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In what experiments do we use 2 tailed and in which experiments do we use 1 tail T tests?
When to use 2 tailed or one tailed T test?
- Thread starter SonhosDaVida
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1) You probably do not need to know this for the MCAT.
2) For basic statistical inference, a 2 tailed T-test refers to an alternative hypothesis stating that the observed sample mean is significantly greater or smaller than the true mean. Imagine a standard normal distribution with cutoffs at the 5th and 95th percentile, such that the right and left tails are shaded. Our alpha level (level of significance) is actually .10 in this case, because .05 + .05 = .10. If our sample mean is lower than the population mean and our t-test yields a p-value < .10, we can reject the null and conclude that the sample mean is likely lower than the population mean. If our sample mean is greater than population mean and the p-value is < .10, we can reject the null and conclude the sample mean is likely greater than population mean.
A 1-tailed T-test is different in that our alternative hypothesis states that the sample mean is different from the population mean in one direction (above or below, but only 1 of the 2). The p-value is equal to our alpha level in this case. The true difference between 1 tailed and 2 tailed is the inability of the 1-tailed to detect a significant difference in the opposite direction. If one were to fail to reject the null hypothesis, there is still a possibility that the sample mean drastically differs from the population mean in the opposite direction but we would not know this. However, this can usually be avoided by understanding the conditions and objectives of the experiment.
2) For basic statistical inference, a 2 tailed T-test refers to an alternative hypothesis stating that the observed sample mean is significantly greater or smaller than the true mean. Imagine a standard normal distribution with cutoffs at the 5th and 95th percentile, such that the right and left tails are shaded. Our alpha level (level of significance) is actually .10 in this case, because .05 + .05 = .10. If our sample mean is lower than the population mean and our t-test yields a p-value < .10, we can reject the null and conclude that the sample mean is likely lower than the population mean. If our sample mean is greater than population mean and the p-value is < .10, we can reject the null and conclude the sample mean is likely greater than population mean.
A 1-tailed T-test is different in that our alternative hypothesis states that the sample mean is different from the population mean in one direction (above or below, but only 1 of the 2). The p-value is equal to our alpha level in this case. The true difference between 1 tailed and 2 tailed is the inability of the 1-tailed to detect a significant difference in the opposite direction. If one were to fail to reject the null hypothesis, there is still a possibility that the sample mean drastically differs from the population mean in the opposite direction but we would not know this. However, this can usually be avoided by understanding the conditions and objectives of the experiment.
