Standard Deviation

Standard deviation measures how spread out the data is.

A lower standard deviation: - Data is closer to the mean - The independent variable may be causing the changes in the dependent variable

A higher standard deviation: - Data is more spread out from the mean - Factors other than the independent variable may be causing the changes in the dependent variable

To calculate standard deviation $s$

$$ s = \sqrt{\frac{\Sigma (x_i - \overline{x})^2}{n - 1}} $$

Standard Error

Standard error (of the mean) is how far the sample mean is from the true population mean.

For example, if you are sampling pine trees with a particular fungus in a forest, you could sample all the trees in a forest (population) and calculate the mean, but it might take too much time. So you sample a small number of trees of the forest and you can calculate your sample mean. The standard error is the comparison of the sample mean to the population mean. How far the sample mean is from the population mean might indicate accuracy in the study.

$$ SE_x = \frac{s}{\sqrt{n}} $$

Which is a valid statement?

Fish2Whale food caused the most fish growth. – Invalid statement. Standard error overlaps

Fish2Whale food caused more fish growth than Budget Fude. – This is a valid statement since the error does not overlap.