However, today I have been working with Damian – a young student preparing for an MSc in Social Sciences.

Damian had read three journal articles at home, which we were discussing during our Skype session.

I asked Damian to interpret correlation coefficients presented in a matrix in one of the journal papers.

Since it did not go very well, I thought that perhaps more students might struggle with the task.

**Explanation**

The correlation matrix is a table which shows relationships between variables in the study.

More precisely the table shows the correlation coefficients between variables.

The matrix also shows p-values indicating if these relationships are statistically significant.

The correlation matrix can be easily computed with software programmes such as SPSS, STATA or R.

**Example**

Damian was asked to explain the relationships among variables in the study on the basis of a correlational matrix which was pretty similar to the one present below.

**I asked the questions like:**

- Can you find an example of a strong correlation at level p < 0.0001?
- Can you find an example of a negative correlation?
- Can you find an example of a weak correlation at level p < .05?
- Can you find an example of a weak correlation which is not statistically significant?
- Can you explain why some values have been replaced with ‘ -‘ ?
- What is the difference between p < 0.05 and p. < 0.0001?
- How many participants were in the study?
- Why is the upper-right triangle of the matrix empty?

Can you answer these questions?

**Possible answers**

- K Eng expressive and K Eng receptive r = .78
- K L1 vocabulary and K Eng receptive r = -.08
- S L1 vocabulary and K Eng receptive r = -.28
- K L1 vocabulary and K Eng receptive r = -.08
- A variable cannot correlate with itself
- p. < 0.0001 suggests a better evidence level than p < 0.05
- 158
- It would be a replication of the bottom-left triangle

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Pearson’s correlation coefficient r measures the strength and direction of a mutual relationship between two continuous variables.

negative values of r = negative correlation (e.g. r = -.342)

positive values of r = positive correlation (e.g. r = .512)

The r closer to 1 or -1, the stronger correlation

Coefficients r close to 0 represent a weak correlation

If the p-value is below or equals 0.05 (sometimes 0.01) the correlation is statistically significant

Changing the p-value from 0.05 to 0.01 reduces a Type I error

A statistically significant correlation suggests a reliable relationship, not a strong or weak relationship

The bigger the sample the bigger chance the correlation becomes significant.

**Strength of correlation**

0.1 – 0.3 weak/small correlation

0.3-0.5 moderate/medium correlation

0.5 -1.0 strong correlation

**Examples**

In the example above, there was a positive moderate correlation between reading and writing (r (62) = .425, p < 0.01).

Children who are better readers tend to be better writers.

This correlation was statistically significant since the p-value was less than 0.01 (p < .01).

The number following r in parentheses signified the degrees of freedom (df), which are related to the sample size.

For a correlation, the degrees of freedom is N – 2. The sample size (N) was 60.

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It is basically an evaluation of tutor feedback for one of the undergraduate modules for

the Faculty of Health & Social Care at The Open University.

I am writing about this paper since students often ask me how their essays and assignments will be marked at a university.

Since most of the international students are worried about their academic vocabulary and grammar, I think you might find the findings of the study interesting.

Have a look at tutors’ feedback for this particular course.

On what essay components do tutors provide most feedback?

As you can see the tutors did not seem to have cared much about language, accuracy, and grammar.

They were much more focused on:

1. Cognitive skills: ways students handling content – interpreting, answering the question, defining terms, using

concepts, developing an argument, synthesis, analysis, and critical skills

2. Content: the use of evidence and source materials

3. Structure: organization of the essay, outlining and paragraphing

4. Referencing

5. Style: flow, signposting, clarity

Now, we shouldn’t generalize. Feedback depends on university, course, tutor, and assignment.

There are also tutors who seem to be obsessed with grammar and score students down even for an absence of definite articles.

In my experience, the majority of tutors look in essay and assignments for evidence of critical thinking which is reflected by choice of source materials, level of analysis, macro-structure (outline), microstructure (paragraphs).

Of course, they like impeccable grammar but they also understand that writing in a second language is not exactly a piece of cake.

Source: http://www.eurodl.org/materials/special/2015/Wilson.pdf

]]>It was written by one of my students – Lisa.

Lisa has been working with me on a small research project as a form of preparation

for Masters in Psychology at the University of Portsmouth.

Generally, Lisa has written an impressive piece of work (4.000 words) with a coherent structure, convincing argumentation, a sensible choice of source material. However, as it is often the case with academic writing, not everything was perfect.

There were some minor issues which had to be addressed: mistakes in referencing, no signposting, too descriptive at times, writing in the first person.

Crucially, Lisa has also mistaken correlation with causation.

Since it is a frequent mistake in both undergraduate assignments and masters dissertations, I think I should write a few words about it.

**Correlation vs. Causation**

As you all probably know correlation is basically a mutual relationship between two (or more) variables.

In other words, correlation shows whether and how strongly variables are related.

The taller (height) you are the heavier (weight) you tend to be. Height and weight often correlate.

Age and amount of hair often correlate too; younger people tend to have more hair on their heads than older people.

Does it mean that the age itself causes the hair loss?

Hair loss can be caused by hormonal changes, medical conditions or medications among many other factors.

On the other hand, causation exists when one variable actually causes another. Drinking alcohol causes accidents.

Smoking causes cancer. There is a strong relationship between smoking (cause) and cancer (effect) which has been evidenced by experimental studies.

For many students, both concepts seem similar, but they are not the same thing.

Many examiners, tutors, and markers get angry when they see students confusing these two basic concepts.

**Back to Lisa**

Lisa in her assignment discussed a link/mutual relationship between depression and suicide.

She quoted some correlational studies and concluded that depression frequently causes suicide.

I read the studies she included in her assignment and on the basis of those studies, I could only say that:

‘people who suffer from depression tend to have higher rates of suicide’.

There was a correlation between those two variables but nothing more than that. We cannot simply say that one causes the other.

Simply, the researchers did not conduct experimental studies to prove causation.

There might have been some other factors at play (confounding variables they have not measured for) such as SES (socio-economic status), age, sex etc.

Lisa needed to rephrase her claims, also where possible I asked her to add experimental studies proving (if possible) the causal relationship (for instance, Randomised Controlled Studies).

**Warning**

Now, it is important to mention that correlation can indeed suggest that causation actually exists.

Phrasing differently, where is correlation often is causation.

But it does not prove it!

**More warning**

Have you heard that the rates of crime have been known to increase when ice cream sales increase too?

You would not assume that ice cream can make you more violent. Would you?

I found another funny example of spurious correlation.

Did you know that the number of people who drowned by falling into a swimming-pool correlates with the number of films Nicolas Cage appeared in? Does one factor cause the other?

Source: http://tylervigen.com/view_correlation?id=359

**Conclusion**

Students tend to assume that correlation proves that one variable causes the other.

Apparently, it is a human nature that we look for patterns which help us explain the world around us.

However, it is often a logical fallacy and a flaw in reasoning and Lisa is not the only person making this mistake.

Some examples from research papers

1.

*‘a strong correlation’* is not causation! However *‘an impressive number of research studies’* might suggest the causation actually exists.

Remember that emotive words such as *‘impressive’* should be avoided in academic writing since they sound rather subjective.

By the way, who knows what *‘a moderately strong correlation’* is? I have heard about weak, moderate, strong correlation only.

2.

*‘statistically significant correlation’* is not causation either

3.

Finally, there is a ‘statistically significant correlation’ between stork populations and human birth rates across Europe.

Does it prove that storks deliver babies?

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I was never close to a PhD burnout either.

I never wished I hadn’t started my PhD in the first place.

My PhD was pretty much a stress-free experience.

However, I am aware that:

- I was lucky to have a good supervisor
- I had a full scholarship for three years (no financial worries)
- I had an interesting project and no major complications along the way
- I did not really want to have PhD
- I was treating PhD more like a by-product of my project
- I was always aware that I might have to quit
- I had a ‘Plan B’ (life without PhD)

In the last five years, I have seen so many of PhD students stressed, depressed and crying that I know I was merely lucky.

Would I have been able to quit my PhD if I had invested several thousands of pounds in education as many international students do?

Would I have been able to finish my project if not for my supportive wife?

What if things with my project and life had gone differently?

No matter how we look at that, doing PhD is a stressful experience and prospective students should take this seriously into consideration before embarking on this ‘journey’.

If you think I am exaggerating, please read the journal article I summarised below.

Levecque at al. (2017) in an interesting study on mental problems in PhD students in Belgium (*N* = 3659) concluded that PhD students are at risk of developing a psychiatric disorder. The researchers employed GHQ – the General Health Questionnaire, a popular instrument in health research on psychological distress and depression. More exactly, they found out that:

51% of the PhD students in Flanders report at least two symptoms on the GHQ-12 (GHQ2+), 40% report at least three symptoms (GHQ3+), while 32% experience at least four symptoms (GHQ4+).

The prevalence of having or developing a common psychiatric disorder (e.g. depression) was 2.43 times higher in PhD students compared to the highly educated in the general population. It was 2.84 times higher compared to highly educated employees and 1.85 times higher compared to higher education students

Levecque and the colleagues attributed the problem to several factors:

Especially work-family interface, job demands and job control, the supervisor’s leadership style, team decision-making culture, and perception of a career outside academia are linked to mental health problems.

Highlights of the study:

• One in two PhD students experiences psychological distress; one in three is at risk of a common psychiatric disorder.

• The prevalence of mental health problems is higher in PhD students than in the highly educated general population, highly educated employees and higher education students.

• Work and organizational context are significant predictors of PhD students’ mental health.

Levecque, K., Anseel, F., De Beuckelaer, A., Van der Heyden, J., & Gisle, L. (2017). Work organization and mental health problems in PhD students. *Research Policy*, *46*(4), 868-879

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