EXAMPLES OF STATS FUNCTIONS

Two species of butterflies: http://www.zipcodezoo.com/hp350/Adelpha_basiloides_0.jpg http://4.bp.blogspot.com/-M8r6K-ZeMas/TWWe7aOgiWI/AAAAAAAAAP8/ck9cmUdqfas/s1600/Adelpha_cytherea_ButterflyPhotography-BB_Blogspot_JGJ.jpg Spot Celled Sister (Adelpha basiloides) Smooth-Banded Sister (Adelpha cytherea) Research Question These are closely related species from the Nymphalidae family - both are found in the tropics of Central America and both feed on the nectar of flowers. "Is there a significant difference in proboscis length and body mass between A. basiloides and A. cytherea?”

Imagine that you have collected data on the proboscis length and body mass of our two butterfly species. Record it properly. You must be neat to reduce problems later! Give the raw data tables proper titles Include uncertainties! Be consistent in your number of decimal places. Don’t use more than the sensitivity limits of your instrument.

Mean: This is the average value of the dataset and all of you should be able to calculate this easily…

Using Excel, we’ve generated the graph shown below... Now what does it tell us? How would you analyze these results? What conclusions would you draw in viewing this graph?

What it tells us is that A What it tells us is that A. cytherea has a higher mean bill length than A. basiloides. But this is only part of the picture! We need to go further in our statistical analysis because Mean values are not always accurate representative scores! Why?

Well… because the mean is a measure of the central tendency of the dataset, but it tells us NOTHING, NOTHING! about the spread of the data. The data points that we are analyzing could be tightly clustered around the mean or they could have high variability.

The greater the SD value the greater the variability! +/- 1 s.d. = 68% of data! The greater the SD value the greater the variability!

Error bars are a graphical representation of the variability of data Error bars are a graphical representation of the variability of data. Error bars can be used to represent range, standard deviation or other measures of variability. In IB Biology STANDARD DEVIATION ERROR BARS will be most useful.

Error bars are a graphical representation of the variability of data Error bars are a graphical representation of the variability of data. Error bars can be used to represent range, standard deviation or other measures of variability. In IB Biology STANDARD DEVIATION ERROR BARS will be most useful. SET A – the bar (mean) for A is higher than B SET B – the S.D. error bar is longer for B than A

The overlap of error bars gives us a clue as to the significance of the results! What do error bars tell us? Overlap! No overlap LOTS OF OVERLAP = LOTS OF SHARED DATA Results are NOT LIKELY TO BE SIGNIFICANTLY DIFFERENT! The difference between means is most likely due to chance NO OVERLAP = VERY LITTLE SHARED DATA Results ARE LIKELY TO BE SIGNIFICANTLY DIFFERENT! The difference between means is most likely to be REAL

Let’s look back at our original data and try to answer the first half of our research question. "Is there a significant difference in proboscis length between A. basiloides and A. cytherea?” Now, given your knowledge about what the standard deviation of a dataset represents, what should your conclusion be in regards to the proboscis lengths of A. cytherea and A. basiloides?

? Is there a significant difference between the data sets? But what about when we look at the mean body mass values for the two species? There is some overlap. This one is hard to call. We need another statistical test to tell us if there is a difference in these data sets. Something more refined… ?

Using a T-test to evaluate a hypothesis: A t-test is a statistical test that allows us to determine the significance of the difference between the means of two data sets. In other words: "Are the means to the two data sets far enough apart that we can say that they are truly different?” When we look at our butterfly body mass data we can see that there is overlap between the SD error bars, but there might still be a significant difference here…

WE USE 0.05 for our P value using the T-Test

DON’T FORGET TO ALSO STATE THE ALTERNATIVE HYPOTHESIS TOO!!

0.1319

∴ ACCEPT Null Hypothesis (Ho) http://www.zipcodezoo.com/hp350/Adelpha_basiloides_0.jpg http://4.bp.blogspot.com/-M8r6K-ZeMas/TWWe7aOgiWI/AAAAAAAAAP8/ck9cmUdqfas/s1600/Adelpha_cytherea_ButterflyPhotography-BB_Blogspot_JGJ.jpg Spot Celled Sister (Adelpha basiloides) Smooth-Banded Sister (Adelpha cytherea) Research Question T-value Critical Value "Is there a significant difference in proboscis length and body mass between A. basiloides and A. cytherea?” 0.1319 > 0.05 ∴ ACCEPT Null Hypothesis (Ho) There is NO statistically significant difference between the two sets of data.