Quantitative methods and R – (2)
... • F=1 if two variances are the same • The farther away F is from 1, the less likely it is that the two variances are the same • F-distribution is sensitive to whether the population distribution is normal ...
... • F=1 if two variances are the same • The farther away F is from 1, the less likely it is that the two variances are the same • F-distribution is sensitive to whether the population distribution is normal ...
t test (one sample)
... Under the assumption of Gaussian statistics, the statistic follows a “t” distribution ...
... Under the assumption of Gaussian statistics, the statistic follows a “t” distribution ...
AP STAT SEMINAR - 1 - Hatboro
... Possibly the most frequently asked and least frequently answered question is why does the definition of the standard deviation involve division by n-1, when n might seem the obvious choice. This is a question which perplexes introductory statistics students and calculator manufacturers alike. The ex ...
... Possibly the most frequently asked and least frequently answered question is why does the definition of the standard deviation involve division by n-1, when n might seem the obvious choice. This is a question which perplexes introductory statistics students and calculator manufacturers alike. The ex ...
Key Probability Distributions in Econometrics
... where µ denotes the mean of the distribution and σ its standard deviation. The probability of x falling into any given range can be found by integrating the above pdf from the lower to the upper limit of the range. A couple of results to commit to memory are P (µ − 2σ < x < µ + 2σ ) ≈ 0.95 and P (µ ...
... where µ denotes the mean of the distribution and σ its standard deviation. The probability of x falling into any given range can be found by integrating the above pdf from the lower to the upper limit of the range. A couple of results to commit to memory are P (µ − 2σ < x < µ + 2σ ) ≈ 0.95 and P (µ ...
quiz3-sum08.pdf
... 3. Consider a completely randomized experiment with t = 4 treatments, and n experimental units randomized to each treatment, for a total of 4n observations. For the questions below, assume the factorial effects model Yij = µ + τi + Eij where Eij are i.i.d. normal with mean 0, unknown variance σ 2 . ...
... 3. Consider a completely randomized experiment with t = 4 treatments, and n experimental units randomized to each treatment, for a total of 4n observations. For the questions below, assume the factorial effects model Yij = µ + τi + Eij where Eij are i.i.d. normal with mean 0, unknown variance σ 2 . ...
HW3sol
... (a) When testing H0: β1 = 5 versus Ha: β1 5 by means of a general linear test, what is the reduced model? What are the degrees of freedom dfR? The reduced model is Y 0 5 X . Since there is only one model parameter to estimate, the error df for the reduced model is n-1. (b) When testing H ...
... (a) When testing H0: β1 = 5 versus Ha: β1 5 by means of a general linear test, what is the reduced model? What are the degrees of freedom dfR? The reduced model is Y 0 5 X . Since there is only one model parameter to estimate, the error df for the reduced model is n-1. (b) When testing H ...
The Moments of Student`s t distribution
... I have my students run a little Monte Carlo to create the sampling distribution of t and then fiddle with sample size and the shape of the population from which the scores are sampled. This allows them to demonstrate the consistency of the mean and the variance, the central limit theorem, and so on. ...
... I have my students run a little Monte Carlo to create the sampling distribution of t and then fiddle with sample size and the shape of the population from which the scores are sampled. This allows them to demonstrate the consistency of the mean and the variance, the central limit theorem, and so on. ...
t-Statistics for Weighted Means with Application to Risk
... In this note we describe how to generalize the standard t-statistic test for for equality of the means when the assumption of a common variance no longer holds. We then discuss an application to financial risk factor modelling. First we describe the standard t-statistic. Suppose we have a sequence o ...
... In this note we describe how to generalize the standard t-statistic test for for equality of the means when the assumption of a common variance no longer holds. We then discuss an application to financial risk factor modelling. First we describe the standard t-statistic. Suppose we have a sequence o ...
SAMPLE STATISTICS A random sample x1,x2,...,xn from a
... affects the variance of a normal population. It is possibile that the mean is also affected. Let xi ∼ N (µx , σx2 ); i = 1, . . . , n be a random sample taken from the population before treatment and let yj ∼ N (µy , σy2 ); j = 1, . . . , m be a random sample taken after treatment. Then (xi − x̄)2 σ ...
... affects the variance of a normal population. It is possibile that the mean is also affected. Let xi ∼ N (µx , σx2 ); i = 1, . . . , n be a random sample taken from the population before treatment and let yj ∼ N (µy , σy2 ); j = 1, . . . , m be a random sample taken after treatment. Then (xi − x̄)2 σ ...