Test no paramétricos: Test de Wilcoxon. Módulo 6

Analysis of the Relationship Between Variables

In this section, the video discusses analyzing the relationship between a quantitative and a qualitative variable, focusing on the Wilcoxon test using an example of testing two creams for wart protection.

Understanding Variable Relationships

• Measurement Example: Two creams (A and B) are tested on patients for wart protection, with measurements taken on the affected area's diameter.

• Data Illustration: Data pairs for each patient show paired data, aiming to study if the protected area depends on the cream used.

• Variable Analysis: Examining if there is a relationship between a qualitative variable (cream type) and a quantitative variable (protected area surface).

Hypothesis Testing and Test Selection

This part delves into hypothesis testing in cases of normal and non-normal data distributions, emphasizing central tendency comparison.

Hypothesis Formulation

• Null Hypothesis: States equal means for both groups in normal data; contrasts central tendency equality against corresponding alternatives.

• Non-Normal Data Handling: Describes working differently with non-normal data or small sample sizes, highlighting variations based on data distribution.

Utilizing Non-Parametric Tests

Focuses on applying non-parametric tests like Wilcoxon when classic tests fail due to small sample sizes or non-normality.

Test Application

• Test Choice: Opting for Wilcoxon test for small samples where classic tests may fail unless differences are substantial.

New Section

In this section, the speaker discusses assigning ranks to values, correcting ties, and calculating sums of ranks based on signs.

Assigning Ranks and Correcting Ties

• Assigns a rank order to values while correcting ties to ensure each value receives a unique rank.

• Explains the process of assigning a median rank when correcting ties to address repeated values.

• Emphasizes summing ranks based on the signs of the differences between values.

New Section

This part focuses on calculating t+ and t- as sums of ranks for positive and negative differences, defining the test statistic for decision-making.

Calculating t+ and t-

• Defines t+ as the sum of ranks for positive differences and t- as the sum of ranks for negative differences.

• Introduces the test statistic as the minimum value between t+ and t-, crucial for decision-making in statistical analysis.

New Section

The discussion centers around hypotheses regarding median differences, data presentation, and assigning order ranks.

Hypotheses and Data Presentation

• Reiterates null and alternative hypotheses concerning median differences.

• Presents data with calculated differences vertically for analysis.

• Demonstrates assigning order ranks by addressing tie corrections through averaging tied values.

New Section

This segment delves into working with calculated differences, removing zeros, assigning order ranks, and addressing tie issues.

Working with Differences and Order Ranks

• Works through identified differences independently of signs.

• Removes zeros from calculations due to their equivalence.

• Assigns order ranks excluding zero values to facilitate further analysis.

New Section

The focus is on ordering remaining values after tie corrections to assign appropriate order ranks effectively.

Ordering Values After Tie Corrections

• Orders non-zero values post-tie corrections for accurate rank assignments.

• Illustrates challenges posed by repeated values necessitating averaged rank assignments.

New Section

In this section, the speaker discusses the use of normal approximation in statistical analysis and its application when sample sizes are large or small.

Normal Approximation in Statistical Analysis

• When using a computer for statistical analysis, a p-value above 0.05 suggests that rejecting the null hypothesis carries a high risk.

• A transformation from T to Z occurs in the normal approximation method, primarily influenced by sample sizes.

• The sample size plays a crucial role in determining if the data follows a standard normal model.

• Comparing the experimental corrected value with a known normal value (e.g., 1.96 for 95% confidence level) aids in hypothesis testing.

• Decision-making based on comparing experimental values with critical points determines accepting or rejecting the null hypothesis.

New Section

This part focuses on interpreting computer-generated statistical outputs and understanding key components within these results.

Interpreting Statistical Outputs

• Computer outputs display negative and positive ranks, ties, and average ranks for better comprehension.

• The appearance of values like H13, T+, and T− aids in identifying positive and negative rank sums for respective differences.

• Despite small sample sizes, computers may provide normal approximations; researchers must evaluate reliability based on literature alignment.

New Section

Here, the speaker delves into interpreting p-values from statistical analyses to draw conclusions about relationships between variables.

Interpreting P-values

• Researchers should assess if computer-generated results align with existing literature before relying solely on normal approximations.

• A p-value of 0.59 indicates no statistically significant difference between variables, leading to acceptance of the null hypothesis.