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Parametric vs Non-Parametric

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Regression Analysis

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Regression Analysis is typically parametric, assuming a linear relationship between variables and normally distributed residuals.

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Central Limit Theorem

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The Central Limit Theorem states that with a large enough sample size, the sample mean distribution will approach a normal distribution, regardless of the population's distribution.

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Sample Size

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Parametric tests often require a larger sample size to ensure the central limit theorem holds, whereas non-parametric tests can be used with smaller sample sizes.

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Parametric statistics

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Parametric statistics refers to inferential statistical techniques that assume the data follows a certain distribution, often a normal distribution.

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Mann-Whitney U Test

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The Mann-Whitney U Test is a non-parametric test that compares the medians between two independent samples without the assumption of normal distribution.

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Kruskal-Wallis Test

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The Kruskal-Wallis test is a non-parametric version of ANOVA used when data does not meet the assumptions of ANOVA, comparing three or more independent samples.

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Non-Parametric statistics

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Non-Parametric statistics refers to inferential statistical techniques that do not assume a specific form for the distribution of the population.

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Scale of Measurement

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Parametric tests often require data to be on an interval or ratio scale, whereas non-parametric tests can be used with nominal or ordinal data.

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Chi-Square Test

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The Chi-Square Test is a non-parametric test used to determine if there is a significant association between two categorical variables.

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Spearman's Rank Correlation Coefficient

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Spearman's Rank Correlation Coefficient is a non-parametric measure of correlation that assesses how well the relationship between two variables can be described using a monotonic function.

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T-Test

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A T-Test is a parametric test used to compare the means of two groups, assuming the data is normally distributed and variances are equal.

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Wilcoxon Signed-Rank Test

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The Wilcoxon Signed-Rank Test is a non-parametric test used to compare paired or matched samples without assuming a normal distribution of differences.

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Homogeneity of Variance

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Homogeneity of variance, or homoscedasticity, is an assumption of parametric tests that states the variances among the groups are equal.

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ANOVA

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ANOVA (Analysis of Variance) is a parametric test used to compare means among three or more groups, assuming equal variances and normally distributed data within each group.

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Normal Distribution Assumption

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Parametric tests typically assume that the data is normally distributed.

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