I have a two-sample t-test where the t-statistic is equal to the critical t-value (at three decimal points) at a p-value of 0.05. does this mean i reject the null hypothesis or the opposite? thank you so much!
124081
This is clearly just a matter of definition or convention, and of almost no practical importance. If $\alpha$ is set to its traditional value of 0.05, is a $p$ value of 0.0500000000000... considered to be statistically significant or not? Is the rule to define statistical significance usually considered to be $p &lt; \alpha$ or $p \leq \alpha$??
77445
I am searching for the formula that will generate the critical values in a t-test instead of using a static critical value table.   I am programming in Java and not R so the qt() function is not what I am looking for.  Any help is appreciated.
52646
I am using the Kolmogorov&ndash;Smirnov two-sample test to compare distributions, and I noticed a $p$-value is frequently reported as the test statistic. How is this $p$-value determined? I know it's the probability of obtaining a result at least as large as the one obtained, but how is this $p$-value determined given this is a nonparametric test? That is, we can't assume Gaussian fluctuations in the distribution and compute the $p$-value using a $t$-test.  Thanks!
52959
Suppose I analyze a distribution and determine that a 95% CI for some measure is [-1, 1] (bearing in mind the actual value in this case cannot be &lt; 0). And suppose another 95% CI for some other measure is [0,1]. Can I, based on the CI, conclude anything different for these two CIs? What if the first CI was [-100,1]? My intuition says that, eg, the [-100,1] example i should expect a lot more values near zero than in the [0,1] example. The question boils down to: Does a CI that contains 'impossible' values contain information above the tradition interpretation of that CI, that conducting after the experiment a lot of times, 95% pf the results will be in [0,1]?
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I have one-sided hypotheses that I want to test with multiple regressions. Does anyone know how to perform a one-sided hypothesis testing? I heard of different positions regarding this matter ("not possible to test one-tailed with regression" and "for one-sided hypotheses just cut the p-value in half"). Or maybe I need another command in with my statistics program (I use R)!?  I didn't think this to be a difficult question but couldn't find a consistent and satsfying solution.  Thank you in advance for any helping comments.
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Let's say I have a large sample ($n&gt;30$) with mean $\bar{X}$ and standard deviation $S$. I can calculate only: $T=\frac{\bar{X}-\mu}{S/\sqrt{n}}$.  If I want to use t-test for a hypothesis, then I have to assume normality of the population. If I want to use z-test for a hypothesis, then I have to assume that $\boldsymbol{s\approx\sigma}$.  What is the less important assumption? What test should I do? Should I do t-test, z-test or doesn't matter?
1898
I am looking for various ways of explaining to my students (in an elementary statistics course) what is a two tailed test, and how its P value is calculated.  How do you explain to your students the two- vs one- tailed test?
109049
I'm being asked to find the p-values for descriptive statistics. However, it's my understanding that p-values are for test statistics.  If I'm not mistaken, a p-value is the probability of observing a value as extreme as the test statistic if the null hypothesis were true.
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Let's say we have the statistics given below  gender mean sd n f 1.666667 0.5773503 3 m 4.500000 0.5773503 4   How do you perform a two-sample t-test (to see if there is a significant difference between the means of men and women in some variable) using statistics like this rather than actual data?  I couldn't find anywhere on the internet how to do this. Most of the tutorials and even the manual deal with the test with the actual data set only.
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Hypothesis testing seeks to reject a null hypothesis ($H_0$) on the basis of an assumption made about the sample following a certain distribution. This assumption is conditional on $H_0$ being true. So what is the flaw with the following reasoning?     If I reject $H_0$ in favor of the alternative hypothesis ($H_1$), I   must then assume that (1) $H_1$ is true, and (2) that at the   same time the variable under examination follows the distribution   used to reject $H_0$. Since we also stated that the assumed   distribution is conditional on $H_0$ being true, it appears that $H_0$   has got to be true in order to justify the assumption made about the   distribution. Logically, it would therefore seem that both $H_0$ and   $H_1$ have to be true, which is a paradox, because they are mutually   exclusive!
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What are the most accepted ways to visualize the results of an independent two sample t-test? Is a numeric table more often used or some sort of plot? The goal is for a casual observer to look at the figure and immediately see that they are probably from two different populations.
1014
After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests.  It seems that students easily learn how to perform the calculations required by a given test but get hung up on interpreting the results.  Many computerized tools report test results in terms of "p values" or "t values".  How would you explain the following points to college students taking their first course in statistics:   What does a "p-value" mean in relation to the hypothesis being tested?  Are there cases when one should be looking for a high p-value or a low p-value? What is the relationship between a p-value and a t-value?
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I'm pretty new to statistics and I need your help. I have a small sample, as follows:    H4U   0.269   0.357   0.2   0.221   0.275   0.277   0.253   0.127   0.246   I ran the Shapiro-Wilk test using R:    shapiro.test(precisionH4U$H4U)   and I got the following result:   W = 0.9502, p-value = 0.6921   Now, if I assume the significance level at 0.05 than the p-value is larger then alpha (0.6921 > 0.05) and I cannot reject the null hypothesis about the normal distribution, but does it allow me to say that the sample has a normal distribution?  Thanks!
50095
I am looking at the probability of opting into a program based on a continuous variables $X_1$, $X_2$, $X_3$, etc.  When I divide the sample into people who opted in and did not opt in and do a t-test I find that the mean of all the $X$'s for those opting in is significantly different from the mean for those not opting in.  However, when I look at a correlation matrix for the $X$'s and opting in I find really low correlation coefficients -- from between $.04$ and $.13$.  But my t-tests are significant at the 95%+ confidence level.  How do I square these two results?
64382
An addition to the common confusion about normality testing in inferential statistics for general linear models:  I understand the assumption of normality refers to the residuals in ANOVA and regression models, but what about t-tests?  Calculation of the t-statistic uses standard deviation as a measure of dispersion, rather than sums of squares for the F-statistic in ANOVA and regression. If I understand correctly, it is because of this that there is an assumption that the samples are normally distributed (i.e. the sample standard deviation provides an accurate estimate of the population standard deviation). Is this right?  What do you do if the statistical population of the dependent variable is not distributed normally (thus samples are unlikely to be normally distributed)? Is this where transformations fit in?
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In practice, using a standard T-test to check the significance of a linear regression coefficient is common practice. The mechanics of the calculation make sense to me.  Why is it that the T-distribution can be used to model the standard test statistic used in linear regression hypothesis testing? Standard test statistic I am referring to here:   $$ T_{0} = \frac{\widehat{\beta} - \beta_{0}}{SE(\widehat{\beta})} $$
88380
I was wondering if anybody could give a concise rundown as to the definitions and uses of p-values, significance level and type I error.  I understand that p-values are defined as "the probability of obtaining a test statistic at least as extreme as the one we actually observed", while a significance level is just an arbitrary cutoff value to gauge if the p-value is significant or not. Type I error is the error of rejected a null hypothesis that was true. However, I am unsure regarding the difference between significance level and the type I error, are they not the same concept?  For example, assume a very simple experiment where I flip a coin 1000 times and count the number of times it lands on 'heads'. My null hypothesis, H0, is that heads = 500 (unbiased coin). I then set my significance level at alpha = 0.05.  I flip the coin 1000 times and then I calculate the p-value, if the p-value is > 0.05 then I fail to reject the null hypothesis and if the p-value is &lt; 0.05 then I reject the null hypothesis.  Now if I did this experiment repeatedly, each time calculating the p-value and either rejecting or failing to reject the null hypothesis and keeping a count of how many I rejected/failed to reject, then I would end up rejecting 5% of null hypotheses which were in actuality true, is that correct? This is the definition of type I error. Therefore, the significance level in Fisher significance testing is essentially the type I error from Neyman-Pearson hypothesis testing if you performed repeated experiments.  Now as for p-values, if I had gotten a p-value of 0.06 from my last experiment and I did multiple experiments and counted all the ones that I got a p-value from 0 to 0.06, then would I also not have a 6% chance of rejecting a true null hypothesis?