Questions tagged [anova]

ANOVA (Analysis of variance) 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 group means in a sample.

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10 views

A question about a proof of unbiased estimate of σ in ANOVA

When i finished the question in 《Statistical Inference》. I could not solve a proof showed that $\frac{\sum_{i=1}^{k}n_i{(\overline{Y_i} - \overline{\overline{Y}})^2}}{k-1}$ is unbiased estimate of $σ{...
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Hypothesis for a linear model where treatment effects sum to zero.

I have a dataset where I have three levels, A, B and C of one independent variable, weight. I want to know if the means of these groups are within the 0.95 confidence interval of the total mean. $$ \...
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Two-way ANOVA for machine learning model analysis.

I have different machine learning models and losses, each trained using 5-fold cross-validation. Would it make sense to run a two-way ANOVA two evaluate which are statistically performing better? ...
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anova in R, summary meaning

Does anyone knows what "Df", "Sum Sq", "Mean Sq", "F value", and "Pr(>F)" stands for when we print a summary of an aov() output? I know it gives ...
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How to do an RBD design with 3 independent variables?

I'm trying to help a student to do an RBD design with 3 independent variables. In other words, 60 people are divided into one of 5 training scenarios, and then they are blocked for what facility they ...
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How can Bartlett's test for equal variances be used for more than two groups in R?

I am looking to test if three groups have equal variances before I run (ANOVA) Analysis of Variance. One method I tried is the Bartlett's test but I only seem to be able to do this between two groups ...
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42 views

How to find the expected sum of squares for a Latin Square

having recently discovered Latin Squares, I wondered how or if it is possible to calculate the expected sum of squares for each column, row and treatment. I have looked at the example of what the sum ...
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38 views

ANOVA parameter estimation

I cannot find a formula for estimating coefficients ($a$ and $b$) of ANOVA model given by: $$\operatorname{weight} = a \cdot \operatorname{sex} + b + \epsilon$$ where $\operatorname{sex}=1$ means male ...
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Residual sum of squares and variance.

So, from the ANOVA table one can get an output of residual sum of squares. Should the RSS be divided by degrees of freedom in ANOVA + 1 or should it be divided by df in ANOVA - 1? Because the residual ...
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33 views

One-way ANOVA assumptions

I'm currently trying to perform a one-way ANOVA test on three groups of race bike athletes following a different training schedule each. The athletes were randomly selected and arbitrarily divided ...
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How to find critical point of t distribution when 1-α can't be determine directly from the table.

I was following a tutorial on Bonferroni's method. As a challenge I was ask to Compute the Bonferroni simultaneous confidence interval For a 95 % overall confidence coefficient using the Bonferroni ...
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How to perform tukey hsd multicomparison on two factor anova

I did two factor anova on this data in python: ...
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How can I derive the variance of the estimator of the interaction term in two way ANOVA model

I want to derive the variance of the estimator of the interaction term in two way anova model $\hat{\alpha\beta}_{ij}=\bar Y_{ij\cdot}-\bar Y_{i\cdot\cdot}-\bar Y_{\cdot j \cdot}+\bar Y_{\cdot\cdot\...
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Constraints of an one-way ANOVA model

I have been given a non-linear model between a response and factor at four levels, which I need to show is a constrained version of a one-way ANOVA model that I developed. The model I developed was $...
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One way analysis of variance in Regression Model perspective

Recently, I have some trouble with One-way ANOVA. Before I raise my doubts, I think it is necessary to make some notation. Suppose that the form of One-way analysis of variance is as follows: \begin{...
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Testing p-value for a linear association using Anova result.

I have a significance level of 0.05, and two different hypothesises: H0 - no relationship between weight and height H1 - there is a relationship between weight and height From my data, my p-value is ...
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What type of statistical analysis can I do on this data to see if there is any difference?

I have to work with the following data: So I'm looking at this and I see that there are essentially four groups: Standing/Congruent-Time, Standing/Incongruent-Time, Sitting/Congruent-Time, and ...
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How do you calculate degrees of freedom in planned, simple and complex contrasts?

I'm a little confused about how degrees of freedom should be calculated when planned, complex contrasts have been done. I understand that when I run the omnibus ANOVA, the degrees of freedom between ...
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141 views

Expected value of MSB in one-way ANOVA

Suppose we have $k$ many machines each producing iron balls and we are interested in weights of the balls. Let $y_{ij}$ be the weight of the $j$th ball produced by $i$ th machine,where $i=1,2,...,k$ ...
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195 views

Calculating Expected value of MSE for ANOVA Variance Components

For a given anova model $$Y_{ijk}=\mu +\alpha_i + \beta_j +\alpha\beta_{ij} +\epsilon_{ijk}$$ where the model can be mixed, random or fixed. I have been trying to calculate or find a source that can ...
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Hoeffding/ANOVA decomposition for vector valued $U$-statistics

Consider a random variable $Z = f(X_1, \dots, X_n)$, where $f: {\bf R}^n \to {\bf R}$ and $X_1, \dots, X_n$ IID random variables, and assume that $Z$ and $X_1, \dots, X_n$ all have finite variance. It ...
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2x3 mixed linear model

I have a 2x3 mixed ANOVA design. There are three treatments, with each being tested before and after treatment. I want to test whether there is a significant difference in treatment, but the results ...
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42 views

How to find the probability of one sample variance is two times larger than another?

I have two normal distribution where $X\sim N(\mu_{x}, 40^{2})$ and $Y\sim N(\mu_{y}, 50^{2})$. 8 samples from X and 16 samples from Y is drawn. How to determine the probability that the variance of ...
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What statistics can compare dataset with shared values from same data source?

I have a dataset structured as follows: I have split the data depending on the Structure column containing either "A", "B" or both as below: In this dataset, if ...
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44 views

Overparametrized Model

I am trying to understand the concept of an overparametrized model: If I am considering a one way model: $$Y_{jk}=\mu + \alpha_j + \epsilon_{jk}$$ Where $\epsilon_{jk}\sim N(0, \sigma^2)$. Why ...
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2 Sample T-Test vs 1-Factor ANOVA

Is it more advantageous to conduct a 2-sample T-test or single factor ANOVA when determining statistical significance between the means of two independent groups? I have run sample tests on mock data ...
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My data is not Normally distributed

I'm working on data and my goal is analyze it with MANOVA. My list question is : Is MANOVA needs data with a condition to be normally distributed? What should i do if my data is not normally ...
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one-way ANOVA model

In the one-way ANOVA model, the model variation SSM is equal to the between-group variation SSB. I found that SSE=SST-SSB => SSB=SST-SSE And that SSM is the difference of STT and SSE => SSM=SST-SSE ...
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How many times should I repeat a test? Use of ANOVA?

I need to repeat a certain test a number of times $n$ and then output the average of the values obtained in these $n$ tests. I have been told that I should use ANOVA to determine $n$ such that the ...
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ANOVA: Should interactions always be tested if there are multiple independent variables (Effects)?

I am attempting to determine if some of my independent variables have a significant effect on my response variables. In my case, I have various sites in which I determined the quantities of some ...
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72 views

Total Sum of Squares Algebraic proofs

learning stats from https://newonlinecourses.science.psu.edu/stat414/node/218/ but having a hard time trying to do the algebra. Need to show $SS(TO)=\sum_{i=1}^{m}\sum_{i=1}^{n}(X_{ij}-\bar{X}_{..})^2=...
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Can we use analysis of variance to replace of t test?

I know that we will get the same results whether use analysis of variance(ANOVA) or t tests when we are comparing the mean between two groups. And this two methods have same assumption: normality and ...
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FIFA19 - overall rating is higher for specific country? [closed]

Hy, I was studying this data set on Kaggle (https://www.kaggle.com/karangadiya/fifa19) for my machine learning problem. Idea is to from features of player to count overall rating. Ok, first we need a ...
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Interpreting ANOVA on regression function to determine model appropriateness

I am working on a data set with two variables; age (x) and wage (y). I created a series of polynomial regression models to fit to the data and I am attempting to identify which model is best (and ...
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How to calculate $\text{cov}(\hat{Y}_{ij}, \hat{Y}_{kj})$ if $Y_{ij} = \mu + a_i + b_j + e_{ij}$?

Let's assume we have the model following Two-Factor model without replications : $$Y_{ij} = \mu + a_i + b_j + e_{ij}, \; i=1,\dots,p \; \text{and} \; j=1,\dots, q $$ I am interested in calculating ...
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Covariance of errors $\text{cov}(\hat{e_{ij}},\hat{e_{i\ell}})$ in Two-Way Anova model

Exercise : Consider the Two-Way Anova model $Y_{ij} = \mu + a_i + b_j + e_{ij}$ with $i = 1, \dots, p$ and $j=1,\dots,q$. Show that : $$\text{cov}(\hat{e_{ij}},\hat{e_{i\ell}}) = -\sigma^2\left(\...