1. The Data Collection and Statistical Analysis in IB Biology John Gasparini The Munich International School Part V – Introduction to Correlation and Linear Regression

2. http://images.fineartamerica.com/images-medium-large-5/queen-butterfly- feeding-on-yellow-flower-art-skopec-state-f-the-art-photography.jpg Most butterflies and moths are nectarivores, meaning they feed on the sugar-rich nectar of flowers. http://www.kidsbutterfly.org/faq/behavior/3 Remember back to the first of these presentations…

3. http://media.tumblr.com/f2f0e4826de319dd44bd7e4737f2e890/tumblr_inline_mll809ojgJ1qz4rgp.jpg Butterflies and moths have an interesting way of feeding. One of the more defining characteristics of Lepidopterans is their straw-like proboscis. It is held coiled under the head when not in use. During feeding, however, it is extended to reach the nectar of flowers. Proboscis coiled Proboscis uncoiled during feeding

4. Some Lepidoptera have extremely long probosci! http://msue.anr.msu.edu/news/whats_hovering_over_my_flowers These exaggerated mouthparts have usually evolved to help the moth reach sugar-rich nectar from flowers with very deep nectaries. The nectar is here! A long proboscis is necessary. Why do plants evolve deep nectaries? Well, most flowers have probably evolved these structures to prevent pollinators from cheating – that is getting the flower’s nectar supply without carrying a sufficient payload of pollen.

5. Some moths have evolved to reach VERY DEEP sources of nectar. Xanthopan morganii praedicta - Darwin's Moth http://www.youtube.com/watch?v=iMz6lApJgu4 The proboscis of X. morganii ranges from 20 to 35 cm in length

6. The question you might ask then is… Well there is a trade off… “Why don’t all Lepidoptera just evolve to have long probosci?” Do you think that flying and handling such a long feeding tube is easy for a small flying insect? Also, it takes quite a bit of effort and specialized mouthparts to suck nectar through such a long proboscis…

7. Let's study a bit of data relating to this question, and let’s learn another data processing skill as well as some associated statistical analysis. “Why don’t all Lepidoptera just evolve to have long probosci?” Data should be collected for several Lepidopteran species to determine AVERAGE BUTTERFLY PROBOSCIS LENGTH, as well as AVERAGE FEEDING HANDLING TIME per species. Does the length of a butterflies proboscis affect the amount of time a butterfly must spend feeding on each individual flower?

8. Average Butterfly Proboscis Length vs. Feeding Handling Time Species Numbe r Average Proboscis Length (cm, +/-0.1cm) Average Feeding Handling Time (s, +/- 0.01s) 11.50.91 21.61.56 31.80.94 41.81.20 51.91.30 62.00.92 72.10.88 82.10.75 92.31.20 102.30.98 112.31.56 122.40.83 132.40.89 142.60.74 152.60.69 162.91.01 173.51.21 183.70.73 193.80.82 204.51.11 Wow! Here’s the exact data set that we need… Now, how do we determine what type of correlation or relationship between Proboscis Length and Average Feeding Time?

9. Average Butterfly Proboscis Length vs. Feeding Handling Time Species Numbe r Average Proboscis Length (cm, +/-0.1cm) Average Feeding Handling Time (s, +/- 0.01s) 11.50.91 21.61.56 31.80.94 41.81.20 51.91.30 62.00.92 72.10.88 82.10.75 92.31.20 102.30.98 112.31.56 122.40.83 132.40.89 142.60.74 152.60.69 162.91.01 173.51.21 183.70.73 193.80.82 204.51.11 Wow! Here’s the exact data set that we need… Now, how do we determine what type of correlation or relationship exists between Proboscis Length and Average Feeding Time. The first step is to graph the data by constructing a SCATTER PLOT.

10. In terms of software that we can use to generate scatter plots from data sets, we have Excel and LoggerPro preloaded on our machines. (Both work well, but I personally think that LoggerPro looks better.) Graph the Average Butterfly Proboscis Length vs. Feeding Handling Time in Excel You can figure our how to do this on your own… Make yours look like mine!

11. In terms of software that we can use to generate scatter plots from data sets, we have Excel and LoggerPro preloaded on our machines. (Both work well, but I personally think that LoggerPro looks better.) Graph the Average Butterfly Proboscis Length vs. Feeding Handling Time in LOGGERPRO You can figure our how to do this on your own… Make yours look like mine!

12. When interpreting a graph: 1)Look at the overall pattern 2)Look for striking deviations (known as outlers) from that pattern. 3)You can describe the overall pattern by the form, direciton, and strength of the relationship. There can be a positive association (direct relationship) or a negative association (inverse relationship) The strength of a relationship depends on how closely the points follow a clear form.

13. In general, a linear relationship is strong if the points lie close to a straight line, and weak if they are widely scattered about a line. Correlation (written as r or r 2 in Excel) measures the direction and strength of the linear relationship between two quantitative variables.

14. Key things to know about correlation: Both variables must be quantitative The units of measurement doesn't matter--correlation stays the same A positive r indicates a positive association, and a negative r indicates a negative association The r is always a number between -1 and 1 Values of r near 0 indicate a weak relationship, but values of r closer to -1 or 1 indicate that the points in a scatterplot lie close to a straight line Correlation is not resistant to the influence of outlier-- outliers do affect it. Correlation does not mean causation!

15. Here are some examples of how correlation measures the strength of a linear relationship. Strength: A strong correlation ranges from.8 to 1.0 A moderate correlation ranges from.6 to.8 A weak correlation ranges from 0 to.6

16. How high must a correlation value be to be considered meaningful? It depends on the discipline: Here are some rough guidelines: Disciplinemeaningful if r or R 2 is… Physicsr < -0.95 or 0.95 < r, or 0.9 < R 2 Chemistryr < -0.9 or 0.9 < r, or 0.8 < R 2 Biologyr < -0.7 or 0.7 < r, or 0.5 < R 2 Social Sciencesr < -0.6 or 0.6 < r, or 0.35 < R 2 Strength: A strong correlation ranges from.8 to 1.0 A moderate correlation ranges from.6 to.8 A weak correlation ranges from 0 to.6

17. y = mx + b Some of this you have done this in your maths courses. Now let's use this skill in Biology Where m is the slope or gradient of the line and b is the y-intercept.