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Introduction to Confidence Intervals :: Smaller Samples Vary More than Larger Samples

There's another important point that's worth noting: The smaller the sample, the more variable the responses will be and the bigger the margin of error. Let's say the population was going to vote 55% for Jim and 45% for John and the Star Tribune only asked five people instead of 1000. With a smaller sample, they increase the chance that they are getting a result that's different than the whole population.




Imagine if the Star-Tribune took the same poll as in the example above but only asked 5 people instead of 1000 people. Let's say they took the poll six times. The results might look something like this:

Result of Star-Tribune Poll done 6 times with only 5 Users

  Poll 1 Poll 2 Poll 3 Poll 4 Poll 5 Poll 6
Votes for Jim 5 4 2 0 1 3
Votes for John 0 1 3 5 4 2
Poll Results 100 to 0 80 to 20 40 to 60 0 to 100 20 to 80 60 to 40

Look at the poll results above. Notice how the results are all over the place? We know that the population will vote 55% for Jim and 45% for John; but if the newspaper reported the results with only 5 people, they could be way off. By sampling more people they will reduce their chances of being way off.

The important point is that as samples get larger, the amount of variability goes down: Larger samples have a smaller margin of error (less variability) and smaller samples have a higher margin of error (more variability). This is a point that will continue to appear in confidence intervals.

Click on the Sample Sizes buttons below.

Notice how confidence intervals get wider with smaller samples?

 


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