Statistics Quiz on Non-Parametric Tests
18 Questions
1 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the most important reason for estimating population mean and variance using sample statistics?

  • To avoid bias in the data
  • To ensure that the data follows a normal distribution
  • Because population parameters are usually unknown (correct)
  • To make it easier to calculate the mean and variance

    • What are non-parametric tests primarily used for?

  • Testing hypotheses about data that does not meet the assumptions of parametric tests (correct)
  • Testing hypotheses about data from multiple populations
  • Calculating the mean and variance of a sample
  • Analyzing data from a normally distributed population

    • Which of the following is NOT a characteristic of non-parametric tests?

  • They are often referred to as rank tests
  • They are used when the data does not follow a normal distribution
  • They rely on the probability distribution of the sampled population (correct)
  • They are distribution-free tests

    • What is the primary reason for relying on sample statistics to estimate population parameters?

    <p>Because it is often impractical or impossible to collect data from the entire population (C)</p> Signup and view all the answers

    Which of the following is a key characteristic of the normal distribution?

    <p>It is represented by a bell-shaped curve (C)</p> Signup and view all the answers

    What is the primary aim of the One Sample Wilcoxon Signed Rank Test?

    <p>To compare the median/average rank of a sample to a specified value. (A)</p> Signup and view all the answers

    Which of the following is NOT an assumption of the One Sample Wilcoxon Signed Rank Test?

    <p>Equal variances between groups (D)</p> Signup and view all the answers

    Based on the provided table, what is the p-value for the Shapiro-Wilk Test of Normality?

    <p>0.002 (C)</p> Signup and view all the answers

    What is the non-parametric equivalent of the paired t-test?

    <p>Paired Sample Wilcoxon Signed Rank test (A)</p> Signup and view all the answers

    What is the purpose of the Kruskal Wallis H test?

    <p>To test for a significant difference between the means of two or more independent groups. (B)</p> Signup and view all the answers

    Why is the Kruskal Wallis H test a good alternative to One-Way Independent ANOVA?

    <p>Because it can handle data that is not normally distributed. (A)</p> Signup and view all the answers

    What is the significance of the z-score of -2.55 in the context of the One Sample Wilcoxon Signed Rank Test example provided?

    <p>It indicates that the sample median is significantly different from the hypothesized value. (C)</p> Signup and view all the answers

    Which of the following tests is appropriate for evaluating the association between two ranked variables?

    <p>Spearman rho (D)</p> Signup and view all the answers

    What is the primary advantage of nonparametric tests based on ranks?

    <p>They require fewer assumptions about the data distribution. (C)</p> Signup and view all the answers

    What is the effect of ties in the data when calculating ranks?

    <p>The tied values are assigned the average of the ranks they would have occupied if they were unique. (A)</p> Signup and view all the answers

    Why is the median a suitable measure for skewed distributions?

    <p>The median is less affected by outliers than the mean. (D)</p> Signup and view all the answers

    Which of the following data types can be analyzed using nonparametric tests based on ranks?

    <p>Both ordinal and ranked data. (B)</p> Signup and view all the answers

    What is a potential drawback of nonparametric tests based on ranks?

    <p>They are not as powerful as parametric tests. (D)</p> Signup and view all the answers

    Flashcards

    Normal Distribution

    A bell-shaped distribution describing outcomes in nature or performance.

    Parameter

    Characteristics that describe an entire population (e.g., population mean μ).

    Statistic

    Characteristics that describe a sample from a population.

    Sample Mean vs. Population Mean

    Sample mean estimates the population mean when the population is unknown.

    Signup and view all the flashcards

    Non-parametric Test

    Tests that don't assume a specific population distribution; used when normality is violated.

    Signup and view all the flashcards

    Ranks in Nonparametric Tests

    Nonparametric tests rely on the rank order of data rather than the actual data values.

    Signup and view all the flashcards

    Corrected for Ties

    Adjusting rank assignments when two or more observations have the same value.

    Signup and view all the flashcards

    Advantages of Nonparametric Tests

    Fewer assumptions, valid for skewed distributions, and can handle ordinal data.

    Signup and view all the flashcards

    Disadvantages of Nonparametric Tests

    Potential loss of information since they use ranks instead of raw data.

    Signup and view all the flashcards

    One Sample Wilcoxon Signed Rank Test

    Non-parametric test to compare a median with a specified value.

    Signup and view all the flashcards

    Assumptions of Wilcoxon Test

    1. Data independence; 2. At least ordinal scale measurement required.
    Signup and view all the flashcards

    Mann Whitney U Test

    Non-parametric test for comparing two independent samples.

    Signup and view all the flashcards

    Kruskal-Wallis H Test

    Non-parametric equivalent to one-way ANOVA for multiple groups.

    Signup and view all the flashcards

    Friedman’s Test

    Non-parametric test used for repeated measures on three or more samples.

    Signup and view all the flashcards

    Spearman rho

    Non-parametric measure of rank correlation between two variables.

    Signup and view all the flashcards

    Normality Tests

    Assess if data follows a normal distribution, e.g., Kolmogorov-Smirnov, Shapiro-Wilk.

    Signup and view all the flashcards

    Statistical Power

    Probability that a test correctly rejects a false null hypothesis.

    Signup and view all the flashcards

    Study Notes

    Non-Parametric Tests

    • Non-parametric tests are statistical tests that do not rely on the probability distribution of the sampled population.
    • They are used when the data are not normally distributed.
    • They are also useful for ordinal data, ranked data, and outliers.

    Introduction

    • Normal distribution is a bell-shaped distribution that describes how many natural, machine-made, or human performance outcomes are distributed.
    • Parameter = population characteristics.
    • Statistic = sample characteristics.
    • Statistics are used to estimate parameters.

    Statistic vs Parameter

    • Sample mean (x̄) estimates population mean (µ).
    • Sample standard deviation (sx)estimates population standard deviation (σ).
    • Sample size (n) estimates population size (N).

    Parametric vs Non-Parametric Test

    • Parametric tests require normally distributed data.
    • Parameters (e.g., population mean and variance) are often unknown.
    • Sample mean and variance are used to estimate these parameters.
    • Non-parametric tests are used if the data is not normally distributed.

    Distribution Free Tests

    • Statistical tests that do not rely on the probability distribution of the sampled population.

    Rank Tests

    • Non-parametric tests that are based on the ranks of measurements.

    Original Data vs Ranked Data

    • Examples are shown comparing raw exam marks to their corresponding ranks.

    Statistic vs Parameter Examples

    • Example data are presented to compare sample statistics to population parameters.

    Level of Measurements (Stevens' Typology)

    • Nominal (weakest): Attributes are only named.
    • Ordinal: Attributes can be ordered.
    • Interval: Distance is meaningful.
    • Ratio: Absolute zero.

    Advantage of Non-Parametric Tests

    • Fewer assumptions.
    • Use median (stable measure for skewed distributions).
    • Valid when data are non-normal.
    • Analyze ordinal data, ranked data, and outliers.

    Disadvantage of Non-Parametric Tests

    • May waste information (original vs ranked data).
    • Less statistical power compared to parametric tests.
    • Critical values table may not be commonly available.

    Critical Values of the Kruskal-Wallis H Distribution

    • Table of critical values for the Kruskal-Wallis H distribution.

    Critical Values of the Mann-Whitney U Distribution

    • Table of critical values for the Mann-Whitney U distribution.

    Choosing the Right Non-Parametric Test

    • Table showing the correspondence between parametric and non-parametric tests.

    One-Sample Wilcoxon Signed-Rank Test

    • Non-parametric equivalent to one-sample t-test.
    • Aim: compare median/average rank with a specified value.
    • Assumptions: Independence and at least ordinal scale of measurement.

    Mann-Whitney U Test

    • Non-parametric equivalent to the independent samples t-test.
    • Aim: compare two independent samples of ordinal (ranked) data or continuous (interval/ratio) data with a non-normal distribution.
    • Assumptions: Independence and at least ordinal scale of measurement.

    Kruskal-Wallis H Test

    • Non-parametric equivalent to one-way independent ANOVA.
    • Aim: compare three or more samples of ordinal (ranked) data or continuous (interval/ratio) data with a non-normal distribution.
    • Assumptions: Independence and at least ordinal scale of measurement.

    Paired-Sample Wilcoxon Signed-Rank Test

    • Non-parametric equivalent to paired t-test
    • Aim: compare two paired (related) samples of ordinal (ranked) data or continuous (interval/ratio) data with a non-normal distribution.
    • Assumptions: independence and at least ordinal scale of measurement.

    Spearman's Rho

    • Non-parametric equivalent to Pearson correlation.
    • Aim: measure the association between ordinal (ranked) data or continuous data with a non-normal distribution or non-linear relationship.
    • Assumptions: independence and at least ordinal scale of measurement.

    Post-Hoc Test for Kruskal-Wallis

    • Dunn's test method (Adjusted for Bonferroni correction).
    • Mann-Whitney U test (Divide the p-value).

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    Non-Parametric Test (2023) PDF

    Description

    This quiz covers key concepts related to non-parametric tests, including their characteristics, purposes, and comparisons to parametric tests. It emphasizes sample statistics and their roles in estimating population parameters. Test your knowledge on various statistical methods and concepts in this engaging quiz!

    More Like This

    Parametric Tests and Two-Sample t-Tests
    5 questions

    Parametric Tests and Two-Sample t-Tests

    PatriLimerick avatar
    PatriLimerick
    Parametric and Non-Parametric Tests Quiz
    15 questions

    Parametric and Non-Parametric Tests Quiz

    CharismaticDouglasFir avatar
    CharismaticDouglasFir
    Tests Non Paramétriques - Associations
    44 questions

    Tests Non Paramétriques - Associations

    TopQualityRuthenium avatar
    TopQualityRuthenium
    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser