Hypothesis Testing. Comparisons Among Two Samples. Hypothesis Testing w/Two Samples. By far a more common statistic to use than any other covered so far
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Ex. If we want to know what effect fire has on water, we have two groups, one that has water over an open flame (the Tx Group), and one that has water unheated (the Control Group). If all other factors that could influence the heat of water are kept constant between the two groups (i.e. the water in the two groups has the same salinity, the air pressure is the same, etc.), if the water in the heated condition is hotter, we can conclude that the difference is due to the fire, and not the other factors that we kept constant
The formula is the same as the one-sample t-test, once again all that is different is that we use two sample means instead of a sample mean and a population mean, and a pooled variance instead of a regular, sample variance
CI = ± Critical t (two-tailed at p=.05) x pooled standard deviation
Much has been made of the concept of experimenter bias, which refers to the fact that for even the most conscientious experimenters there seems to be a tendency for the data to come out in the desired direction. Suppose we use students as experimenters. All the experimenters are told that subjects will be given caffeine before the experiment, but half the experimenters are told that we expect caffeine to lead to good performance, and half are told that we expect it to lead to poor performance. The dependent variable is the number of simple arithmetic problems the subject can solve in 2 minutes. The obtained data are as follows: