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Since you are primarily interested in the effects of your covariates, I would recommend an OLS model due to the high degree of interpretability. The mathematical regression specification would be the following: $Attribute_{3i} = \alpha + \beta_1*Atribute_{1i}+\beta_2*Attribute_{2i}+\beta_3*Attribute_{4i}$ An implementation of this in R would look roughly ...

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ANOVA is used to detect a difference in means of 3 or more independent groups. It tests whether the mean of any group differs from the overall mean. T-test is used to compare the means between 2 groups. So to compare e.g. 3 groups (A,B,C) with each other using T-tests, you would require 3 tests (A-B, A-C, B-C). The problem: each single test is associated ...

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I think there's a pretty simple way to check for this using dummies and interaction terms, without needing a separate statistical test. Just run OLS using the following regression specification: $strength_i = \alpha+\beta_1*Age_i + \beta_2*Male_i + \beta_3*Male_i*Age_i$ where $Male_i$ is a dummy equal to 1 if Male and 0 if Female. Subsequently $\beta_2$ ...

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I think I got it. For $u \neq v$, suppose w.l.o.g. that $w = v \setminus u \neq \emptyset$. Then, we have: $$\langle f_u, f_v \rangle = L_S f_uf_v = L_{(S \setminus w) \cup w} f_uf_v = L_{S \setminus w} L_w f_u f_v$$ Since $w \cap v = \emptyset$, $f_v$ is a constant w.r.t. $L_w$, so: $$\langle f_u, f_v \rangle = L_{S\setminus w} (f_v (L_w f_u)) = L_{S \... 3 This can be tested using a "general linear hypothesis test", which involve specifying a contrast matrix and performing a 1 df Wald test of the hypothesis. If the mean vector is is$$\mathbf{m}=\begin{bmatrix}\mu_1 & \mu_2 &\mu_3 \end{bmatrix}$$you specify a matrix a contrast matrix \mathbf{a} as$$\mathbf{a}=\begin{bmatrix}1 & -2 &...

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Let's look at at some specific fictitious data to illustrate the two estimates of $\sigma^2 = 16,$ the common variance of the $k=3$ levels of a factor in a balanced design with $r = 30$ replications in each of the three groups. Data and summaries. set.seed(2022) x1 = rnorm(30, 50, 4) a1 = mean(x1); v1 = var(x1) x2 = rnorm(30, 60, 4) a2 = mean(x2); v2 = var(...

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If all you care about is the proportion of binary "true positives" estimated by 4 different methods, then you have a pretty simply logistic regression model.* The binary outcome for the regression would be success/failure, with a "true positive" being a success and all other results being failures. The 4 methods would be treated as 4 ...

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As the comments point out, you have to deal with the possibility that the treatment combinations themselves affected germination. If you can rule that out adequately, then you might be OK with your approach. It would be more reliable to model the germination process directly. One possibility related to your proposed logistic regression would be an ordinal ...

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Reading Datanovia's guide on Anova with repeated measures I think my ANOVA should be specified as follows: Dependent variable is LST Sample/case ID is Buffer (100-1900) Within-subjects variables are Month (1-12) and TimePeriod (0/1) (before/after constuction) i.e. This is a "two-way repeated measures ANOVA used to evaluate simultaneously the effect of ...

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I think you could use a linear mixed model here. A basic example using the lme4 package: lme4::lmer(performance ~ DelayGroup * StudyCondition + TimeOfDay + (Condition | SubjectID), data) This would allow you to probe interaction effects for group and condition on the outcome, performance, while accounting for the time of day covariate.

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So anyone with a basic knowledge of R would have been able to help me here... You must first convert the column to factor with csv$Column = factor(csv$Column) You can't perform inline conversions within the ART call. Glad to have it figured out finally, hopefully this can help someone else

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Assumptions are hypothetical but they are not part of the null hypothesis. When I say "do we assume this or this in null hypothesis" I actually ask "what is our null hypothesis". From you answer I understood that our null hypothesis is that all the observations come from one normal distribution. If the null hypothesis and also the ...

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Thanks for the revised question. For Game A. The two conditions were scored very similarly, and you have only 7 scores. a1 = c(4, 3.5, 3, 4, 4.5, 4, 4) a2 = c(4, 4, 4, 3, 4, 4, 4) A paired Wilcoxon signed rank test finds no difference between conditions. The P-value is not exact because of the ties in the data. Tests from R. wilcox.test(a1, a2, pair=T) ...

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The pooled 2-sample t test is equivalent to a one-way ANOVA with two levels of the factor. Suppose one level has 10 replications from $\mathsf{Norm}(\mu_1=1, \sigma_1=10)$ and the other level has 100 replications from $\mathsf{Norm}(\mu_2=1,\sigma_2=1).$ In the example below, the pooled t test strongly rejects the null hypothesis (nominally that $\mu_1=\mu_2)... 5 ANOVA assumes all group distributions under consideration to be normal with the same variance. Consequently, the only way they can differ is in their means. However, you allude to the fact that the test could pick up on other differences, and if you want to use ANOVA to test something else, it is common in statistics to use a surrogate test. The best example ... 2 I think, "assume within the null hypothesis" is not a valid statement. We do not assume nothing in null hypothesis. We check if hull hypothesis can be rejected. And to be able to check it, we make some assumptions. These assumptions help us to develop formulas for test statistic and p-value. So: if we also assume that standard deviation in all the ... 1 With multiple continuous dependent variables, ANOVA is referred to as MANOVA. Suppose you save your dataset to the variable$X\$. Then the following R code will run the desired MANOVA model manova(cbind(pH,OD,DBO,N_Total, P_Total, Coli_Termo, Sol_Totais,Turbidez,IQA)~as.factor(station)+as.factor(season),data=X)

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You can do this with something similar like contrasts. You model it with variables that are linear sums of your original variables. The coefficients of the alternative model express the difference between your coefficients (and by expressing the model in terms of differences, you can ensure that your constraint is fulfilled). Possibly there is a simple way ...

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As Frank Harrell says in his answer (+1), "It is very difficult to understand plant growth conditional on the plant not dying." That makes it hard to address your interest in whether treatments have different effects on "plant growth" at different times. Would you, for example, be interested in finding rapid growth of a single plant even ...

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It is very difficult to understand plant growth conditional on the plant not dying. I would opt for an unconditional analysis of an ordinal outcome Y where the lowest level of Y codes for death and all other levels are actual plant heights. That way you don't need to use a hard-to-interpret "missing" data imputation. Consider a longitudinal ...

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The 'power and sample size' procedures for one-way ANOVAs usually give answers for models in which the number of replications at each level of the factor is equal. I suppose this is for simplicity and because the most efficient use of resources (to pay for replications) is usually a 'balanced' design with equal number of replications per level. However, in ...

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Do not use either approach; ultimately the choice of the model (multi-level or not) is dictated by the modelling task at hand and our research questions. Sure, we can go ahead and try to pick the error structure that squeezes the most significance out of our coefficients but that is just cheery picking. (I view RM ANOVAs as mostly superseded by mixed effects ...

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I also find in my research that the results are sometimes different. The paired-samples t-test shows no statistical significance, while the repeated measures anova witihin subjects factor shows significance in both groups. My two groups of speakers are different in numbers (49 and 23) and from the paired samples test I find no significance for the second ...

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At this point, you probably have your Masters, if not your Ph.D., so congratulations!! However, we all must do out part to slowly shrink the yawning void of unanswered questions, so I will take a stab here. There are many tests you can use, but they depend on what question are you trying to answer. For example, in your case, you are interested solely in an ...

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