whether that is done by simply adding responses or by obtaining the mean of the nine responses.

Ordinal data is non-parametric use Kendal or Spearman

After converting my ordinal data (because its scored using 5-point likert scale) to interval by combining the full set of items. Can I use Pearson correlation coefficient even if my data isnt normally distributed and the relationship between both variables isnt linear?

Silas Memory Madondo Robert Trevethan Mirza Mohammad Didarul Alam Ertuğrul Şahin Daniel Wright

The correlation, just as a descriptive measure, just relies on the linearity. The standard method for calculating p-values and CIs are what use the Normal distribution assumption. But you can bootstrap it if you are worried. The ordinal-interval aspect is only about interpreting the meaning, so is more subjective (see Lord's football number example, https://marces.org/EDMS623/Lord%20FM%20(1953)%20On%20the%20Statistical%20Treatment%20of%20Football%20Numbers.pdf).

Shereen Zalloum. That your data are not normally distributed should not be a problem. That the two variables are not linearly related is, however, a problem. But how nonlinear are they, and how did you investigate / come to a conclusion about linearity?

Maybe attach a scatterplot of your two variables and we might be able to help you further.

Robt.

Pearson should be appropriate if all conditions are met ie normality assumption and interval data (now sorted by conversion as you said) becaz Pearson is not a robust measure l advice you to use Spearman though it is a weak measure

Silas Memory Madondo. Hello Silas, I don't like being disagreeable (so please forgive me if I come across as being so - it's not my intention), but I'm pretty sure that Pearson's product-moment correlation coefficient is, indeed, robust in the face of nonnormality of data (in fact, normality doesn't really matter much, despite a common misperception that it's extra important).

If you have contradictory evidence or authoritative information to the contrary, I would appreciate your letting me know.

Robt.

Hi Robert Trevethan and Silas Memory Madondo

Bishara and Hittner (2012) conducted two simulation studies to compare 12 methods (including Pearson, Spearman’s rank-order) to test the significance of a correlation with nonnormal data. They concluded that:

"Generally speaking, Pearson’s r is fairly robust to nonnormality. Exceptions include markedly nonnormal distributions (e.g., the highly kurtotic distributions) where Pearson’s r demonstrates poor Type I error rate control, and increasing sample size does not necessarily alleviate this problem. Spearman’s rank-order correla- tion has also shown better Type I error rate control, compared with Pearson’s r, in some cases. Furthermore, Spearman’s r is often more powerful than Pearson’s r in the context of nonnormality." (p.402)

Source: Bishara, A.J. and Hittner, J.B. (2012), “Testing the significance of a correlation with nonnormal data: Comparison of Pearson, Spearman, transformation, and resampling approaches”, Psychological Methods, Vol. 17 No. 3, pp. 399–417.

Tahani Aldahdouh. Thank you for following up on this for us. As is often the case, things are not as simple as the first seem or as might be desirable. But it's better to be aware of the complexities.

Thanks again.

Robert Trevethan academic critique makes us grow, have noted your critique and to explore it deep. You are welcome. However, the position is appearing to be controversial.

Tahani Aldahdouh thanks for the clarification backed by empirical evidence. I believe that the position is still to enjoy widespread usage

Silas Memory Madondo Robert Trevethan Tahani Aldahdouh Scot W McNary Mirza Mohammad Didarul Alam

Thank you all so much for your help! Could someone please read the result draft that I have written? My dissertation is due in about 4 days, and just making sure I have interpreted my results correctly would be a huge help. If anyone could provide their e-mail address, Ill send it right away!

Thank you so much.

Shereen Zalloum. If you provide your email address, either here or via a "private" message on RG, I would be happy to have a glance over it for you.

That's partly because I'm a graduate of LSE. :-)

You can send a private RG message by pressing the downward arrow in the upper right-hand corner of a person's post, and then click on Follow. A message box will open up for you.

Shereen Zalloum [email protected]

Robert Trevethan Silas Memory Madondo Daniel Wright

Thank you so much for your reply! I will e-mail.

Shereen Zalloum check your email I have just sent my contribution back to you

Spearman Rank Order Correlation may employ

By plotting your data, you can see if there is an increasing or decreasing monotonic relationship. If this is true, you can use a Spearman or a Kendall correlation coefficient to evaluate the strength of this relation. Pearson is not a good measure because of nonlinearity you have mentioned.

you can use a Spearman correlation coefficient to evaluate the strength of relation.

Spearman correlation is a conservative approach to determining the correlation between your two variables. Many researchers would feel that your two variables represent interval data and, as such, could be examined with Pearson correlations.

Hi Shereen Zalloum

Since both variables are ordinal scale, Spearman's rank differences correlation coefficient is appropriate. However, you can also use Pearson correlation between their total scores ( There are those who accept the sums of 5 grade Likert type scale items as continuous data). One of the important points here is what the sample size is.

Good luck

Dear Nuri Doğan

May I ask you for the reference regarding the acceptance of Spearman's correlation for the total scores of scales? Many thanks in advance.

To find out relationship between ordinal variables, you can use Spearman rank correlation or Kendall's Tau c. In the same way, for graphical representation you can use multiple bar chart.

I suggest using multiple regression using SPSS statistical software. It will make your life easier.

Hello Robert

Please could you provide any reference to support it?

Samuel Foli, my name is Robert, so I wonder if you are asking me for a citation. If so, please do confirm that you're asking for that of me.

The information provided by Tahani Aldahdouh on 16 August 2019 might satisfy your needs, however.

Thanks a lot

GOOD LUCK

Hello Asif Rahman,

Can you please elaborate on the usage of multiple regression here? For one of my research, I've used 2 scales; one of Pregnancy Experience (20 items) with 4 points Likert scale and the other of Well-being (5 items) with 6 points Likert scale. My sample size is 101. I was planning for Spearman's Correlation. What are the other possibilities for analysis?

Thanks in advance.

To calculate the correlation between two ordinal scales you need polyserial correlation.

Good luck