Demonstration of 95% confidence intervals. Approximately 95 out of 100 samples will result in confidence intervals that contain the true slope. Note, if a confidence interval contains zero, the slope is not statistically significant at the 0.05 level.
If we want to increase the statistical power to ensure that we have more confidence in our results (achieve statistical significance) we can increase the sample size from 10 to 25. Notice how much smaller the confidence intervals become.
If we have a small sample size, but a large effect size, we still have good statistical power. There is a trade-off between the size of the program effect, and how much data we need to detect it.
Measurement Error: imprecise measures of variables impacts the model in different ways depending upon whether it is in the dependent or independent variable.