Statistics

Statistics

• Standard Error of the Mean (SEM) is the standard deviation of the estimate of the samplemean of a given population mean. To break down that definition, think about finding the error of deviation of the given sample from the entire population. In statistics, we need to know how good our sample is. So, we ask, howwell does the sample fit the population? There will always be a certain level of error with any statistical estimate. We can calculate SEM by (sample standard deviation) divided by the square root of the sample size (also expressed as n). SEM is often represented by the following formula:

is the sample standard deviation

•

is the number of observations for our given sample

•

Using the previous example from above, we calculated:

• = 5 (number of observations from the previous example) • Sample Standard Deviation = ≈ 12.04 • = ̅̅̅ = 12.04 √5 ≈ 5.38

We can now interpret our sample of the population by saying the standard deviation is 12.04 with a calculated sample error of 5.38. For our sample of weights, the mean was 117; our sample falls within the mean with a deviation of + or – 12.04 points from the mean with an error of 5.38 or just 5 if rounded up.

Let’s check the math:

Our mean is 117 +12 (deviation from the mean) = 129; we have an error of 5 points, so if we add 5 = 134 (max weight). Now let’s look at the lowest weight. 117 - 12 (deviation from the mean) = 105 with an error of 4, so if we subtract 4 we get 101 (pretty close to 100!) – note it does not have to equal the upper and lower values, but it should be pretty close. So, our sample does not deviate too much from the mean! The more deviation from the mean and the higher the error, the less effective the sample is at representing the population. Confidence interval (CI) is used to indicate the reliability of a statistical estimate; meaning how confident we are in our estimation. We can calculate the confidence interval boundaries: the mean minus a calculation of uncertainty, to the mean plus that calculation of uncertainty.

= ̅± ( ∗ ×

)

√

= sample mean

• ̅

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