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Non-parametric statistics refers to statistical methods that do not assume a specific probability distribution for the data, making them particularly useful for analyzing data that do not fit traditional parametric models. These methods are flexible and robust, often used for ordinal data or when the sample size is too small to validate assumptions of parametric tests.
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Ordinal data represents categories with a meaningful order but without a uniform scale, allowing for the ranking of data points. Unlike interval data, Ordinal data does not quantify the difference between categories, making it suitable for non-parametric statistical tests.
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The Mann-Whitney U test is a non-parametric statistical test used to determine whether there is a significant difference between the distributions of two independent groups. It is particularly useful when the data do not meet the assumptions of normality required for a t-test, and it evaluates whether one group tends to have higher values than the other.
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The Wilcoxon signed-rank test is a non-parametric statistical test used to compare two related samples or matched pairs to assess whether their population mean ranks differ. It is particularly useful when the data does not meet the assumptions of a parametric test like the paired t-test, such as normality or when dealing with ordinal data.
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The Kruskal-Wallis test is a non-parametric statistical method used to determine if there are statistically significant differences between the medians of three or more independent groups. It is an extension of the Mann-Whitney U test and is particularly useful when the assumptions of ANOVA are not met, such as when the data is not normally distributed or when sample sizes are small.
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Distribution-free methods, also known as non-parametric methods, are statistical techniques that do not assume a specific probability distribution for the data. These methods are particularly useful when dealing with data that do not meet the assumptions of parametric tests, allowing for more flexibility and robustness in analysis.
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Hypothesis testing is a statistical method used to make decisions about the properties of a population based on a sample. It involves formulating a null hypothesis and an alternative hypothesis, then using sample data to determine which hypothesis is more likely to be true.
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Data ranking is the process of ordering data points based on specific criteria, often used to prioritize or identify the most significant items within a dataset. It is crucial in fields like search engines, recommendation systems, and data analysis to enhance decision-making and improve user experience.
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Robustness to outliers refers to the ability of a statistical method or model to remain effective even when data points significantly deviate from the overall pattern. This characteristic is crucial for ensuring that the model's predictions or inferences are not unduly influenced by anomalies or errors in the dataset.
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The Friedman Test is a non-parametric statistical test used to detect differences in treatments across multiple test attempts. It is an extension of the Wilcoxon signed-rank test to more than two groups and is particularly useful when the data violates the assumptions of normality required for a repeated measures ANOVA.
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