I doubt that I can help with your specific question, but maybe my thoughts may be of interest.

From my experience in trying to match A - E results with any other factor, your comment that the band width is too great to observe correlation is likely true. As well, semester results integrate so many underlying performance characteristics that correlation won't be strong. Semester results integrate cognitive, skill and behavioural characteristics and writing ability is only one, and probably not the strongest factor. As well, I am sorry to say, that teacher expectations also play some part, sometimes, in semester results.

My main field is Science, so I am referring specifically to Science criteria in the following:

I have specifically directed and trained teachers to look beyond writing (and general communication) ability for the majority of criteria except those directly referencing writing. I once taught a student who was so skilled at communication and writing particularly, that I couldn't really tell how much she understood. She was so skilled at manipulating  text. I gave her the benefit of the doubt. Also, I have seen many instances of students writing that was fluent and skilled but contained little evidence of understanding. It was like 'word barking' in reading. I had to train teachers to look for content not just quality of writing. As well, I have had poor writers that had clear understanding in oral situations. I had to train teachers to look deeply for meaning to avoid prejudicing these students. Obviously they scored more poorly in the criteria directly referencing writing.

I guess my summary is that I would not expect the correlation between writing and semester results to be strong anyway, and the band width is so great that that limited correlation will not be evident. In fact, this is one of my great beefs with A - E. It is hard to demonstrate progress.

Thanks for that Mark.

The project that I have been implementing across the curriculum in this high school tracks writing specifically as a subset of literacy. It uses 14 NAPLAN like criteria to establish data sets. It has been used in other large scale projects, so this is more likely to give results that have validity - but all of the points you have raised are relevant.

It just seems a shame that when I have the data and could track potential correlation - should it exist - that there is no easy way to do so. I guess it's a bit like the current system with QCAA and the 10 bands within each of the 5 levels of achievement used at exit. I even thought of this, but the work involved could never justify the outcome and would be incredibly subjective.

Thanks for your thoughts.

Hi Zena, While the writing marks may be valid, I am always doubtful of semester achievement results. Not that they are specifically wrong, but that they are restrictive. Once a students position is established (ie a 'C' student), it is hard for them to move.

As for the 10 levels, I find it difficult to get teachers to make consistent decisions on a 15 point scale in junior school. Again, I think a major problem is the whole structure of the A - E standards based system. The writing marks are a much better system because they describe clear learnings in a continuum.

I would use Spearman's rank correlation coefficient rho. Unlike Pearson's correlation coefficient, which assumes linear correlation, Spearman's doesn't. It is specifically used with ordinal data (or ordinal and metric).

There is a simplified formula in case there are no ties (no same ranks) -  which I assume you have. The full formula is not for the faint of the heart, typically you would use software like SPSS. If this is not available, search for free software. As far as I know there is also an add-on for Excel. Good luck!

Many thanks Leopold

I am able to access SPSS via a colleague so will investigate this further. I appreciate your response greatly.

Zena

@Zena Carusi-Lees

Generally, I endorse Leopold's recommendation as well as Mark's cautionary remarks. Please take the time to gather at least some understanding of Pearson's rank correlation (e.g. on the level of Wikipedia, see link). In particular, the special version for distinct ranks is easy to understand, as its mathematics is just at high school level.

However, I would also suggest some further considerations, as your question is a bit unclear /ambiguous about what you really need. In your description you speak about "... any relationship between ...", in the title of your question your ask about ".. to correlate interval data with ordninal data ...".

IMHO, you are moving (too?) fast from a more general approach - finding any relationship - to a purely statistical approach - calculating a correlation. Now, whether this is warranted and/or plausible at all depends on a lot of background information and verification steps, we don't know about. What makes you so certain that student marks are interval scale data? Just looking at the resolution (43 points) doesn't prove anything. How many data do you effectively have? If the range is low, doing ordinary statistics is not much of help (as Mark already suggested).  How many data do you effectively have? If the range is low, doing ordinary statistics is not much of help (as Mark already remarked). Are there any clusters of students, you should better not mix up (merge), because that would create artificial noise in your data or blur out any potential relationships. 

Sanity checking your data before doing any statistical calculations is a must. Finding outliers is not enough. What is very helpful in this stage is so-called "exploratory data analysis" (EDA), by hand or using dedicated software (cf. Wikipedia). Perhaps the patterns you will be able to find by some simple EDA techniques are all what you need.

Once you have found such evident patterns, you may ask two types of further questions:

• (Type I, qualitative:) Is there any reasonable explanation for the patterns you have found and for the exceptions from those patterns?
• (Type II, quantitative:) is it possible to quantify the found relationships by means of appropriate statistics, e.g. chi-tests, rank order test, and the like.

Although many people like Type II results, most of the time it will only codify what you have found out with Type I analyses, so reversing the steps, will just postpone a step you have to make anyhow.

https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient

https://en.wikipedia.org/wiki/Exploratory_data_analysis

Very sound advice from Paul Hubert.

As a matter of fact, I wanted to follow up my previous comment with something of the sort. Like: how large (small) is your sample. A small sample is not necessarily a problem, but you may not arrive at statistically significant results (e.g., p < 0.05).

Generally, go through Paul's advice first and at the end, carry out the correlation analysis. Given sufficient time and other resources, a mixed-methods - approach may be preferable.

Many thanks to both of you for your very sound and helpful advice.

 I have spent a great deal of time reading and attempting to understand - as a practitioner researcher this is challenging but fascinating.

The study I have completed involved 6 students across 6 classes in 2015 but am completing the 2016 data now for a similar study that should include 6 students from about 14 classes.

I have completed a paired t test looking at growth in pre and post testing of one of the variables and the work is statistically significant - which is expected because of its research background application in Australia and abroad with rates of between 2-4 times growth.

I will review both of your comments and references.

Again many thanks Leopold and Paul

Zena

 Hi Zena, I recommend that you separate the respondents into student's grades levels and make the correlation test within groups. Thus you will have correlation scores that will can you comparison.

to use the correlaction test with differes measuration levels variables is very problematic.

If you are using, for exemple, the SPSS software, you will can create a variable categoric and under it to realize the test of correlation.

Best regards

Dirceu 

Again this seems sensible Dirceu. I will try this.

warm regards

Zena

Thanks for this response and clarification, Hassan

regards Zena

Hi Zena,

Some infos are missing, but responses items theory (as Rasch model of measure) may be usefull (transform ordinal to interval scale). Check if it is usefull for your data.  

The best, 

Pierre

Many thanks, Pierre

Hi Zena

      I think that you can transform student grade level to number  and asume it as intervel scale then just use Pearson correlation is the easy solutions

 best regards

Thanks for that Pairatana