Students will apply these statistical tests to their

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Students will apply these statistical tests to their data. Students will discuss their results with the class. M A T E R I A L S Laptops notebooks Worksheets, Laptops with Excel P R E P A R A T I O N None required
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Science Research Mentoring Program STATISTICS © 2013 American Museum of Natural History. All Rights Reserved. 25 Session Five: T-tests and Chi Square: WORKSHEET T-tests and Chi Square I N T R O D U C T I O N Data collection is meaningless without statistics. Today we will investigate the use of the Student’s t-test. In biology you often want to compare two sets of replicated measurements to see if they’re the same or different. If the means of the two sets are very different, then it’s easy to tell. But, often the means are quite close and it is difficult to judge whether the two sets are significantly different. The t-test compares the actual difference between two means in relation to the variation in the data (expressed as the standard deviation of the difference between the means). In other words, the t test compares two sets of data and tells you the probability (P) that the two sets are basically the same. P varies from 0 (not likely) to 1 (certain). The higher the probability, the more likely it is that the two sets are the same and that any differences are due to random chance. The lower the probability, the more likely it is that that the two sets are significantly different, and that the differences are real. Where do you draw the line between these two conclusions? In biology the critical probability is usually taken as 0.05 (or 5%). This may seem very low, but it reflects the facts that biology experiments are expected to produce quite varied results. So if P > 0.05 then the two sets are the same, and if P < 0.05 then the two sets are different. For the t test to work, the number of repeats should be as large as possible, and certainly > 5. W H E N T O U S E I T Use Student’s t-test when you have one nominal variable and one measurement variable, and you want to compare the mean values of the measurement variable. The nominal variable must have only two values, such as “male” and “female” or “treated” and “untreated.” N U L L H Y P O T H E S I S The statistical null hypothesis is that the means of the measurement variable are equal for the two categories – i.e. there is no difference between the means of the two samples.
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Science Research Mentoring Program STATISTICS © 2013 American Museum of Natural History. All Rights Reserved. 26 WORKSHEET: T-tests & Chi Square (continued) F O R E X A M P L E : We collected leaves from the perimeter of Turtle Pond. What if we analyzed the leaf length of oak trees growing in two different locations around the pond, a suitable null hypothesis would be that there is no difference in length of leaves between the two locations. The t-test will tell us if the data are consistent with this or depart significantly from this expectation. Therefore, the null hypothesis is simply something to test against. We may well expect a difference between
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