## 统计代写|非参数统计代写Nonparametric Statistics代考|Multiple Comparisons and Scoring

statistics-lab™ 为您的留学生涯保驾护航 在代写非参数统计Nonparametric Statistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写非参数统计Nonparametric Statistics代写方面经验极为丰富，各种代写非参数统计Nonparametric Statistics相关的作业也就用不着 说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据 分析
• Foundations of Data Science 数据科学基础

## 统计代写|非参数统计代写Nonparametric Statistics代考|Multiple Comparisons and Scoring

One might adjust for multiple comparisons in the presence of blocking in the same way as was done without blocking, as discussed in $\S 4.5$. That is, one might use the variances and covariances to show that under the null hypothesis, $\left(\bar{R}{i .}-\bar{R}{j .}\right) / \sqrt{K(L K+1) / 6}$ is approximately Gaussian, and employ the method of Bonferroni, Fisher’s LSD, or Tukey’s HSD.

One might also use scoring methods, including normal and Savage scores, as before. Recall also that treating ranks as general scores, with tied observations given average ranks, makes tie handling automatic.

One might also use scores that are data values. In this case, the test statistic is similar to that of the Gaussian-theory $F$ test, but the reference distribution is generated from all possible permutations of the data within blocks and among treatments.

## 统计代写|非参数统计代写Nonparametric Statistics代考|Tests for a Putative Ordering in Two-Way Layouts

This test was proposed by Page (1963) in the balanced case with one replicate per block-treatment pair, and is called Page’s test.

For more general replication patterns, the null expectation and variance for the statistic may be calculated, using $(5.6),(5.7)$, and $(5.8)$, and
$\mathrm{E} 0\left[T_{L}\right]=\sum_{k=1}^{K} k \mathrm{E} 0\left[R_{k .}\right]$
$\operatorname{Var}{0}\left[T{L}\right]=\sum_{k=1}^{K} k^{2} \operatorname{Var}{0}\left[R{k . .}\right]+\sum_{i=1}^{K} \sum_{k=1, k \neq i}^{K} i k \operatorname{Cov}{0}\left[R{i_{.} .}, R_{k . .}\right]$
In the balanced case, with $M_{k l}=M \forall k, l$, moments simplify to
\begin{aligned} \mathrm{E} 0\left[T_{L}\right] &=(K+1) K L M(K M+1) / 4 \ \operatorname{Var}{0}\left[T{L}\right] &=L M^{2}(K M+1)\left(\sum_{k=1}^{K} k^{2}(K-1)-\sum_{i=1}^{K} \sum_{k=1, k \neq i}^{K} i k\right) \ &=L M^{2}(K M+1)\left(K \sum_{k=1}^{K} k^{2}-\left(\sum_{i=1}^{K} i\right)^{2}\right) \ &=K^{2}(K+1) L M^{2}(K M+1)(K-1) / 12 \ \text { using }(3.20) . \end{aligned}

## 统计代写|非参数统计代写Nonparametric Statistics代考|Exercises

Page (1963) presents only the case with $M_{k l}$ all 1, and provides a table of the distribution of $T_{L}$ for small values of $K$ and $L$. For larger values of $K$ and $L$ than appear in the table, Page (1963) suggests a Gaussian approximation.
The scores in $(5.10)$ are equally spaced. This is often a reasonable choice in practice. When the $M_{k l}$ are not all the same, imbalance among numbers of ranks summed may change the interpretation of these scores, and a preferred statistic definition to replace $(5.10)$ is
$$T_{L}^{*}=\sum_{k=1}^{K} k \bar{R}{k \ldots}$$ with moments given by \begin{aligned} \mathrm{E}\left[\bar{R}{k . .}\right] &=\sum_{l=1}^{L}\left[M_{k l}\left(\sum_{j=1}^{K} M_{j l}+1\right) / 2\right] / \sum_{l=1}^{L} M_{k l l} \ \operatorname{Var}\left[\bar{R}{k . .}\right] &=\frac{\sum{l=1}^{L}\left{M_{k l}\left(\sum_{j \neq k} M_{j l}\right)\left(\sum_{j=1}^{K} M_{j l}+1\right)\right}}{12\left(\sum_{l=1}^{L} M_{k l}\right)^{2}}, \end{aligned}
and
$$\operatorname{Cov}\left[\bar{R}{k . .}, \bar{R}{m . .}\right]=-\sum_{l=1}^{L}\left[M_{k l} M_{m l}\right]\left(\sum_{j=1}^{K} M_{j l}+1\right) /\left(12 \sum_{l=1}^{L} M_{k l} \sum_{l=1}^{L} M_{m l}\right)$$

## 统计代写|非参数统计代写Nonparametric Statistics代考|Exercises

Page (1963) 只提出了这种情况米到一世所有 1，并提供了一个分布表吨一世对于小值到和一世. 对于较大的值到和一世Page (1963) 建议使用高斯近似。

## 广义线性模型代考

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