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Parametric vs Non-Parametric
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Regression Analysis
Regression Analysis is typically parametric, assuming a linear relationship between variables and normally distributed residuals.
Central Limit Theorem
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.
Sample Size
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.
Parametric statistics
Parametric statistics refers to inferential statistical techniques that assume the data follows a certain distribution, often a normal distribution.
Mann-Whitney U Test
The Mann-Whitney U Test is a non-parametric test that compares the medians between two independent samples without the assumption of normal distribution.
Kruskal-Wallis Test
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.
Non-Parametric statistics
Non-Parametric statistics refers to inferential statistical techniques that do not assume a specific form for the distribution of the population.
Scale of Measurement
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.
Chi-Square Test
The Chi-Square Test is a non-parametric test used to determine if there is a significant association between two categorical variables.
Spearman's Rank Correlation Coefficient
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.
T-Test
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.
Wilcoxon Signed-Rank Test
The Wilcoxon Signed-Rank Test is a non-parametric test used to compare paired or matched samples without assuming a normal distribution of differences.
Homogeneity of Variance
Homogeneity of variance, or homoscedasticity, is an assumption of parametric tests that states the variances among the groups are equal.
ANOVA
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.
Normal Distribution Assumption
Parametric tests typically assume that the data is normally distributed.
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