As sample size increases, confidence interval narrows (FA2020 p263). So decreasing the sample size would increase the width of the confidence interval.
If you are like me and need a rationale for this rather than just memorization, this happens because the standard error decreases with increasing sample size.
Remember a 95% confidence interval is approximately equal to the sample mean +/- 2(SE).
The Standard Error is equal to the standard deviation divided by the square root of the sample size
SO if you increase the sample size, you decrease the SE which decreases the width of the confidence interval
Here is a good general explanation of confidence intervals, confidence level, and sample size with numbers:
bboucherI think that was very well explained! For those that are not very good with numbers and formula like me, the way I understand it is :
If I have more people in my study, I get closer to a real representation of the population by mean my study become more representative of the reality. That being said, it means that I can say with more confidence that my true result is actually true so I don't need to say ''the result will be between 10 and 100'' which would be a very large standard deviation compared to saying ''my result will be between 10 and 20'' which I can say with more confidence because my study has more people so more power. The bell curve become more steap because the average become more representative of reality so by default my standard deviation become decreased because I know for a fact that I am more accurate so that I don't need such a large gap to make sure that my result actually falls in+1
fatboyslimExcellent explanation cassdawg, thank you so much+
submitted by โcassdawg(1780)
As sample size increases, confidence interval narrows (FA2020 p263). So decreasing the sample size would increase the width of the confidence interval.
If you are like me and need a rationale for this rather than just memorization, this happens because the standard error decreases with increasing sample size.
Here is a good general explanation of confidence intervals, confidence level, and sample size with numbers:
http://www.opentextbooks.org.hk/ditatopic/9471