1. The Data Collection and Statistical Analysis in IB Biology John Gasparini The Munich International School Part III – Hypothesis Testing with T-tests

2. 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… ? Remember where we left off… we were looking at our butterfly body mass data.

3. 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…

6. In a t-test we must calculate a “t” value for a pair of data sets and compare it to calculated critical values that depend on a number of factors: In Biology we want to be conservative in drawing our conclusions. Therefore it is convention to run hypothesis testing at a 95% confidence level or a probability value (P) of 0.05 P: Confidence: 90%90% 95%97.5%99% dfdf

7. In a t-test we must calculate a “t” value for a pair of data sets and compare it to calculated critical values that depend on a number of factors: P: Confidence: 90%90% 95%97.5%99% dfdf We also need to consider how many degrees of freedom are involved in our experiment. d f = (Total sample size – 2) d f = (30– 2) = 28 In the case of our two butterfly species… Our critical t-value is 1.701 according to this table

8. In a t-test we must calculate a “t” value for a pair of data sets and compare it to calculated critical values that depend on a number of factors: P: Confidence: 90%90% 95%97.5%99% dfdf d f = (30– 2) = 28 In the case of our two butterfly species… Our critical t-value is 1.701 according to this table. Your experimental data’s t-value was calculated as 2.34 T-valueCritical Value 2.34 1.701 >

9. In a t-test we must calculate a “t” value for a pair of data sets and compare it to calculated critical values that depend on a number of factors: P: Confidence: 90%90% 95%97.5%99% dfdf d f = (30– 2) = 28 In the case of our two butterfly species… Our critical t-value is 1.701 according to this table. Your experimental data’s t-value was calculated as 2.34 T-valueCritical Value 2.34 1.701 > ∴ Reject Null Hypothesis (H o )

10. 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 Smooth-Banded Sister (Adelpha cytherea) Spot Celled Sister (Adelpha basiloides) "Is there a significant difference in proboscis length and body mass between A. basiloides and A. cytherea?” Research Question T-value Critical Value 2.34 1.701 > ∴ Reject Null Hypothesis (H o ) Therefore we can confidently state that there IS a significant difference in the body mass between the two species. A. cytherea has a greater mean body mass than A. basiloides.

11. P: 90%90% 95%97.5%99% dfdf Bigger t-numbers = more confidence Decreasing P = more confidence

12. 1.61

15. 1.725 There is a significant difference in resting heart rate between swimmers and non-swimmers.

18. Now view this podcast on YouTube on how to conduct a “Student t-test” using Excel. It’s pretty easy to do and will allow you to conduct this hypothesis test very quickly! http://youtu.be/0hGnjp-o-Xw Remember: In Excel the t- values that are calculated are really Probability values, P-values T-values > 0.05 = No Sig. Dif! T-values < 0.05 = Sig. Dif!