Two-tailed test: The first figure below shows that with a two-tailed test in which we acknowledge that one group's mean could be either above or below the other, the alpha error rate has to be split into the upper and lower tails, i.e., with half of our alpha (0.025) in each tail. In other words, we will use p≤0.05 as the criterion for statistical significance. Suppose also that we have specified an "alpha" level of 0.05, i.e., an error rate of 5% for concluding that the groups differ when they really don't. The test statistic could be either a t score or a Z score, depending on the test we choose, but if the sample is very large the t or Z scores will be similar. Suppose we conduct a test of significance to compare two groups (call them A and B) using large samples. Similarly, a hypothesis that a mean in a sample group will be greater than the mean in a historic comparison group is also a one-tailed hypothesis.
In contrast, a research hypothesis that specifies direction, e.g., that the mean in a sample group will be less than the mean in a historic comparison group is a one-tailed hypothesis. One-Tailed and Two-Tailed Tests of SignificanceĪ research hypothesis that states that two groups differ without specifying direction, i.e., which is greater, is a two-tailed hypothesis. The investigators wish to use a one-tailed test of significance. In the sample of 100 children who had been born prematurely the data for IQ were as follows: X̄ = 95.8, SD = 17.5". In essence, the normative IQ is a historical or external (μ 0). To investigate they enrolled 100 children who had been born prematurely and measured their IQ in order to compare the sample mean to a normative IQ of 100.
#T TEST WITH MEAN AND STANDARD DEVIATION EXCEL FULL#
Investigators wanted to determine whether children who were born very prematurely have poorer cognitive ability than children born at full term.
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