what is the relationship between levels of confidence and statistical significance?
The relationship between levels of confidence and statistical significance relates to how certain we are in the results of a statistical analysis.
Statistical significance is typically measured using a p-value, which indicates the probability of obtaining the observed data, or data even more extreme, assuming the null hypothesis is true. The null hypothesis is a statement that assumes there is no relationship or difference between variables being compared. A p-value below a certain threshold (usually 0.05 or 0.01) is considered statistically significant, indicating that the observed data is highly unlikely to have occurred by chance alone, assuming the null hypothesis is true.
On the other hand, confidence level is a measure of how confident we are in the estimate or result obtained from a statistical analysis. It is expressed as a percentage and indicates the probability that the true population parameter lies within a specified range. For example, a 95% confidence level implies that, if we repeatedly sampled from the same population and estimated the parameter, we would expect the true parameter to fall within the range 95% of the time.
The relationship between statistical significance and confidence level is that they both represent the level of confidence we have in our results. A high level of statistical significance (i.e., a low p-value) implies that there is strong evidence against the null hypothesis, increasing our confidence in rejecting the null hypothesis and concluding that there is a true relationship or difference. A high confidence level (e.g., 95%) indicates that we are highly confident that the true population parameter lies within the specified range.
In summary, statistical significance and confidence level both provide measures of confidence in statistical analysis. However, statistical significance is focused on the probability of obtaining the observed data assuming the null hypothesis is true, while the confidence level relates to the probability that the true parameter lies within a specified range.