Confidence Intervals for the Difference Between 2 Proportions

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter. It is expressed with a certain level of confidence, such as 90% or 95%.

If a confidence interval includes 0, it suggests that there is no statistically significant difference between the two proportions being compared.

The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default assumption that any observed difference is due to sampling variability.

The alternative hypothesis (Ha) is a statement that indicates the presence of an effect or a difference, opposing the null hypothesis.

A test statistic is a standardized value that is calculated from sample data during a hypothesis test. It is used to determine whether to reject the null hypothesis.

A p-value represents the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true.

The significance level (alpha) is the threshold for determining whether a p-value indicates a statistically significant result, commonly set at 0.05 or 0.01.

If a test statistic is beyond -2 or +2, it indicates that the result is more than 2 standard deviations away from the mean, suggesting a small p-value and potential significance.

A 90% confidence interval of (-0.5, 0.7) suggests that we are 90% confident that the true difference in proportions lies within this range, including the possibility of no difference.