OK, I posted a thread similar to this earlier in the day, but now I’m having trouble with what the number of tails has to do with the z value. For instance, wouldn’t the z value for a 2 tail 95% confidence interval be 1.96? The shaded region in between the tail and the median would be 47.5% and 2.5% would lie in each tail correct? Well, wouldn’t the same z value of 1.96 hold true for a 1 tail 95% confidence interval? The only other thing I could think of would be to take 100-95 = 5/1 for a 1 tailed test the z value would be .05
=5/2 for a 2 tailed test the z value would be .025
these answers just don’t seem right though and I’m leaning more on chart that reads:
90% CI = 1.64
95% CI = 1.96
99% CI = 2.58
Am I right in thinking this is where I should get my z values from and not worry about subtracting the confidence interval percent from 100 then dividing by the number of tails?
If you’re talking about confidence intervals, you’re going with the “two-tailed” thing pretty much by definition—except that the confidence interval corresponds to the part in the middle, between the two tails. Your confidence interval comes from your sample mean plus or minus a certain amount—it goes in both directions. The z’s you listed from your chart are correct for confidence intervals.
Where the one- vs. two-tailed business comes in is in hypothesis testing, which usually involves a “confidence level” alpha. This is the probability of committing a type I error, and it corresponds to the area under the tail(s) of the standard normal curve. A 95% confidence interval would involve the same z as a two-tailed hypothesis test with alpha = 0.05, or as a one-tailed test with alpha = 0.025. (If 5% of the area is in the two tails, there’s 2.5% in each one of the tails.)
Note that the 0.05 and 0.025 are not z-values; they’re areas under the curve. z is where you are along the z-axis.
Here’s the deal … when you do a confidence interval, you need to know two things: (1) the confidence level CL; and (2) is it one-sided or two-sided. The entire non-confidence level 1-CL is allocated to the tail(s). If you’re dealing with a two-sided confidence interval, split this 1-CL in half and put each half on each tail. If you’re dealing with a one-sided confidence interval, put the entire 1-CL value on the tail (either on the left or on the right). The numbers that you’ve listed (1.645, 1.96, 2.58) are the correct z-values to use for two-sided confidence intervals. The corresponding numbers for a one-sided confidence interval are 1.28, 1.645, 2.33.
I think is easier to focus either on CL or significance level. The CL is easier for me.
One tail - you add or substract .5
Two tail - you multipy or divide by 2
If you have a z value, then to find the CL, look up the value on the inside of the table. If one tail, you add .5 to the value in the chart, if two-tail, multiply by 2.
If you have a CL and want to find the z, then one-tail, subtract .5 from CL and find that value in the table, then the z value. If two-tail, divide the CL by 2, find that value in the table, then the z value.