Talk:Z-test

message: Hey, shouldn't the z score be \frac{X - \mu}{\sigma}? as in Standard_score?
I think there is confusion with standardization.  The above formula is used to standardize each data point (X) so that the population has a mean of zero and a range of unity.
194.176.105.153 (talk) 11:24, 15 November 2013 (UTC)
thread_title:  Z score 

message: Hi all,
in the line "a mean score of 96 is -2.47 standard deviation units from the population mean", shouldn't it say "standard error units"? I'm not sure about this, so if you know for sure, please change or don't.
Regards
WikiBasti 12:16, 25 November 2005 (UTC)
thread_title:  SD / SE unit? 

message: This sentence in the article: "What this tells us is that 49.32% plus 50% or 99.32% of the students who took the test scored better than did the fifth grade students in our sample" is misleading. It's not true that 99.32% of all students do better: what's true is that 99.32% of the time, a randomly selected group of 55 students have a higher average score than these 55 students had.  MvH Jan 16, 2006.
:I think there's actually a factual error in the example. "Next we look the z score up in a Z table and we find that a z score of −2.47 is 49.32%". Typically, Z tables provide cumulative probabilities, not percentages difference from the mean, so -2.47 would produce 0.0068. Furthermore, the example currently is very wordy and would greatly benefit from editing, and possibly the inclusion of an image of a bell curve with alpha shaded and -2.47 indicated. Any volunteers? Evlshout (talk) 02:51, 15 May 2009 (UTC)
replies: text: I decided to restructure the example, hopefully eliminating this and other issues that have been raised.  I agree that a figure would be nice, I'll try to get back to it. Skbkekas (talk) 04:09, 15 May 2009 (UTC)
thread_title:  Example misleading 

message: The article states that the sample must be a simple random sample from the population, but I can't make sense of this. Isn't this the null hypothesis, and consequently, isn't the test only meaningful if the sample is NOT random? The test is used to see if the sample that you drew from the population behaves like a simple random sample...it's only interesting if it doesn't  -anon
:I think you are referring to Z-tests for the population mean.  These are tests of the null hypothesis that the population mean is a given value, say zero, against the alternative that the population mean is something else (say, any non-zero value).  Regardless of whether the mean is zero or non-zero, the data can still be a simple random sample.  This doesn't mean that the data necessarily are a simple random sample, but the simplest form of Z-test for expected values is derived under this assumption.  Whether or not the data can be modeled as a simple random sample is usually a product of the design of a study, so is known to the researcher.  See the sampling (statistics) article for a discussion of different types of sampling.  It is rare that one would want to test whether the data formed a simple random sample.  The test is more commonly about the expected value. Skbkekas (talk) 03:24, 15 May 2009 (UTC)
thread_title:  Simple random sample 

message: In the formula under "First calculate the standard error (SE) of the mean:" shouldn't the sigma instead be 's'?  I believe the question here is whether your value falls into your estimated confidence based on your sample.  I am not sure what the population standard deviation is used here.  I am not certain about this, but it seems intuitively wrong to me
The Sleepwalker (talk) 07:11, 5 June 2008 (UTC)
thread_title:  Error Regarding Population Standard Deviation and Sample Standard Deviation? 

message: I edited the top parts of this page to make it more parallel to the t-test page, which defines a t-test as being any test for which the test statistic follows a t-distribution (rather than just covering the one-sample and two-sample t-tests). Nevertheless, I agree that the one-sample/two-sample tests need to be covered in detail.  Also, I generally disagree with the way these tests are presented now.  Granted, the test statistic will only be exactly normal if the variance is known, however if the sample size is not too small, many t-statistics are very well approximated by a normal distribution. All statistical testing requires approximations.  It simply is not an accurate reflection of how modern professional and academic statisticians think to say that the Z-test can only be applied if the population is known.  Skbkekas (talk) 15:24, 23 April 2009 (UTC)
thread_title:  Edits 

message: I think the equation is  P(z) = \frac{1}{1 + e^{-\Phi z}} \!  , but I can't find a source. Dude1818 (talk) 03:07, 16 April 2010 (UTC)
thread_title:  Equation 

message: The following paragraph in the example seems to have an error in the first sentence. Shouldn't it state that 'with probability 0.014, a simple random sample ....'?
"Another way of stating things is that with probability 1 − 0.014 = 0.986, a simple random sample of 55 students would have a mean test score within 4 units of the population mean. We could also say that with 98.6% confidence we reject the null hypothesis that the 55 test takers are comparable to a simple random sample from the population of test-takers."
MarkThoreau (talk) 18:19, 6 March 2021 (UTC)
thread_title:  Example