What's the deal: One-tailed hypothesis test & two tailed hypotheses tests

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ken_griffey_jr

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I’m reading through the Stats section and, for some reason, can’t seem to understand why One-tailed hypothesis tests and Two tailed hypotheses tests are important. The math seems simple enough.
For instance (taken from the Study guide), a researcher gathers the daily returns on a porfolio of call options for 250 days. the daily return mean is 0.1 % and the standard deviation is 0.25%. The researcher believes that the mean portfolio return is not equal to zero.
Construct a hypothesis test:
Test stat
= 0.001 / (0.0025/ 250^2)
= 6.33
because 6.33 is above 1.96, we reject the hypothesis.
So…my quetsion is why is this important?
- why is it so important that we know that the test statistic is way above 1.96? what does it mean for our porfolio of calls?
- what would’ve happened if the test stat was between -1.96 and 1.96? And what would this mean?
Sorry about the bombardment. Can’t seem to grasp the significance of this concept, for some reason.
 
Read the text, then re-read what you have written.
Please realize this is pretty significant, you can be questioned in any which way you can.
It is not about the math, it is the concept.
Go on to understand why a two tailed test is set up, and when someone would set up a 1-tailed test. Also how you calculate the limits for the parameter you are estimating. All that is what is significant about the hypothesis testing.
CP
 
Thanks for your input, CP.
I did read the text, and understood the general principle. If the test statistic falls within the parameters then you can’t reject the null hypo test. If it doesn’t fall within the parameters, then you can reject the null hypo test.
Implications:
When the null hypo test is NOT rejected, then the statement is validated. (eg. avg. portfolio return is 9-10%, with 5% significance.)
When the null hypo test is rejected, statement turns negative. (avg. portfolio return is not 9-10%)
I understand this - that’s simple enough. The math isn’t a problem too…
but in terms of the big picture, is there something else that I should take note of? it feels like I’m missing something…
thanks
 
know the diff between setting up the hyp for the 1-tail vs. the 2-tail
know what the diff is in the t-value or z-value u use for each type and why
when to reject vs when to accept
what is the concept of p-value
type I error vs type II error
 
Yeah, you’re right. It’s all about the LOS. I am getting carried away, focusing on minute details, when I should be concentrating the big picture. Thanks for the reminder.
 
I’m not entirely sure what you’re confused about, so I’ll try to explain the entire thing.
When you calculate the test statistic, you’re dividing the sample mean by the standard error of the sample mean (s/n^0.5). This tells you how many standard deviations you are away from the actual mean (the thing you hypothesized to be unequal to zero). After your calculation, you found that your sample mean (10%) is 6.33 standard deviations away from the hypothesized mean (0%). Given a 95% confidence interval you’re well outside the acceptable range were the actual mean really 0%.
So you’re figuring out if this:
Population mean = 0.0
Fits with this that you determined from your sample:
Xbar = 0.1
s = 0.25
n=250
Since you’d feel confident with any test statistic that fell within a 95% confidence interval of 0.0 (which is +-1.96 standard deviations), you DON’T feel confident with a sample mean that is 6.33 standard deviations from 0. So you can be 95% confident that the population mean IS NOT 0.0. Reject null, accept alternative.
Hope this helps.
 
Hockey, that was exactly the explanation I was looking for.
IF a Z-test, Chi-test, and F-test had an answer of 6.33, would that also mean that it’s 6.33 away from the Standard deviation, and that we must reject the null, accept alternative?
You’re freaken awesome, seriously.
 
No - and that standard deviation is a standard deviation of the sampling distribution of X-bar not the standard deviation of the observations.
There is just no simple way to get this without doing the work.
 
JoeyDVivre Wrote:
——————————————————-
> No - and that standard deviation is a standard
> deviation of the sampling distribution of X-bar
> not the standard deviation of the observations.
You’re welcome, griffey.
Right. You’re taking the difference between xbar and the hypothesized population mean and dividing it by the standard deviation of xbars (the standard error of the sample means). This tells us how many standard deviations of xbar we are from our hypothesis.
With regard to chi-sq tests and F tests, I’m unsure if those are counted as “standard deviations” as such, but the principle remains the same. When you calculate the test statistic, it represents the F-number associated with your real number. You do this in order to find some standard way of representing a statistic so you can compare it to a hypothesized value. Again, if the F-stat is outside the region you designated as your “confidence interval,” you reject the hypothesis that says it is inside the confidence interval.
 
Hockey Wrote:
——————————————————-
> JoeyDVivre Wrote:
> ————————————————–
> —–
> > No - and that standard deviation is a standard
> > deviation of the sampling distribution of X-bar
> > not the standard deviation of the observations.
>
>
> You’re welcome, griffey.
>
> Right. You’re taking the difference between xbar
> and the hypothesized population mean and dividing
> it by the standard deviation of xbars (the
> standard error of the sample means).
>
Yes
>
>This tells us
> how many standard deviations of xbar we are from
> our hypothesis.
>
…from our hypothesized mean.
>
> With regard to chi-sq tests and F tests, I’m
> unsure if those are counted as “standard
> deviations” as such,
No - the test statistics that use F-tests and Chi-square tests have F-distibutions and Chi-square distributions if the null hypothesis is true. The usual hyp. testing paradigm is that you compare the observed value of that test statistic with the distribution of the test statistic assuming the null is true. If the test statistic lies out in the tail you are left with two (actually three) possibiities: either a weird event has happened or the null hypothesis is not true. The general case of hypothesis testing has little to do with standard deviations (I would have to look up what the std. dev. is of an F-distribution)
>
>but the principle remains the
> same. When you calculate the test statistic, it
> represents the F-number associated with your real
> number.
Bag that part
>You do this in order to find some standard
> way of representing a statistic so you can compare
> it to a hypothesized value. Again, if the F-stat
> is outside the region you designated as your
> “confidence interval,” you reject the hypothesis
> that says it is inside the confidence interval.
This part is good
 
Typically when you have a question that starts with “why” then you’re going beyond the basic facts and trying to understand the big picture. So don’t feel like you’re “bombarding” anybody with these questions; what you’re asking is completely in bounds. It’s answering the “why” questions where you truly learn.
Why does the standard error decrease when the sample size increases? What does this have to do with consistency? Moreover the CLT?
Why do we use a z-test/t-test/chi-square/f-test/nonparametric test? Why is the chi-square test used when making inferences on the population variance–as opposed to a t-test?
Why is the topic of inferential statistics important in the field of finance?
 
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