z and t test
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 This topic has 15 replies, 12 voices, and was last updated 14 years, 7 months ago by Siamack.

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January 12, 2005 at 3:49 pm #38057
Joseph BanerjeeParticipant@JosephBanerjee Include @JosephBanerjee in your post and this person will
be notified via email.Can some one explain whats the difference between one sample t and z test personally I dont find any in the Hypothesis testing except in z test you should know the standard deviation of the population ..Help please ..
0January 12, 2005 at 4:11 pm #113389
Da AgentParticipant@DaAgent Include @DaAgent in your post and this person will
be notified via email.Joseph,
Hopefully I can help shine some light on your question. (By no means am I an expert)…..The Ttest is used when the standard deviation is unknown while the Ztest is used when the standard deviation is known.
The Ttest is a robust test where you can choose between a 1 sample test to compare 1 group against a fixed target or known value and a 2 sample test to compare 2 groups to see if the means are the same.0January 12, 2005 at 6:39 pm #113396A couple more points on the differences between the t and z statistic…
The z statistic assumes that we know the standard deviation of the population. In most cases we do not know the standard deviation of the entire population, but only of our population sample.
The z statistic has the same distribution for different sample sizes; the t statistic has a different distribution for different sample sizes. For small sample sizes, the t distribution has more area under the curve at the outer regions (tails) and less area under the center of the distribution. However, once you get up to about 30 samples the t distribution is very close to the z.
Jimbo0January 12, 2005 at 8:14 pm #113404Let me throw this out …
I have often used Z distribution to compare a single data point relative to a population with a known standard deviation.
Ttests which are just comparing populations of means–e.g. why the distribution changes depending on the degrees of freedom, sample size. It is true that the tdistribution effectively follows the z distribution for samples sizes of 30.
Ttests are conservative since the tails are longer so to get 95% confidence the required delta between test statistics and “estimated population means” is larger since the area under the tails is higher with t curves.0January 12, 2005 at 10:03 pm #113406If you want to really simplify the answer, you could say the following:
n = sample size
n < 30, use T distribution (Ttest)
n > 30, use Zdistribution (Ztest)
When comparing two samples, remember that your sample size is (n1 + n2)
Lass0January 12, 2005 at 10:19 pm #113410Lass,
I haven’t done a manual ttest in quite a while but are you SURE? that the sample size of n1+n2 would determine which t curve you used?
Don’t have my Box Hunter Hunter to check.0January 12, 2005 at 10:27 pm #113411mmmmm
maybe n1+n2 – 2 is the df, assuming equal variances from what I can gather searching online….
what is the answer?0January 12, 2005 at 10:41 pm #113412How did we jump from determining what type of distribution to use, to determining what type of tcurve to use?
Allow me to backtrack….
The orginal poster wanted to know the difference between Z and T tests. From the tone of the post, I got the impression that the poster was a newbie and completely confused. The resulting responses seemed a little complicated for someone who was “new”. I was trying to simplify what criteria to use to decide between using the T or Z distributions.
That being said…if your sample size was smaller than 30 (i.e. n1 + n2 < 30) you would use the Tdistribution. Your degrees of freedom (v) = n1 + n2 – 2, which would determine your tcurve.
If I am mistaken in this, please let me know.
Lass0January 13, 2005 at 10:23 am #113433
Joseph BanerjeeParticipant@JosephBanerjee Include @JosephBanerjee in your post and this person will
be notified via email.Thank you jimbo i think you are right when the sample size more than 30 choose z sample test
thank you0January 13, 2005 at 1:33 pm #113441From Box Hunter Hunter:
“…when the size of the sample is infinite, there is no uncertainty in the estimate s2 [the sample size standard deviation] and the t distribution becomes the standard normal distribution of z.”
“Except in the extreme tails of the distribution, the normal distribution provides a fair approximation of the t distribution when v [degrees of freedom] is greater than about 15.”0March 23, 2006 at 2:33 am #135391I am new and have a few questions. Your assistance would be greatful. What would be two examples that I could use for each and how can I apply them? Plese help.
0March 23, 2006 at 4:44 am #135395
JagadeeshParticipant@Jagadeesh Include @Jagadeesh in your post and this person will
be notified via email.I am completely agree with Lass.
T test is using for Small samples (N<30) and Z test is for large samples.
When N is large, T distribution tends to Normal distribution.0June 19, 2006 at 3:04 am #139277T tests are used when you have an unknow standard deviation.
Assumptions:
Sample size < 15: Use t procedures if the data are close to normal. If the data are clearly nonnormal or if outliers are present, do not use t.
Sample size at least 15: The t procedures ca be used except in the presence of outliers or strong skewness.
Large Samples (> 40): The t procedures can be used even for clearly skewed distributions. This is because the t test is robust against skewness when you have a large sample.
Z tests are used to test for a population mean. Used when you want to test the hypothesis that a parameter has a specified value.0June 19, 2006 at 12:57 pm #139289I’ll agree with Lass on this one, with one proviso:
If you are comparing a sample to a single value to determine if the means are the same or different,
and
n>30
Then use the OnesampleZ (which is pronounced “Zed” by the way).
If
If you are comparing a sample to a single value to determine if the means are the same or different,
and
n<30
and
The population is normally distributed
Then
Use onesamplet
Lorax
0December 8, 2007 at 3:46 am #165895i was confused with what kind of test should i use if the the 2 samples are given and the first sample is >30 and the second sample is 30 and the second sample is 30 and the second sample is
0March 2, 2008 at 9:07 am #169173Hello Ann,
with regard to your question, I think that t test is applicable with all sample sizes. In larger samples t becomes similar to z. so I think that you can use t test to compare two samples which are not equal in size.0 
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