HOW LARGE OF A SAMPLE SHOULD YOU USE? The larger the sample size, the more likely: o It will be representative of the whole population o The conclusions.

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Presentation transcript:

HOW LARGE OF A SAMPLE SHOULD YOU USE? The larger the sample size, the more likely: o It will be representative of the whole population o The conclusions that you draw from your experiment will be true for the whole population

Example: What was the average age of people in the US in 2000? How could we figure this out? What if we selected a sample size of 10 people? Would that be able to represent the population of the United States? Why or why not?

Example: What was the average age of people in the US in 2000? How could we figure this out? o If we selected a sample size of 10 people, it is possible, just by chance alone, that the individuals we selected could all be very old or very young. o They would not show the same variability as the population. o Any conclusions drawn will be based on erroneous results. This would be considered a biased sample because it is not representative. o A sample of 30 individuals would increase the likelihood of a sample looking like the population. o Sample sizes of 100 or even 500 would be even more representative.

Average age of people in the US in 2000 Sample size 10 Sample size 500Sample size 100 Sample size 30 Blue bar is the mean Red bar is the standard deviation (variation or spread of the data) Graph: Results if we did 20 trials, each time looking at the ages of only 10, 30, 100, or 1000 people. Each bar represents a different trial.

What do you notice about the range of means over all 20 trials?

If we looked at the range of means for all 20 trials, we can see a large range (spread) with a sample size of 10 (10 people sampled in each trial). The range decreases a lot by a sample size of 30 people per trial.

What do you notice about the standard deviations over all 20 trials?

Major Points: Sample size influences the potential that your sample is representative of the population Larger sample size will be more likely to be representative of the population Smaller sample size has a greater possibility of being biased away from the population Sample of size of 30 is a good starting point