Statistics in Biology.

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Presentation transcript:

Statistics in Biology

The Mean Mean (x̄) is a measure of the central tendency of a set of data. (average) Ex. Calculate the mean. Answer = 11.6

The Mean Graphing the Mean  Bar Graph

Measures of Variability Range: difference between largest/smallest values in data set Standard deviation (s) is a measure of the spread of most of the data

Standard Deviation

Standard Deviation 68% of all data fall within ± 1 standard deviation of the mean 95% of all data fall within ± 2 standard deviation of the mean 99.7% of all data fall within ± 3 standard deviation of the mean

Standard Deviation

Standard Deviation

Standard Deviation

Standard Deviation

Standard Deviation

Calculating Standard Deviation Calculate the mean Determine the differences Square the differences Sum the Squares Divide by sample size (n) – 1 Take the square root

Measurements of Confidence Uncertainty: the margin of error in a measurement Ex: digital scale: 126.4g (±0.1g)

Standard Error of the Mean Standard Error of the Mean (SE or SEM): measures how close the sample mean is to the population mean Measure of accuracy (if the true mean is known) Measure of precision (if the true mean is not known) The greater the sample size, the less the uncertainty in the calculations

Standard Error (SE or SEM)

Standard Error

Standard Error 95% confidence interval (95% CI): 95% confident that the true means falls between 2 SE above/below calculated mean Graph with error bars Graph with error bars representing representing SE of the mean 95% confidence interval

Error Bars

Error Bars

Error Bars Look for overlap of error lines If overlap- difference is NOT significant If no overlap- difference IS significant

Error Bars Significance of Data Which graph shows two means that are significantly different? Hint: Look for the non-overlapping error bars. Answer: The means in (c) are statistically different.

Error Bars Statements Fish2Whale food caused the most growth Fish2Whale food caused more fish growth than did Budget Fude

Error Bars Statements More males in all four regions exhibited the trait measured than did females More males in region 3 exhibited the trait measure than did females

The End