Podcast
Questions and Answers
What is a primary reason to utilize non-parametric statistical tests over parametric tests?
What is a primary reason to utilize non-parametric statistical tests over parametric tests?
- Non-parametric tests are less susceptible to the influence of extreme values than parametric tests.
- Non-parametric tests inherently provide more precise p-values than parametric tests, regardless of data distribution.
- Parametric tests require data to follow a specific distribution, which may not always be the case. (correct)
- Parametric tests are restricted to nominal data.
Which scenario best illustrates an appropriate application of the Mann-Whitney U test?
Which scenario best illustrates an appropriate application of the Mann-Whitney U test?
- Assessing the change in blood pressure in a group of patients before and after treatment.
- Determining if the distribution of survey responses differs significantly from a uniform distribution.
- Comparing the effectiveness of a drug based on patient recovery time across two independent hospitals. (correct)
- Evaluating the correlation between income level and years of education in a population.
How does the Kruskal-Wallis test extend the functionality of other statistical tests?
How does the Kruskal-Wallis test extend the functionality of other statistical tests?
- It extends the sign test to accommodate paired samples when data violates normality assumptions.
- It extends the Wilcoxon signed-rank test for use with nominal data.
- It extends the Chi-square test for independence to handle continuous data.
- It extends the Mann-Whitney U test to compare more than two independent groups. (correct)
In the context of hypothesis testing using the sign test, what does rejecting the null hypothesis imply?
In the context of hypothesis testing using the sign test, what does rejecting the null hypothesis imply?
What is the critical assumption underlying the valid application of the Wilcoxon signed-rank test?
What is the critical assumption underlying the valid application of the Wilcoxon signed-rank test?
When might a researcher choose the Chi-square test of independence over other statistical tests?
When might a researcher choose the Chi-square test of independence over other statistical tests?
What is a key disadvantage of non-parametric tests compared to parametric tests when assumptions for parametric tests are met?
What is a key disadvantage of non-parametric tests compared to parametric tests when assumptions for parametric tests are met?
When applying the Kruskal-Wallis test, rejection of the null hypothesis leads to what conclusion?
When applying the Kruskal-Wallis test, rejection of the null hypothesis leads to what conclusion?
Which of the following is a critical step in preparing data for non-parametric tests like the Mann-Whitney U or Wilcoxon signed-rank test?
Which of the following is a critical step in preparing data for non-parametric tests like the Mann-Whitney U or Wilcoxon signed-rank test?
What is the primary focus when using the Chi-square test to assess the goodness-of-fit?
What is the primary focus when using the Chi-square test to assess the goodness-of-fit?
A researcher is analyzing fluoride concentration levels in a city's water supply. Which type of data is this considered, and why?
A researcher is analyzing fluoride concentration levels in a city's water supply. Which type of data is this considered, and why?
In what scenario would non-parametric tests be most appropriate over parametric tests for statistical analysis?
In what scenario would non-parametric tests be most appropriate over parametric tests for statistical analysis?
A dataset concerning patient satisfaction is collected using a Likert scale (e.g., very dissatisfied, dissatisfied, neutral, satisfied, very satisfied). What type of data is this, and which statistical test is most appropriate?
A dataset concerning patient satisfaction is collected using a Likert scale (e.g., very dissatisfied, dissatisfied, neutral, satisfied, very satisfied). What type of data is this, and which statistical test is most appropriate?
Which assumption about data is critical when deciding whether to use a t-test or a Mann-Whitney U test?
Which assumption about data is critical when deciding whether to use a t-test or a Mann-Whitney U test?
A researcher aims to compare two groups of patients based on their recovery time from a surgery. The data is highly skewed. What is the appropriate statistical test?
A researcher aims to compare two groups of patients based on their recovery time from a surgery. The data is highly skewed. What is the appropriate statistical test?
When is the Kruskal-Wallis test most appropriately used?
When is the Kruskal-Wallis test most appropriately used?
Which of the following scenarios would necessitate the use of a Shapiro-Wilk test?
Which of the following scenarios would necessitate the use of a Shapiro-Wilk test?
In the context of non-parametric tests, what does it mean for a test to be 'distribution-free'?
In the context of non-parametric tests, what does it mean for a test to be 'distribution-free'?
A medical researcher wants to determine if there's a significant difference in pain levels reported by patients after three different types of surgeries. The pain levels are measured on an ordinal scale. Which statistical test is appropriate?
A medical researcher wants to determine if there's a significant difference in pain levels reported by patients after three different types of surgeries. The pain levels are measured on an ordinal scale. Which statistical test is appropriate?
Why did nonparametric methods see limited use between Arbuthnot's initial work and Wolfowitz's revival of the term in 1942?
Why did nonparametric methods see limited use between Arbuthnot's initial work and Wolfowitz's revival of the term in 1942?
Flashcards
What is Data?
What is Data?
A collection of observations (numerical or categorical).
Qualitative Data
Qualitative Data
Data based on qualities or attributes (e.g., color).
Quantitative Data
Quantitative Data
Data obtained through measurements (e.g., arch length).
Discrete Data
Discrete Data
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Continuous Data
Continuous Data
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Normal Distribution
Normal Distribution
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Normality Tests
Normality Tests
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Non-Parametric Tests
Non-Parametric Tests
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Parametric Tests
Parametric Tests
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Q-Q Probability Plot
Q-Q Probability Plot
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Ranking Data
Ranking Data
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Uses for Non-Parametric Tests
Uses for Non-Parametric Tests
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Advantages of Non-Parametric Tests
Advantages of Non-Parametric Tests
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Disadvantages of Non-Parametric Tests
Disadvantages of Non-Parametric Tests
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Chi-Square Test
Chi-Square Test
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Sign Test
Sign Test
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Wilcoxon Signed-Rank Test
Wilcoxon Signed-Rank Test
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Mann Whitney U Test
Mann Whitney U Test
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Kruskal Wallis Test
Kruskal Wallis Test
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Study Notes
- Statistical Workshop Series 2023 discusses Non-Parametric Statistical Tests.
Goals of Non-Parametric Statistical Tests
- Data's Scale of Variables
- Normality of Distributions
- Statistics for Test selection
Data Classification
- Data is a collective recording of observations either numerical or categorical.
- Qualitative data: Data is collected based on attributes like sex or color, and are Nominal and Ordinal.
- Quantitative data: Data is collected through measurement using calipers like arch length and fluoride concentration.
- Quantitative data can be discrete or continuous.
- Discrete Data: Variables take only fixed values like whole numbers, e.g., DMF (1, 4, 5, 77, 102).
- Continuous Data: Variables take any value in a given range, decimal or fractional, like arch length (1.33, 34.6, 11.11).
Scales of Measures
- Nominal: Provides identity.
- Ordinal: Provides identity and magnitude.
- Interval: Provides identity, magnitude, and equal units.
- Ratio: Provides identity, magnitude, equal units, and true zero.
- "Order" of values is known for Ordinal, Interval, and Ratio scales.
- "Counts" or "Frequency of Distribution" are available in Nominal, Ordinal, Interval, and Ratio scales.
- Mode is applicable for Nominal, Ordinal, Interval, and Ratio scales.
- Median is applicable for Ordinal, Interval, and Ratio scales.
- Mean is applicable for Interval and Ratio scales.
- Differences between values can be quantified in Interval and Ratio scales.
- Values can be added or subtracted in Interval and Ratio scales.
- Values can be multiplied or divided in the Ratio scale.
- True zero exists in the Ratio scale.
- Kelvin is an absolute thermodynamic temperature scale where 0 K is absolute zero.
- Celsius is a temperature scale where 0°C is the freezing point of water and 100°C is the boiling point.
- Fahrenheit is a temperature scale where 32°F is the freezing point of water and 212°F is the boiling point.
Normal Distribution (Gaussian Distribution)
- Many statistical tests like ANOVA, t-tests, and regression require normally distributed variables in the population.
Normality Tests
- Statistical tests such as the Kolmogrov-Smirnov and Shapiro-Wilk tests.
- Graphical methods such as Q-Q probability plots and box plots.
- Normality tests should be conducted before performing parametric tests on continuous data.
Parametric and Non-parametric Tests
- Parametric tests include: One sample t-tests, Two sample independent and paired t-tests.
- Non-Parametric Tests: Chi-Square, one sample z tests and K-S tests, two sample Runs Tests, Mann-Whitney, Median, K-S, Paired sample Sign, Wilcoxon, McNemar and Chi-square tests.
Nonparametric Tests
- Nonparametric tests are statistical analysis methods that do not require a distribution to meet assumptions, especially when data is not normally distributed.
- Nonparametric tests are referred to as distribution-free tests.
History of Nonparametric Tests
- John Arbuthnot introduced nonparametric analytical methods in 1710, performing an analysis similar to the sign test.
- Jacob Wolfowitz used the term "nonparametric" again in 1942.
- Frank Wilcoxon introduced a nonparametric analysis method using rank in 1945.
- Henry Mann and Donald Ransom Whitney expanded on Wilcoxon's technique to compare two groups with different sample sizes in 1947.
- William Kruskal and Allen Wallis introduced a nonparametric test method to compare three or more groups using rank data in 1951.
Non-parametric Test Methods
- Relies on ranks assigned to ordered data.
- Use Transform > Rank Cases to apply in SPSS.
Applications of Non-Parametric Test
- Used when parametric tests are not satisfied.
- Used for testing when data does not have any distribution.
- Use for quick data analysis.
- Use when unscaled data is available.
Advantages and Disadvantages of Non-Parametric Tests
- Advantages: Easily understandable, short calculations, no distribution assumption required, applicable to all types of data.
- Disadvantages: Less efficient compared to parametric tests, results may not provide an accurate answer.
Parametric and Non-parametric tests
- Wilcoxon Signed Rank: Compares 1 Median to a specified value, the Parametric Counterpart is z-test, 1-Sample t-test.
- The Mann-Whitney: is a non-parametric tests that Compares 2 Independent Medians, the Parametric Counterpart is 2 (Independent) Samples t-test
- The Kruskal-Wallis: Campares 3 or more Medians, 1 Variable, the Parametric Counterpart is 1-way ANOVA
- Friedman : Compares 3 or more Medians, 2 Variables, the Parametric Counterpart is 2-way ANOVA
- Chi-Square Test of Independence: Tests 2 Categorical Variables for Independence (lack of Association), with non Parametric Counterpart
Non Parametric Tests Explained
- Chi-square test: Examines the differences between categorical variables from a random sample to determine well-fitting results.
- Sign Test is to compare the outcome in paired or matched samples.
- Null hypothesis, Ho: Median difference should be zero.
- Decision Rule: Reject the null hypothesis if the smaller number of positive or negative signs is less than or equal to the critical value from the table.
- Wilcoxon Signed-Rank Test: Compare the outcome in matched samples.
- Null hypothesis, Ho: Median difference should be zero.
- Decision Rule: Reject the null hypothesis if the test statistic, W is less than or equal to the critical value from the table.
- Mann Whitney U Test is to compare the outcomes in two independent samples.
- Null hypothesis, Ho: The two populations should be equal.
- Decision Rule: Reject if the test statistic, U is less than or equal to critical value.
- Kruskal Wallis Test is for comparing the outcome in greater than two independent samples.
- Null hypothesis, Ho: Population medians are equal.
- Decision Rule: Reject the null hypothesis if H ≥ critical value.
- Spearman's correlation ranks the correlation between two variables assessing how the relationship can be described using a monotonic function.
Chi-Square Tests and Attributes
- Attribute: Test of Independence; Sampling type: Single dependent sample; Interpretation: Association; Null hypothesis: no association between variables.
- Attribute: Test of Homogeneity; Sampling type: Two independent samples; Interpretation: Difference in proportions; Null hypothesis: No difference in proportion between groups.
- Attribute: Test of Goodness of Fit; Sampling type: Sample from population; Interpretation: Difference from population; Null hypothesis: No difference in distribution between sample and population.
Variables and Homogeneity
- Goodness of fit-Variable Categories Sample/Data-1 sample, 1 variable
- Homogeneity-Variable-2 samples, 1 variable
- Independence-Variable 2 Variables 1 -1 sample, 2 variables
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Description
Explore Non-Parametric Statistical Tests, part of the Statistical Workshop Series 2023. Understand data scales, variable types, and distribution normality. Learn key statistics for effective test selection and data classification.
