1. Excel How To Mockingbird Example BIO II Van Roekel

2. Hummingbirds are nectarivores (herbivores that feed on the nectar of some species of flower). In return for food, they pollinate the flower. This is an example of mutualism – benefit for all. As a result of natural selection, hummingbird bills have evolved. Birds with a bill best suited to their preferred food source have the greater chance of survival. Photo: Archilochus colubris, from wikimedia commons, by Dick Daniels.wikimedia commonsDick Daniels

3. Researchers studying comparative anatomy collect data on bill-length in two species of hummingbirds: Archilochus colubris (red-throated hummingbird) and Cynanthus latirostris (broadbilled hummingbird). To do this, they need to collect sufficient relevant, reliable data so they can test the Null hypothesis (H 0 ) that: “there is no significant difference in bill length between the two species.” Photo: Archilochus colubris (male), wikimedia commons, by Joe Schneidwikimedia commons

4. The sample size must be large enough to provide sufficient reliable data and for us to carry out relevant statistical tests for significance. We must also be mindful of uncertainty in our measuring tools and error in our results. Photo: Broadbilled hummingbird (wikimedia commons).wikimedia commons

5. The mean is a measure of the central tendency of a set of data. Table 1: Raw measurements of bill length in A. colubris and C. latirostris. Bill length (±0.1mm) nA. colubrisC. latirostris 113.017.0 214.018.0 315.018.0 415.018.0 515.019.0 616.019.0 716.019.0 818.020.0 918.020.0 1019.020.0 Mean s Calculate the mean using: Your calculator (sum of values / n) Excel =AVERAGE(highlight raw data) n = sample size. The bigger the better. In this case n=10 for each group. All values should be centred in the cell, with decimal places consistent with the measuring tool uncertainty.

6. The mean is a measure of the central tendency of a set of data. Table 1: Raw measurements of bill length in A. colubris and C. latirostris. Bill length (±0.1mm) nA. colubrisC. latirostris 113.017.0 214.018.0 315.018.0 415.018.0 515.019.0 616.019.0 716.019.0 818.020.0 918.020.0 1019.020.0 Mean 15.918.8 s Raw data and the mean need to have consistent decimal places (in line with uncertainty of the measuring tool) Uncertainties must be included. Descriptive table title and number.

8. DELETE X DELETE X

11. Descriptive title, with graph number. Labeled point Y-axis clearly labeled, with uncertainty. Make sure that the y-axis begins at zero. x-axis labeled

12. From the means alone you might conclude that C. latirostris has a longer bill than A. colubris. But the mean only tells part of the story.

14. Standard deviation is a measure of the spread of most of the data. Table 1: Raw measurements of bill length in A. colubris and C. latirostris. Bill length (±0.1mm) nA. colubrisC. latirostris 113.017.0 214.018.0 315.018.0 415.018.0 515.019.0 616.019.0 716.019.0 818.020.0 918.020.0 1019.020.0 Mean 15.918.8 s 1.911.03 Standard deviation can have one more decimal place. =STDEV (highlight RAW data). Which of the two sets of data has: a.The longest mean bill length? a.The greatest variability in the data?

15. Standard deviation is a measure of the spread of most of the data. Table 1: Raw measurements of bill length in A. colubris and C. latirostris. Bill length (±0.1mm) nA. colubrisC. latirostris 113.017.0 214.018.0 315.018.0 415.018.0 515.019.0 616.019.0 716.019.0 818.020.0 918.020.0 1019.020.0 Mean 15.918.8 s 1.911.03 Standard deviation can have one more decimal place. =STDEV (highlight RAW data). Which of the two sets of data has: a.The longest mean bill length? a.The greatest variability in the data? C. latirostris A. colubris

16. Standard deviation is a measure of the spread of most of the data. Error bars are a graphical representation of the variability of data. Which of the two sets of data has: a.The highest mean? a.The greatest variability in the data? A B Error bars could represent standard deviation, range or confidence intervals.

17. Put the error bars for standard deviation on our graph.

19. Delete the horizontal error bars

20. Title is adjusted to show the source of the error bars. This is very important. You can see the clear difference in the size of the error bars. Variability has been visualised. The error bars overlap somewhat. What does this mean?

21. Excel can jump straight to a value of P for our results. One function (=ttest) compares both sets of data. As it calculates P directly (the probability that the difference is due to chance), we can determine significance directly. In this case, P=0.00051 This is much smaller than 0.005, so we are confident that we can: reject H 0. The difference is unlikely to be due to chance. Conclusion: There is a significant difference in bill length between A. colubris and C. latirostris.

23. Two tails: we assume data are normally distributed, with two ‘tails’ moving away from mean. Type 2 (unpaired): we are comparing one whole population with the other whole population. (Type 1 pairs the results of each individual in set A with the same individual in set B).

25. 95% Confidence Intervals can also be plotted as error bars. These give a clearer indication of the significance of a result: Where there is overlap, there is not a significant difference Where there is no overlap, there is a significant difference. If the overlap (or difference) is small, a t-test should still be carried out. no overlap =CONFIDENCE.NORM(0.05,stdev,samplesiz e) e.g =CONFIDENCE.NORM(0.05,C15,10)

26. Error bars can have very different purposes. Standard deviation You really need to know this Look for relative size of bars Used to indicate spread of most of the data around the mean Can imply reliability of data 95% Confidence Intervals Adds value to labs where we are looking for differences. Look for overlap, not size Overlap  no sig. diff. No overlap  sig. dif.

29. http://click4biology.info/c4b/1/gcStat.htm

30. http://mathbits.com/MathBits/TINSection/St atistics1/Spreadsheet.html