## Statistics – Correlation

Hi, last week I talked about “Cronbach’s Alpha” that is based on Pearson’s correlation so I will show you the correlation command and the result for the same variables (questions from a questionnaire of traffic behaviour).

Some of you maybe joined my webinar about Factor Analysis (to measure the unmeasureable), or you have watched the recording? Factor Analysis is also based of correlation, so that’s why I want to talk about that today as a continue.

See the result from Factor analysis, the first factor belongs of 3 variables within my red oval:

So let’s have a look of the correlations between them, using the command:

**Analysis – Correlate – Bivariate **

Put the variables you want to compare into the right box under: “**Variables**“.

Result, after some pivoting (so you don’t have to see the p-values and N). The correlation values is between -1 and +1. If the value is 0 you don’t have a high correlation between the 2 variables. If closer to -1 or +1 then you have higher correlation:

The original variables is questions or attitues with values between a scale from 1 to 5 (where 5 is highly agree), so I couldn’t expect so high correlations. So with this types of ordinal variables, if I have correlations above 0.4 I will be happy, so due to my experience that means high correlation. The highest correlation here is 0.396 between the variables: “I think it is OK to run a bit faster…” and “It is annoying to drive behind…”.

**Compare to Cronbach’s alpha from last week**

Last week when I did the Cronbach’s alpha, you might remember that I was not so satisfied as the alpha value was only **0.621** between these 3 variables above, because the treasure value should be above 0.70 as a common rule. *(Cronbach’s alpha is some type of average correlation between several variables at the same time)*.

What I also could see was a higher Cronbach’s alpha value for 3 other variables, that showed a value of: **0.711**. So let’s have a look of the correlation matrix for these 3 variables, that had to do with car interests reading.

The reason why the Cronbach’s alpha value was higher, was because of the very high correlation : **0.598** between “I often read magazines…” and “I follow what’s happening in the…” .

**Compare to Factor analysis**: Just for fun, if you are interested of factor analysis, you can also see that the **factor loadings** are higher in this factor (this group of variables) that is included in the green ovale compared to the red ovale:

**Spearmans correlation**

If you are working with very skewed distributions a recommendation is to use Spearman’s correlation. Some researchers or users also prefer to use Spearman’s correlation when they work with ordinal variables (like the variables I used in my example above, with scale between 1-5). But as always: different schools.

The command is the same but you will then tick the box at Spearman:

Greetings Gunilla Rudander