One Tail vs Two Tail

A one-tail test refers to when only one side of the range of values is being looked at. A two-tail test refers to when *both* sides of the range of values are being looked at. So a researcher would use the one-tail test when they only care about results which are located on one side of the range. They would use the two-tail test when they care about both sides.

Here are some examples.

Let's say we were worried about people who were not making enough money, how they were paying their heating bills and food bills. We wanted to look at people who were earning less than $12,000 a year. We don't worry about people in the middle, or people making more than a value. We only care about people on one side of the range of values - the ones on the low side.

Now let's say we wanted to look at people who were making a lot of money to make sure they were paying their taxes fairly. So we want to look at people making $500,000 a year or more to examine their tax records. Again we're just looking at one side of the range, just people over $500,000.

Normal Distribution Graph

So in both cases those are one-tail tests. It is above something, or below something. It is just one side.

In comparison let's say we wanted to look at dock workers in a union who were not making the mean of $50,000 a year. Those not in that mean range would be 'odd' and we want to figure out why they are making more or less than that value. So in this case we are looking at both ends of the tail. We are looking at those making less than the mean and also those making more than the mean.

Another situation with a two tail test might be looking at parakeets that do not have the mean weight of 30 grams. We want to both look at parakeets who are too light and parakeets who are too heavy to figure out why they are that way. So we want to look at both sides of the tail.

We use the Z test when we know the entire population's standard deviation and can work with that. We need to use a t test in cases where we do not know the population's standard deviation. In that case we have to work with the sample's standard deviation as our parameter since it's all we know.

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