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What does a significant correlation between two variables mean?
Correlation coefficients measure the strength of the relationship between two variables. For example, height and weight are correlated—as height increases, weight also tends to increase. Consequently, if we observe an individual who is unusually tall, we can predict that his weight is also above the average.
What is considered a weak positive correlation?
A weak positive correlation would indicate that while both variables tend to go up in response to one another, the relationship is not very strong. A strong negative correlation, on the other hand, would indicate a strong connection between the two variables, but that one goes up whenever the other one goes down.
When is a relationship between two variables significant?
Comparing the computed p-value with the pre-chosen probabilities of 5% and 1% will help you decide whether the relationship between the two variables is significant or not. If, say, the p-values you obtained in your computation are 0.5, 0.4, or 0.06, you should accept the null hypothesis. That is if you set alpha at 0.05 (α = 0.05).
What happens when the correlation coefficient of two variables is zero?
If the correlation coefficient of two variables is zero, there is no linear relationship between the variables. However, this is only for a linear relationship. It is possible that the variables have a strong curvilinear relationship.
The Pearson product moment correlation coefficient between Y on X and the slope term of the regression of Y on X are intimately related, both are based on linearity, so I do not think it is that is the issue. When both variables are measured as z scores (that is, when both X and Y are measured as z scores), r = b, that is correlation equals slope.
Do you know the cause and effect of a correlation?
The key point is that is impossible just from a correlation analysis to determine what causes what. You don’t know the cause and effect relationship between two variables simply because a correlation exists between them. You will need to do more analysis to define the cause and effect relationship.