anova Definition and 15 Threads

Theorem 11.2.8 in Casella & Berger defines the ANOVA statistic as a maxima of T^2 statistic as: \sup_{\sum a_i = 0} T_a^2 = \sup_{\sum a_i = 0} \left( \left( S^2_p \sum a_i^2 / n_i \right)^{-1/2} \left( \sum a_i \bar Y_{i \cdot} - \sum a_i \theta_i\right) \right)^2 = \left( S^2_p...

Kindly note that i do not have the solution or mark scheme to this question. My take on this, From stats...my points are in summary... ( am assuming the reader is literate on this), we shall have; ##k=3, N=15## ##d.f.N=2## ##d.f.D=12## ##α=0.05## The critical value = ##3.89## Let ##H_0...

I have recorded the dominant hand strength from all of my participants. I have also recorded a number of anthropometric properties of my participants, including a measure of skin-fold adjusted forearm girth, with the intention of estimating the amount of musculature in the forearm. I have...

What does it mean when I reject the null in an ANOVA but fail to reject the null when doing something such as Hartleys FMAX? Also, what's the difference between ANOVA AND T-TEST?

Hello, Can someone please let me know of a resource (book or other) that explains how to use ANOVA in linear regression? I didn't even know what ANOVA was until some days ago so I'm looking for something that explains it thoroughly with deductions. The resources I've read focused solely on...

Have I completed this 2 x 3 factorial ANOVA chart correctly? A sample of ¬N = 36 is recruited to participate in a study about speech errors. The researchers believe that there is an interaction between whether the speaker is distracted (distracted or not distracted) and the difficulty of the...

Here is the problem: The data referred to in this question were collected on 41 employees of a large company. The company is trying to predict the current salary of its employees from their starting salary (both expressed in thousands of dollars). The following is ANOVA table for simple...

I know that one of the key conditions of performing an ANOVA test is that the variances of the groups has to be broadly similar. I have some data sets that I need to compare and the variance of some of them is very different to the rest. Surely this in itself proves (indicates?) that the samples...

Homework Statement http://studyterps.com/files/STAT401-FE-SP09-CREMINS.pdf #5Homework Equations The Attempt at a Solution How did they get the MSTr and MSE form that table? I'm aware of the formulas such as MSE= SSE/(N-k) and so on, but usually you have some values given. Do I first...

Koosis: Statistics..., 4th ed., p. 177: The given answer is yes. "You must be prepared to assumed the populations from which you are sampling are normally distributed" and that "the teaching method is the only reasonable explanation of the differences between groups." In the next problem, the...

I have five groupings of data measurements, each group with a different quantity of measurements. I want to see if one grouping has higher measurements than the rest, but was told that using multiple t-tests was incorrect and that I should use ANOVA. I'm using R for the analysis. Exactly...

Homework Statement I am using Anova to check if length is dependent of age. The question is, "why is it better to use ln(length)?" How should I answer this? I think both seems linear on the two plots(attachment) But ln(length) gives lower F-value and isn't that a bad thing so why is it better...

Hello all, Does anyone know where I could find a formal proof that \frac{\text{MS between}}{\text{MS within}} has a F distribution under the null in ANOVA?

I'm currently looking to use a nonparametric alternative to the parametric repeated-measures with a between-subjects variable. I'm aiming to investigate three sets of subscores of a test taken by three groups of participants. I was initially using the parametric repeated-measures ANOVA using the...

I am having a lot of trouble conceptually understanding the idea of a random effect in ANOVA testing - more specifically identifying whether a factor is random or fixed Thanks, Thrillhouse86