Non-parametric Tests and Regression Analysis

This set of flashcards covers key concepts related to non-parametric tests and regression analysis as discussed in the lecture notes.

What are non-parametric tests?

Statistical methods used to analyze data that do not meet the assumptions of parametric tests.

How do non-parametric tests differ from parametric tests?

Non-parametric tests make fewer assumptions about data distribution compared to parametric tests.

When are non-parametric tests appropriate?

They are used for ordinal data, non-normal data, small sample sizes, or when outliers are present.

What is the Mann-Whitney U Test used for?

It compares the medians of two independent groups measured on an ordinal scale.

What does the Wilcoxon Signed-Rank Test compare?

It compares the medians of two related groups (paired samples) measured on an ordinal scale.

What is the purpose of the Kruskal-Wallis H Test?

It is used to compare the medians of three or more independent groups.

What does the chi-square test of independence test for?

It tests the association between two categorical variables.

What is the chi-square goodness of fit test used for?

It determines whether an observed frequency distribution differs from an expected distribution.

What is Spearman's rank correlation coefficient?

A non-parametric test used to measure the degree of association between two variables.

What does a Spearman correlation coefficient of +1 indicate?

A perfect positive monotonic relationship between the two variables.

What does a Spearman correlation coefficient of -1 indicate?

A perfect negative monotonic relationship between the two variables.

What is meant by a correlation coefficient of 0?

It indicates no monotonic relationship between the variables.

Why might a researcher use Spearman’s correlation?

It does not assume any specific distribution of the data and is appropriate for ordinal scales.

What are some common non-parametric tests for correlation?

Spearman's rank correlation and Kendall's tau.

What is the main purpose of regression analysis?

To examine the relationship between one dependent variable and one or more independent variables.

What is simple linear regression?

A regression analysis with only one independent variable.

What is multiple linear regression?

A regression analysis involving two or more independent variables.

What is logistic regression?

A regression analysis used when the dependent variable is binary.

What are the main steps in regression analysis?

Data collection, data cleaning, model specification, estimation, model evaluation, interpretation, and prediction.

What type of data is the Kruskal-Wallis test used for?

Ordinal data or non-normally distributed continuous data.

What are the assumptions of the Wilcoxon signed-rank test?

Data must be on at least an ordinal scale, and the differences between paired observations are independent.

What type of research often employs non-parametric tests?

Research in medical fields to compare treatment effects in groups.

What is the impact of outliers on parametric tests?

Outliers can significantly affect the results of parametric tests.

When is the chi-square test for independence used?

To examine if two categorical variables are independent or related.

What does a p-value less than 0.05 indicate in chi-square tests?

It suggests rejecting the null hypothesis, indicating a significant association between variables.

What does the null hypothesis represent in chi-square tests?

The assumption that there is no association between the variables being tested.

What is the null hypothesis for the chi-squared goodness of fit test?

That the observed frequencies match the expected frequencies.

How is the chi-square test statistic calculated?

By comparing observed and expected frequencies in contingency tables.

What is the significance of degrees of freedom in chi-square tests?

It helps determine which chi-square distribution curve to use when assessing significance.

How does one determine the critical value for chi-square tests?

By using the degrees of freedom and the chosen significance level (e.g., 0.05).

What does a rejection of the null hypothesis imply in chi-square tests?

There is a statistically significant difference or association between variables.

Why may non-parametric tests be used instead of parametric tests?

They are used when assumptions of parametric tests are not met, such as non-normal distributions.

What are the similarities between Spearman's correlation and Kendall's tau?

Both are non-parametric tests used to assess relationships between variables.

What assumption must be met for the Mann-Whitney U Test?

Data must be measured on at least an ordinal scale.

What is one limitation of the chi-square test of independence?

It does not indicate the direction or size of the relationship between variables.

How can the Wilcoxon Signed-Rank test be visualized?

By comparing medians of paired samples before and after an intervention.

What is a practical application of the Mann-Whitney U Test?

Comparing treatment effects or outcomes in clinical trials where data is ordinal.

What does a non-parametric test's robustness allow?

It allows for analysis under less stringent conditions regarding data distribution.

How can researchers test for normality of data?

Using both statistical tests like the Shapiro-Wilk test and graphical methods like Q-Q plots.

What does a Q-Q plot compare?

It compares the observed distribution of data to a theoretical distribution.

Why are parametric tests typically preferred over non-parametric tests?

They usually have more statistical power and provide more detailed insights about populations.

What is the main difference in results interpretation between parametric and non-parametric tests?

Parametric tests allow for inference about population parameters, while non-parametric tests do not.

What is one reason regression analysis is integral in research?

It helps quantify relationships and make predictions based on independent variables.

What are expected genotype frequencies based on Hardy-Weinberg equilibrium?

Theoretical frequencies calculated under assumptions of genetic equilibrium.

What is a key strength of using parametric methods in regression analysis?

They allow the estimation of parameters and confidence intervals for the population.

How can outliers affect non-parametric tests?

They can still influence results but to a lesser extent than in parametric tests.

What does chi-square goodness of fit analyze?

It analyzes how well observed data fits a particular distribution.

What is the primary focus of regression analysis in public health?

To identify and predict factors influencing health-related outcomes.

What can non-parametric tests reveal in research?

They can uncover trends or differences that parametric tests may miss due to assumptions.

What role does data cleaning play in regression analysis?

It ensures the accuracy and reliability of data before analysis.

What is the implication of a high p-value in a statistical test?

Failing to reject the null hypothesis; insufficient evidence for a significant effect.

What is the appropriate context for using the Kruskal-Wallis test?

When comparing more than two medians across independent groups.

What does it mean if the chi-square statistic exceeds the critical value?

It indicates a significant difference from expected frequencies or an association.

What can the significance of the Mann-Whitney U Test suggest?

It suggests that there is a difference in the distribution of the two independent groups.

What must be true for the use of regression analysis?

A continuous dependent variable and one or more independent variables.

What is a real-world application of chi-square tests in healthcare?

Analyzing the relationship between treatment type and patient recovery rates.

What does the effect size in regression analysis indicate?

The strength of the relationship between independent and dependent variables.

What can a researcher infer if regression coefficients are statistically significant?

The independent variable has a meaningful impact on the dependent variable.

Why is graphical verification important in normality testing?

It provides a visual assessment of how closely the data follows a normal distribution.

What is a potential pitfall when using non-parametric tests?

Overreliance on them can overlook valuable insights from parametric methods.

How is the power of statistical tests defined?

The probability of correctly rejecting a false null hypothesis.

What should a researcher consider when interpreting non-parametric test results?

The test's limitations in making broader conclusions about population parameters.

What are the implications of using parametric tests with non-normal data?

It may lead to inaccurate results and misinterpretation of significance.

What is the impact of sample size on the choice between parametric and non-parametric tests?

Small sample sizes may limit the validity of parametric tests and favor non-parametric.

What is the significance of the regression line in a scatter plot?

It visually represents the predicted relationship between independent and dependent variables.

In regression analysis, why is model evaluation critical?

To assess how well the model explains the data and its predictive capabilities.

What does the term 'testing for normality' refer to?

Assessing whether a dataset follows a normal distribution before applying statistical tests.

Why is the q-q plot an important tool in validating normality?

It identifies deviations from normality through a visual comparison of quantiles.

How can researchers ensure a robust use of statistical tests?

By understanding the assumptions and conditions required for each test.

What general advice is given regarding the use of non-parametric tests?

Despite their flexibility, consider the context and specific research questions.

What does the term 'graphical tests for normality' signify?

Visual methods such as histograms and Q-Q plots used to evaluate data distribution.