UNIVARIATE ANALYSIS: PARAMETRIC AND NON-PARAMETRIC TESTS

Q: What is univariate analysis in statistics?

A:

  • 📊 Univariate analysis focuses on analyzing and summarizing the distribution and characteristics of a single variable at a time.
  • 📈 It involves examining the frequency, central tendency, dispersion, and shape of the distribution of a single variable.

Q: What are parametric and non-parametric tests in univariate analysis?

A:

  • 📏 Parametric tests are statistical tests that make specific assumptions about the population distribution, such as normality and homogeneity of variances.
  • 📊 Non-parametric tests are statistical tests that do not require strict assumptions about the population distribution and are often used when data does not meet the assumptions of parametric tests.

Q: Why are parametric and non-parametric tests important in univariate analysis?

A:

  • 📈 Parametric tests are powerful and efficient when the underlying assumptions are met, providing precise estimates and accurate hypothesis testing.
  • 📊 Non-parametric tests are robust and flexible, allowing for hypothesis testing even when data violate the assumptions of parametric tests or when dealing with ordinal or non-normally distributed data.

Q: What are some common parametric tests in univariate analysis?

A:

  • 📏 t-tests: Compare means between two groups.
  • 📊 Analysis of Variance (ANOVA): Compare means across multiple groups.
  • 📈 Correlation analysis: Examine the relationship between two continuous variables.
  • 📊 Regression analysis: Predict the value of a dependent variable based on one or more independent variables.

Q: What are some common non-parametric tests in univariate analysis?

A:

  • 📈 Mann-Whitney U test: Compare medians between two independent groups.
  • 📏 Wilcoxon signed-rank test: Compare medians between two related groups.
  • 📊 Kruskal-Wallis test: Compare medians across multiple independent groups.
  • 📈 Spearman’s rank correlation: Assess the relationship between two variables when the data are ranked.

Q: How are parametric and non-parametric tests applied in univariate analysis?

A:

  • 📏 Parametric tests assume that data follow a specific distribution (usually normal) and make inferences based on parameters such as means and variances.
  • 📊 Non-parametric tests do not assume a specific distribution and use ranks or frequencies of data values to make inferences.
  • 📈 Researchers select the appropriate test based on the nature of the data, the research question, and the underlying assumptions of the statistical test.
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Q: What are the key considerations in choosing between parametric and non-parametric tests?

A:

  • 📏 Parametric tests are preferred when data meet the assumptions of normality and homogeneity of variances, as they tend to have higher statistical power.
  • 📊 Non-parametric tests are preferred when data are non-normally distributed, have outliers, or violate the assumptions of parametric tests.
  • 📈 Researchers should assess the robustness of results across different tests and consider the interpretability of findings in the context of the research question.

In summary, parametric and non-parametric tests are essential tools in univariate analysis, providing researchers with options for hypothesis testing and making inferences about the characteristics of a single variable, depending on the nature of the data and the underlying assumptions of the statistical tests.

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