How could I describe the relationship between two scores with an r obtained of 0.007248, with a p value = 0.9726 and between two scores with an r obtained of -0.4490, with a p value = 0.0278?
the p-value indicates that the probability that you obtain that result under the assumption that the null-hypothesis is correct, that is that they are not correlated. Therefore if you have two vectors of value and the p-value is very high (.92), then it means that the two vectors might be independent or not to have a clear relationship with each other. As values in vector A increases, values of vector B do not show any particular trend.
The second result instead shows that the two vectors of values are negatively correlated. Therefore, at higher values in vector A correspond lower values in vector B.
does that make any sense to you?
Hello Raquel Martinho.
The pearson correlation coefficient can range between -1 and +1. +1 indicates a positive linear relationship, whereas -1 indicates a negative linear relationship. 0 indicates no linear relationship. Thus the sign of the coefficient indicates the direction of the relationship. But be aware that the pearson correlation coefficient is very sensitive to extreme data values. So you should check your data for extreme values before you start interpreting results. Furthermore be aware that a coefficient value of 0 does not mean that there is no relationship at all. It just mean that there is very likely no linear relationship. A non linear relationship could exist in such cases. A plot could be useful to check for non linear relationships.
To determine whether the correlatio is significant or not a p-value is used. The p-value tells you whether the correlation coefficient is significantly different from 0 or not (related to your data). If the p-value is less than or equal to the significance level, then you can conclude that the correlation is different from 0.
I hope this helps to interpret your results.
Best regards Paul
For the first correlation you calculated, there does not seem to be any real relationship between the two variables (your r value is extremely low), and besides, the p-value (which is extremely high) shows that what little relationship there is, is not significant. That means the relationship between your two variables is most likely due to random chance.
For the second one, your p-value is low enough that you can say (given your alpha of 0.05) that the relationship between your two variables is most likely not random, and you can see from your correlation coefficient that there is an inverse, moderately strong association between your two variable. As one of your variables increases, the other tends to decrease.
Hi Raquel
Very simplified, correlation is the “co-occurrence” of phenomena. A positive correlation means that two phenomena change together (simultaneously) and in the same direction (both are increasing or decreasing). If the correlation is negative, they change in opposite directions (one increases, the other decreases). Both can be full (total) or partial. A full positive correlation (r=+1) means that both phenomena change in the same direction and at the same rate. If the correlation is full negative, both phenomena change at the same rate, but in opposite directions (r=-1). A partial positive correlation means, that the change is in the same direction, but the rate is different, by partial negative correlation both the direction and the rate of the change is different (r= between 0 and +/-1). Correlation is (usually) not a causal relation. In large samples r=+/- 0.20 is not significant, r =+/-0.20─+/-0.40 means small, r=+/-040─+/-0.60 moderate, r=+/- 0.60 > is high. Besides r, in the interpretation of results Cohen’s d (the index of effect size) is the most significant indicator. There are very good formulas on the internet for the calculation of d. If the value of d is around 0.2 or less, the effect is small (negligible near zero), if around 0.5 it is medium or moderate, and if it is 0.8 or more, the effect is very large or significant (regardless of whether the result of r is statistically significant or not). The higher the d, the greater the practical significance of the obtained correlation (as generally accepted after Cohen, J. (1988). Statistical power analysis for the behavioral sciences, 2nd ed. Hillsdale, NJ: Erlbaum.
All the best, Lajos
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