![]() This is certainly not the only possible range it is the range that we have deduced from observations of our sample. The history of this concept and a more extensive explanation of the reasoning are detailed by Curran-Everett ( Curran-Everett, 2009b).įigure 3A shows the difference between the actual means we found, and also the range of differences between means that could occur, entirely by chance, on 95% of occasions. We decide arbitrarily, but in common with many other researchers, that we will be willing to conclude that training has an effect if the probability of seeing this observed difference in the means, or a more extreme difference, is less than 5%, if truly the jumps came from the same population. This method of finding a shift in a set of variable's values is analogous to picking out a signal from background noise – which depends on the signal to noise ratio. We compute this using a formula that relates the sizes of the differences between the values to the scatter of the values. We calculate the probability (or P-value) of finding the observed difference between the mean distances jumped by the two groups, or something more extreme, given that they are taken from the same population. If we propose that the mean values have been calculated from samples taken from the same population, any difference we do find between the mean values would be the consequence of chance alone. ![]() That is, we assume that training has no effect on the mean distance jumped. We can examine whether there is indeed a training effect, by first assuming the opposite. The effects of training a random sample of frogs. However, because the values in the 2500 frogs entered in the competition show quite a scatter, it is not likely that a small random sample will give us a mean that is quite the same as the mean of another random group. These sample mean values seem to be different and we suspect that the training could have had a positive effect. As we suggested in a previous article ( Drummond and Vowler, 2011), we will display the results by plotting individual data, and calculate the mean distance jumped by each group ( Figure 2). You start with two groups of 20 frogs, both drawn at random from the competitors registered for the 1986 frog jumping competition: one group is left alone, you train the others, and then you see how far they all can jump. This is perhaps the most frequent question in biology that is subjected to statistical analysis: does a treatment make a difference? In fact, the standard test used is not posed in this way. You might even want to place a bet on them, like Jim Smiley. You would like to know if this training makes them do substantially better when they enter the competition. How effective is training frogs to jump? Would you bet on the result? Suppose you were able to take some frogs, at random, from these contestants, and train them to jump well. This distribution is a frequent pattern in biology, and can be described mathematically. ![]() ![]() This frequency function is ‘bell’-shaped, and is known as the Normal or Gaussian distribution. ![]() The imaginary data come from a commonly encountered distribution and are summarized in a frequency curve (right side of Figure 1). On the right, the distribution of these distances is summarized. The square marks the record breaking jump of Rosie the Ribeter, and the circle is the runner-up, Jumping Jack Flash. The distance jumped by each contestant is shown on the left. ![]()
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |