# Statistics ?: howis the z value affected when it there are two tails instead of one? **URL:** \ **Category:** Factual Questions\ **Created:** [March 7, 2005, 4:26pm UTC](https://boards.straightdope.com/t/statistics-howis-the-z-value-affected-when-it-there-are-two-tails-instead-of-one/293380 "2005-03-07T16:26:52Z")\ **Posts on this page:** 4\ **Page:** 1
**Author:** ![saluki\_fan](https://avatars.discourse-cdn.com/v4/letter/s/b2d939/32.png) [@saluki\_fan](https://boards.straightdope.com/u/saluki_fan)\ **Post date:** [March 7, 2005, 4:26pm UTC](https://boards.straightdope.com/t/statistics-howis-the-z-value-affected-when-it-there-are-two-tails-instead-of-one/293380/1 "2005-03-07T16:26:52Z")
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? Thanks ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [March 7, 2005, 5:20pm UTC](https://boards.straightdope.com/t/statistics-howis-the-z-value-affected-when-it-there-are-two-tails-instead-of-one/293380/2 "2005-03-07T17:20:29Z")
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. ---
**Author:** ![nivlac](https://avatars.discourse-cdn.com/v4/letter/n/3bc359/32.png) [@nivlac](https://boards.straightdope.com/u/nivlac)\ **Post date:** [March 7, 2005, 5:33pm UTC](https://boards.straightdope.com/t/statistics-howis-the-z-value-affected-when-it-there-are-two-tails-instead-of-one/293380/3 "2005-03-07T17:33:15Z")
> [@saluki\_fan](#): > > 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? > > Thanks 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. ---
**Author:** ![aahala](https://avatars.discourse-cdn.com/v4/letter/a/a88e4f/32.png) [@aahala](https://boards.straightdope.com/u/aahala)\ **Post date:** [March 7, 2005, 6:26pm UTC](https://boards.straightdope.com/t/statistics-howis-the-z-value-affected-when-it-there-are-two-tails-instead-of-one/293380/4 "2005-03-07T18:26:38Z")
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.