Statistical Significance vs correlation coefficient

A general discussion of significance tests for relationships between two continuous variables.

• Factors in relationships between two variables
  • The strength of the relationship:
    • is indicated by the correlation coefficient: r
    • but is actually measured by the coefficient of determination: r²
  • The significance of the relationship
    • is expressed in probability levels: p (e.g., significant at p =.05)
    • This tells how unlikely a given correlation coefficient, r, will occur given no relationship in the population
      • NOTE! NOTE! NOTE! The smaller the p-level, the more significant the relationship
      • BUT! BUT! BUT! The larger the correlation, the stronger the relationship

Note:

If statistical significance is less than 5% or P> 0.05, it means there is not much different between the null hypothesis and what is measured. It also means there is less sample errors. The null hypothesis is found to be almost true of what is measured or what the study was aimed at.

P-Value: The lower the P value, the less likely the finding would occur by chance alone.  P-Value the probability that a finding has occurred randomly rather than as a result of a treatment or other intervention.