# How can two variables have different means but not be correlated?

A t-test confirmed that two variables had significantly different means, but Spearman said they’re not correlated. One variable is ordinal (strong, weak) and the other is interval (scores). So the strong folks have significantly higher test scores than the weak group, but the "strong" category is not associated with higher test scores? I can wrap my head around these stats. Can someone explain this to me conceptually?

I agree. You are absolutely right. It is a bit confusing my mind also. Let me consult my mentor today evening and let you know tomorrow.

I agree. You are absolutely right. It is a bit confusing my mind also. Let me consult my mentor today evening and let you know tomorrow.

References :own

An independent t-test and Pearson’s correlation are mathematically equivalent, the same is not true of a t-test and a Spearman’s correlation. It would be more appropriate to use Pearson’s point-biserial correlation coefficient (which is actually also just equivalent to the standard Pearson’s one in SPSS, but as it’s identical to the t-test, there’s no point in doing both).

As for why they’re different, the most likely answer is the distributions of the data. Minor differences can come simply from Spearman’s being a less powerful test, as Spearman’s is a Pearson correlation performed on the ranked data, depending on your data, big differences in the actual values can become small ones, e.g.:

Data Rank

1 1

10 2

15 3

100 4

The magnitude of the difference between 15 and 100 is ignored in the ranks.

Larger differences can come if the data in one of your groups isn’t normally distributed, e.g.:

Group|Score

11

12

13

14

15

14

13

12

11

15

21

21

23

21

23

244

254

289

2200

2100

T-test (Equal variances assumed): t(18) = -2.262, p=.036

T-test (Equal variances not assumed): t(9.009) = -2.262, p=.050

Pearson’s correlation: R = .47, p=.036 *same as t-test

Spearman’s correlation: Rho = .228, p =.333

The differences in the actual values means that the mean of group 2 is much higher than group 1, but the ranks don’t reflect this tendency particularly strongly. You should check whether the data for both of your groups is normally distributed.

References :Researcher