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Statistics in Biology: Standard Error of the Mean & Error Bars

Statistics in Biology: Standard Error of the Mean & Error Bars. Essential Question: How are statistics used to interpret data and determine the accuracy of experimental results?. Sampling and Capturing the Actual Mean.

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Statistics in Biology: Standard Error of the Mean & Error Bars

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  1. Statistics in Biology: Standard Error of the Mean & Error Bars Essential Question: How are statistics used to interpret data and determine the accuracy of experimental results?

  2. Sampling and Capturing the Actual Mean Let’s suppose that 3 students are assigned to determine the mean of black-eyed peas from a 1 pound bag of black-eyes peas. It would take hours to mass each and every pea. So the students decide to mass a random sample of the peas and determine the mean of the sample.

  3. Standard Error or Standard Error of the Mean It was agreed that each group would mass 100 black-eyed peas. The mean and standard deviation was determined for each of the three random samples. All three means are different but certainly close. What is the probability that each group captured the actual mean?

  4. Standard Error or Standard Error of the Mean In statistics, a sample mean deviates from the actual mean of a population; this deviation is the standard error or the standard error of the mean (SEM). To compute the SE or SEM just simply divide the standard deviation by the square root of the number of data points.

  5. Mean Bar graph of the three sample means. What is the probability of capturing the actual mean?

  6. Use the SE equation to calculate the standard error for the sample data

  7. Mean Bar graph with +/-1 SE bars inserted

  8. So what conclusions can I draw from using +/- 1 SE bars? Error bars that DO NOT overlap, suggest there is a significant difference in the data of samples 1 & 3 • Difference in means is due to something OTHER THAN random sampling • 68 % confidence level

  9. How do I report this conclusion?TWO Conclusions… At a 68% confidence level, the difference in means of samples 1 and 3, is statistically significant because the error bars do not overlap, using +/- 1 Standard Error of the mean. At a 68% confidence level, the population mean of a one pound bag of black-eyed peas is between 0.2161g and 0.2239g using data from sample 1.

  10. Calculate the 2x the standard error for the sample data

  11. Mean How does the confidence interval and conclusions change with +/- 2 SE bars?

  12. So what conclusions can I draw from using +/- 2 SE bars? Error bars that overlap suggest there is NO significant difference in the data of the 3 samples • Difference in means IS due to random sampling • 95 % confidence level

  13. How do I report this conclusion?Your Turn!! At a 95% confidence level, the difference in means of samples 1, 2 and 3, is not statistically significant because the error bars overlap, using +/- 2 Standard Error of the mean.

  14. How do I report this conclusion?Your Turn!! At a 95% confidence level, the population mean of a one pound bag of black-eyed peas is between 0.2200g and 0.2278g using data from sample 1.

  15. Video on Calculating Standard Error of the Mean & Error Bars YouTube: Bozeman Standard Error

  16. Calculate +/- 2 SEM for problem 1 and add the error bars to YOUR graph Using +/- 2 SEM write a conclusion based on problem 1 data & graph

  17. Notice what happens to the error bar as the sample size increases

  18. The larger the sample size, the smaller the standard error tends to be. • The greater the probability of capturing the actual mean of the population

  19. Comparing the Mass of Pinto Beans and Black-eyed Peas A student was interested in determining if the mass of pinto beans was significantly larger than the mass of black-eyed peas. It is obvious that the mass can vary.

  20. Comparing the Mass of Pinto Beans and Black-eyed Peas Upon observation, it appears that pinto beans are larger but it needs to be quantified. The mass of 300 random seeds are measured and recorded and histograms are made.

  21. Which sample of seeds will have a larger standard deviation, the pinto beans or black-eyed peas?

  22. The mean for black-eyed peas is 0.21 g and the mean for pinto beans is 0.37 g. Remember this is only a sample of a larger population.

  23. Is the difference in the means of these two samples statistically significant? • Is the difference in means due to sampling?

  24. The 2 SE bars do not overlap, so it is most likely that the difference between the mass means is statistically significant.

  25. Should I report Standard Deviation or Standard Error of the Means Bars???? If you are trying to support or reject a hypothesis -- in other words, when you are reporting on the results of an experiment -- you will most likely be using standard error of the means (usually 2 SE for a 95% confidence level for your error bars) but if you want to illustrate the variation in the population, you will use standard deviation bars.

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