t is the distribution of the t-statistic that results from a t-test. Use this tag only for questions about the distribution; use [t-test] for questions about the test.

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Equivalence of the dt and pt function in R

in my own curiosity I decided to question the equivalence of dt and pt in R. pt denotes the cumulative density function of the t-distribution. So this gives us $P(X \le x)$. So if I want to find the ...
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How to calculate t-score and critical domain of t-statistics test

A factory specializes in the production of metal rods. According to the standards, the expected length of the rods should be 80 cm. If we investigate a population of 10 different rod lengths, we ...
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79 views

Proof: $T \sim \chi^2(N-1)$

I'm a maths student, this is my first statics class and I'm studying Confidence Intervals. When it's time to estimate the CI for the mean of $\{X_i\}_{i=1..N}$ - gaussian random variables i.i.d. with ...
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59 views

Relationship between F and Student's t distributions

According to Wikipedia, $Y\sim F_{1,v}$ has an F-distribution if $Y=X^2$ and $X\sim t(v)$ has a Student's t distribution. The proof of this makes sense to me. But I don't understand the relationship ...
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Fitting a student t distribution in R using fitdistr() yields error “non-finite finite-difference value” [migrated]

Reproducable example which will give the mentioned error code every time is: (Note that even without set.seed, the error comes up every time) ...
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282 views

What is exactly distributed according to t-distribution?

I try to understand the idea behind the t-distribution. Here are the steps that I have understood so far: We use a sample of N elements to estimate the population mean. In more details, we use the ...
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36 views

Generating t statistics from p values - binomial test multiple comparisons

I am using the binomial test to generate a series of p values. However, my method of multiple comparisons correction that I wish to apply to this series requires that I also have the corresponding t ...
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54 views

t-statistic before-after

I’m doing an exercise on the Udacity's Intro to Inferential Statistics course (Problem set 10b) where I need to calculate the t-statistic on a before\after treatment situation. My null hypothesis ...
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33 views

Deriving a probability using a more fat tailed T distribution rather than the normal distribution in Excel

I have an estimate of the central limit and standard deviation (SD) of a physical phenomenon. The SD is specifically derived from a limited sample of 12 observations. Using the 'NORMDIST' function ...
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27 views

Transformation of any normal distribution into a standardized t-distribution

What will be the transformed Mean and transformed standard deviation if any normal distribution is transformed into a standardized t-distribution? Does t force ...
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2answers
66 views

What will be the t-value if my sample size increases to an infinity compare to z value?

I do not know where to check this. Any reference/help is much appreciated. If the sample size, n increases to an infinity then will the t-value be larger/smaller ...
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32 views

Finding z-scores from z table relating to confidence intervals

I'm having trouble finding the proper $z$ score so that I can find the $99\%$ confidence interval. $\bar{x} = 6.01231$. with an $s$ of $1.96833$ and $n$ of $26$, and I got $2.575$ for ...
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53 views

How to test a hypothesis about the mean based on an assumed normal distribution?

The entrance onto a major bridge in New York City was engineered to accommodate an average of $3800$ vehicles per hour. However, a random sample of nine observations gives an average of ...
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54 views

t Student test for two samples (and paired) in R. How to Apply for my specific data table?

I'm having a trouble trying to apply the t Student test for two samples in the data of the in the image below : The diff column is the difference of the observations. The experiment is: "A field ...
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58 views

Inverse CDF of a Student's t-Distribution

I'm trying to implement a mathematics library in C# .NET which includes some basic statistics. I need to be able to determine the inverse CDF of a Student's t-distribution from a given ...
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1answer
91 views

Estimating mean of Normal with unknown variance and then predict the future observation

I am trying to estimate population mean of 9 observations when the variance is unknown. I marginalized the posterior and understand that the t- distribution would give me the distribution of ...
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26 views

Inferences with non-normal data

I have the data of index closing values that I later will use to run some regressions. When examining the data, I find heteroscedastic residuals and that the distribution is non-normal. In fact, it ...
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47 views

GARCH estimation, reduce outlier effect with t distribution

I am trying to estimate GARCH(1, 1) using MLE. As my data contains a lot of outliers, I think using t distribution to represent errors makes a lot of sense. But I am completely lost at how to ...
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22 views

VARMA with t-student innovations

I'm wondering if there is a possibility to estimate VARMA model with t-student innovations in R. I found package MTS, but all models here seem to be estimated assuming multivariate normal ...
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60 views

How to show that the t-distribution density function is a pdf?

We know that the pdf of the t-distribution is : $$f(t|p)=\frac{\Gamma(\frac{p+1}{2})}{p^{\frac{1}{2}}\Gamma(\frac{1}{2})\Gamma(\frac{p}{2})}\cdot\frac{1}{(1+\frac{t^2}{p})^{\frac{p+1}{2}}} \;\;\;\; ...
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109 views

How to calculate how many standard deviations a number is from the mean [closed]

I have 25 integers and I would like to find how many standard deviations each of them is from the mean. Apparently, normal distribution is not applicable here and therefore I have to move on with ...
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1answer
49 views

Copula - Correlation Help

I need some help with copula. I am using the copula with either the multinormal or the student t kernel. I thought before that when I input in my correlation matrix, if I simulate enough random ...
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51 views

Which distribution do I get?

Be $X\sim N(\mu,1)$ and $Y\sim Inverse-Gamma(\alpha,\beta)$. For the Inverse-Gamma, I usually use the parameterization which leads to the following probability distribution function for Y: ...
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31 views

Multivariate t-distribution definition

I have the following marginal posterior of a vector $\phi$ ($p$ by $1$): $$p(\phi | Y) \propto \left[1+\frac{1}{h}\left(\phi - \tilde{\phi} \right)' \Gamma \left(\phi - \tilde{\phi} \right) ...
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199 views

Generating random samples with bivariate t-copula

I'm trying to generate a bivariate random sample of the t-copula (using rho = 0.8), without using the "copula" package and its function "rCopula" with method "tCopula". I'm using the following R-code: ...
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T-test for a small sample with unknown distribution [duplicate]

Consider a simple hypothesis test concerning the mean of a single sample. If the sample is normally distributed and the variance is known, the exact distribution of the sample mean is known ...
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43 views

Confidence interval for a multiple of regression coefficient

I am trying to model relationship between length of stay of patients in hospital(Y) vs Age in years(X). The data set I've got doesn't specify the unit of length of stay. So now estimated value of my ...
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76 views

How do I obtain a t distribution?

I performed an independent groups t-test and got a t value of 4.48. Each group is of 26 and I used a criterion of 0.05 (just because...). Before doing the t-test I had to transform my values because ...
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2answers
129 views

What is the formula for a normal-theory confidence interval of the mean?

A psychologist is collecting data on the time it takes to learn a certain task. For $55$ randomly selected adult subjects, the sample mean is $10.5$ minutes and sample standard deviation is $3.25$ ...
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31 views

Is this estimator for the standard error of a sample mean difference biased and what is the relation to Student's t-test?

In the situation of two indepdent samples, the variance of the difference in sample means $\bar{x}_1$ and $\bar{x}_2$ is $$Var(\bar{x}_d)=\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}=\sigma_d^2$$ and ...
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1answer
95 views

Log-normal random variables and the distribution of shocks in AR(1) model

Assume, X and Y are jointly lognormally distributied and let X follow AR(1) process: $$X_{t+1} = \mu_t + \alpha X_t+ u_{t+1},$$ $\alpha < 1$. Thereafter, I can't come up with an answer to the two ...
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122 views

Regression with t-distributed errors and MASS::rlm

I have some data that I'm fitting a multiple regression to, with the twist that the error distribution is t (with user-defined degrees of freedom) instead of Gaussian. I've been coding up my own ...
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When do we “bootstrap” and then use “t-dist” versus just using “t-dist”?

I'm taking a Data Analysis class on Coursera, and we are learning about bootstrapping when you have a small sample size (>30). What I don't understand, is when do you bootstrap and then use the ...
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How can I work out the standard deviation of a t-distribution?

Given a t-distribution with a certain degrees of freedom, how can I work out what the standard deviation of that distribution is?
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421 views

Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom

Background Suppose we have an Ordinary Least Squares model where we have $k$ coefficients in our regression model, $$\mathbf{y}=\mathbf{X}\mathbf{\beta} + \mathbf{\epsilon}$$ where $\mathbf{\beta}$ ...
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311 views

Using R to calculate qt (t-dist) using qf(f dist) help?

I am having quite some trouble using R to calculate, say, qt(0.975,6) using qf instead of qt. I know the relationship between the t-distribution and the f-distribution which I understand as follows: ...
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Explanation for non-integer degrees of freedom in t test with unequal variances

The SPSS t-Test procedure reports 2 analyses when comparing 2 independent means, one analysis with equal variances assumed and one with equal variances not assumed. The degrees of freedom (df) when ...
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314 views

Why not use the T-distribution to estimate the mean when the sample is large?

Basic statistics courses often suggest using a normal distribution to estimate the mean of a population parameter when the sample size n is large (typically over 30 or 50). Student's T-distribution is ...
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How do I calculate the standard error of the ACF if the errors are t-distributed?

I am modeling my data with ARIMA and to check if my model is good I have to compute the residuals and plot the correlation function and partial correlation function of the residuals. If the results of ...
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Why does the t-distribution become more normal as sample size increases?

As per Wikipedia, I understand that the t-distribution is the sampling distribution of the t-value when the samples are iid observations from a normally distributed population. However, I don't ...
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675 views

Studentized residual distribution

I read that in a regression with $k$ regressors, the t-statistic corresponding to a certain coefficient follows a $t(n-k)$ distribution. However, later on I read that studentized residuals follow a ...
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198 views

Non-central scaled Student's t cumulative density function required (alternatively the pdf)

I need to cite the pdf(density) or cdf(distribution function) of a non-central scaled Student's t distribution. There is an article about the non-central Student's t distribution ...
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111 views

T-Distribution using Excel?

I was given this sample problem: Find the t-value such that the area under the t distribution to the right of the t-value is 0.2 assuming 10 degrees of freedom. So, I went poking around in ...
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855 views

Is the sampling distribution for small samples of a normal population normal or t distributed? [closed]

If I know that the population is normally distributed, and then take small samples from this population, is it more correct to claim that the sampling distribution is normal or instead follows the t ...
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Finding a proper t-distribution given a constraint about the weight of its tail

I wish to find the parameter $\nu>2$ for the student t-distribution such that the following constraint will hold: if $F_T$ is the CDF of that distribution and $F_N$ is the CDF of the normal ...
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179 views

Is there a theorem that says that $\sqrt{n}\frac{\bar{X} - \mu}{S}$ converges in distribution to a normal as $n$ goes to infinity?

Let $X$ be any distribution with defined mean, $\mu$, and standard deviation, $\sigma$. The central limit theorem says that $$ \sqrt{n}\frac{\bar{X} - \mu}{\sigma} $$ converges in distribution to a ...
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204 views

Self-study question on t-Distribution

I am currently doing a True/False exercise. One of the questions as follows: A marine drill instructor recoded the time in which each of 20 recruits completed an obstacle course both before and ...
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31 views

Inconsistency in output from my implementation of noncentral t CDF and R's pt()

I am trying to implement a noncentral t CDF as expressed by Guenther (1978), Lenth (1989), and the Wikipedia article on the non-central t in R. I have got my algorithm half working: when the signs of ...
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87 views

Robust standard errors for cross-sectional data: what is a “large” sample size?

I know that others have asked about robust standard errors (Robust standard errors in econometrics and Always Report Robust (White) Standard Errors?). An answer to the latter question made this ...
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Why t distribution in confidence level for the mean?

This is a basic question, but when I was asked about it I only could give a weak answer. That's why I am asking it here. If we want to calculate the confidence level for the mean there is the ...