Final answer:
Statistical significance depends on effect size, sample size, and the strength and direction of association measured by the correlation coefficient. Large samples and strong correlations increase the reliability of concluding a significant relationship in the population.
Step-by-step explanation:
Statistical significance calculations primarily depend on several key factors, which include effect size, sample size, and the strength and direction of association as indicated by the correlation coefficient (r).
The effect size reflects the magnitude of the difference or relationship present, while the sample size (n) affects the precision of the statistical estimate. A larger sample size typically confers more reliability on the model. Furthermore, the correlation coefficient, which measures the strength and direction of the linear relationship between two variables, is crucial in determining how closely the variables are related to each other.
When testing for significance, assumptions such as linearity between the variables and a representative sample are essential. This process involves setting up a null hypothesis that assumes no effect or relationship and an alternate hypothesis that suggests the presence of an effect or relationship. The p-value obtained from the test is compared against a threshold (say 5% significance level) to determine if the results are statistically significant.