# What is anova: Definition and 24 Discussions

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means.

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1. ### I Casella Berger: Why is distribution of F-statistic in ANOVA not T^2

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...
2. ### Solve the problem involving Anova -Statistics

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...
3. ### MHB Require assistance with possible ANOVA use

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...
4. ### MHB What Does Rejecting the Null in ANOVA but Not Hartley's FMAX Mean?

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?
5. ### I ANOVA and Linear Regression Resource

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...
6. ### Perfoming ANOVA test using orthogonal contrasts

I have to test treatments B,C,D and E where ##H_0:\mu_B=\mu_C=\mu_D=\mu_E## vs ## H_1: not H_0##. Use ##\alpha=0.05## given this problem. Now ##\mu_A## is not included in the hypothesis so I am trying to figure out how to go about this problem. I was thinking of using orthogonal contrasts and...
7. ### MHB Correcting a 2 x 3 Factorial ANOVA Chart

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...
8. ### Solving Anova Table? (stats problem)

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...
9. ### Hypothesis Testing: Factorial ANOVA

Hello! So I had to propose a research design as an assignment and I chose to look at cognitive function in an exercise group vs. a control group over the period of 10 years. -subjects are tested at the beginning and end of each year The groups were not randomized on perfectly (I used two...
10. ### Can ANOVA Be Used with Unequal Variances?

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...
11. ### Statistics - ANOVA table calculation

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...
12. ### How Should Condition Be Represented in a Mixed Two-Way ANOVA Analysis?

two-way analysis of variance Hi, any insights regarding the accuracy of my analysis are welcome. I used two-way analysis of variance (ANOVA) to do the analysis on 32 participants, who were either in the control group or in the divided attention condition; all subjects tried to memorize two...
13. ### Question about repeated measures Anova and multiple regression

This is for my coursework. I have two problems. The first one. Homework Statement I have two time messures. Before and after a scheme was introduced.I have to answer a question if it made a statistically significant difference or not. And also as it was introduced in 3 places I need to...
14. ### Why is randomization necessary in ANOVA experiments?

Homework Statement Tablets were made on six different tablet presses from an available 10 during the course of a run (batch). Two tablets from each press were collected during each hour of the 4-hour run. The tablets were then assayed in random order. The results are as follows...
15. ### How Can I Get an r^2 Value from an ANOVA Test in SPSS?

Does anyone here use the SPSS statistical software package? I am currently performing an ANOVA analysis for house type (detached, semi, flats and terraced) against occupancy (range 1-6 people). Initial results show that there is a difference between the groups (detached have the most people...
16. ### Confidence Interval for Diet 1 Mean

Homework Statement There's no need to write out the full question, but basically we have 6 diets, and for each one a list of the levels of protein in 10 independant samples for each. Sample mean and standard deviation given. Calculate and interpret a confidence interval centered on the...
17. ### Sample variances & ANOVA: How different is too different?

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...
18. ### F-test and One-way ANOVA (in R)?

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...
19. ### Answering "Why ln(length) is Better for ANOVA & F-Test Homework

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...
20. ### Formal Proof of ANOVA's F Distribution?

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?
21. ### Nonparametric ANOVA w/ Between-Subjects Variable: Advice Appreciated

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...
22. ### Random vs fixed effects in ANOVA

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
23. ### Can i get some help with an Analysis of variance table ANOVA?

having a little trouble with the question below. its on a sample exam paper I'm doing. any help would be appreciated 155 hospital patients completed a questionnaire about their hospital stay. We examine the variables Satisfaction and Stay (length of stay). Stay is measured in days and...
24. ### Confusion In which ANOVA to use?

Just getting confused but here is my work : I think since there are 2 independant measures(not shown here) and there are different participants used for each tool (with same tape)...therefore it should be independant! But then I thought : 2 Independent variables: Tapes and Tools – not all...