Strength of Correlation on these Graphs

Vivara

I would be inclined to say:

(i) Moderate Positive Correlation
(ii) Moderately Strong Positive Correlation
(iii) Strong Positive Correlation

Would these be correct?

Thanks.

TheBody

Looks good to me. I guess everyone will have their own opinion on what constitutes weak, moderate or strong though.

hivizman

See the previous thread on this topic.

I was able to use the underlying data to calculate the actual correlation coefficients:

Cycle v Swim 0.55
Run v Swim 0.49
Run v Cycle 0.77

The Run v Swim data are more clustered in the middle, but there is a larger number of outliers at the top end of the distribution, and this, I think, is reducing the correlation coefficient in comparison with Cycle v Swim.

The OP on the other thread noted that the suggested solution was:

Cycle v Swim = weak correlation
Run v Swim = moderate correlation
Run v Cycle = strong correlation

The consensus was that there was little difference between Cycle v Swim and Run v Swim, so both of them should be considered as moderately correlated. The Run v Cycle distribution is clearly "tighter" than the other two, so a verdict of strong correlation seems sensible.

By the way, this sort of description of the relationship is a separate matter from the statistical significance of the correlation coefficient. In all cases, the value of the coefficient is large enough to allow you to reject the null hypothesis that, in a population from which the participants in the underlying triathlon event (see previous thread for a link to the data) are regarded as a sample, the true correlations would be zero. So we can be confident that there's a relationship between the times in the different events - but this statistical test doesn't tell us the strength of the relationship.

Vivara

Thank you so much! I would have used the search function, but I doubted that it had been asked before and would have had no idea as to what keywords to use in the search.

Responses make sense... also found it interesting that the first one actually has a stronger correlation than the second.

V.

Vivara

P.S. It is fantastic to see a Moderator who goes above and beyond the call of duty as you did in that previous thread. I was a Lead Admin on a large forum before and it's difficult to find someone who truly loves the topic they're modding. You clearly do and it's great.

hivizman

Vivara wrote: »

P.S. It is fantastic to see a Moderator who goes above and beyond the call of duty as you did in that previous thread. I was a Lead Admin on a large forum before and it's difficult to find someone who truly loves the topic they're modding. You clearly do and it's great.

Thanks - I'm not actually a moderator on the Mathematics Forum, just an interested bystander. I'm one of the moderators on the Islam Forum.

Fremen

hivizman wrote: »

I'm one of the moderators on the Islam Forum.

Interesting. Another al-Khwārizmī, maybe...

Capt'n Midnight

would that look like a globular cluster on a 3D graph ?