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Kernel density estimation (KDE) is a non-parametric method to estimate the probability density function of a random variable, allowing for a smoothed representation of data distribution. It is particularly useful for visualizing the underlying structure of data without assuming a specific parametric form, making it a flexible tool in exploratory data analysis.
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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 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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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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Spearman's rank correlation is a non-parametric measure of the strength and direction of association between two ranked variables. It assesses how well the relationship between two variables can be described using a monotonic function, making it ideal for ordinal data or non-linear relationships.
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Bootstrap resampling is a statistical method used to estimate the distribution of a sample statistic by repeatedly resampling with replacement from the data set. It allows for the assessment of the variability and accuracy of estimates without relying on traditional parametric assumptions, making it particularly useful for complex data structures or small sample sizes.
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Permutation tests are non-parametric statistical tests used to determine the significance of an observed effect by comparing it to the distribution of effects generated by all possible permutations of the data. They are particularly useful when the assumptions of traditional parametric tests, such as normality, do not hold, allowing for more robust inference in a wide variety of experimental designs.
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The Kolmogorov-Smirnov Test is a non-parametric test used to determine if a sample comes from a specified distribution or to compare two samples to assess if they come from the same distribution. It is based on the maximum distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution or between the empirical distribution functions of two samples.
The Chi-Square Test of Independence is a statistical method used to determine if there is a significant association between two categorical variables. By comparing the observed frequencies in a contingency table with the expected frequencies, it helps to assess whether the variables are independent or related in the population from which the sample is drawn.
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Nonparametric regression is a type of regression analysis that makes no assumptions about the form of the relationship between independent and dependent variables, allowing for more flexibility in modeling complex data patterns. It is particularly useful when the underlying data distribution is unknown or when the data exhibits nonlinear relationships that cannot be adequately captured by parametric models.
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Non-normality refers to statistical data that do not follow a normal distribution, often characterized by skewness, kurtosis, or the presence of outliers. Understanding non-normality is crucial for selecting appropriate statistical tests and accurately interpreting data analyses, as many classical methods assume normality.
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Nonlinear time series analysis deals with time-dependent data where the relationship between variables is not a straight line, allowing for more complex dynamics and patterns such as cycles, chaos, and abrupt changes. It is crucial in fields like economics, meteorology, and engineering where linear assumptions often fail to capture real-world phenomena accurately.
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Small sample inference involves making statistical conclusions from datasets that are not large enough to reliably approximate the normal distribution. It often requires using specialized techniques, such as the t-distribution, to account for the increased variability and potential bias in parameter estimation.
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Censored data refers to data where the value of an observation is only partially known, often occurring in survival analysis where the event of interest has not been observed for all subjects by the end of the study. This type of data requires specialized statistical methods to properly analyze and interpret, as it can lead to biased estimates if not handled correctly.
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Change Point Analysis is a statistical technique used to identify points in time where the properties of a data sequence change significantly. It is crucial for detecting shifts in trends, variances, or other statistical properties in time series data, aiding in better understanding and forecasting of data patterns.
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