Statistics in Biology The Mean Mean ( x ) is a measure of the - PDF document

3/15/2017 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 Measures of Variability Graphing the Mean  Bar Graph Range : difference between largest/smallest values in data set Standard deviation (s) is a measure of the spread of most of the data 1

3/15/2017 Standard Deviation 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 2

3/15/2017 Standard Deviation Standard Deviation Calculating Standard Deviation Measurements of Confidence 1. Calculate the mean 4. Sum the Squares Uncertainty : the margin of error in a measurement Ex: digital scale: 126.4g ( ± 0.1g) 2. Determine the differences 5. Divide by sample size (n) – 1 3. Square the differences 6. Take the square root Standard Error of the Mean Standard Error (SE or SEM) 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 3

3/15/2017 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 Error Bars • Look for overlap of error Significance of Data lines Which graph shows two means that are significantly different ? Hint: Look for the non-overlapping error bars. • If overlap- difference is NOT significant • If no overlap- difference IS significant Answer: The means in (c) are statistically different. 4

3/15/2017 Error Bars 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 Statements • Fish2Whale food caused the most growth • Fish2Whale food caused more fish growth than did Budget Fude The End 5