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Questions and Answers
What are statistical tests?
What are statistical tests?
Statistical tests are methods that help determine if we should reject or not reject the null hypothesis. They are based on probability distributions and can be either one-tailed or two-tailed, depending on the hypothesis.
What are the two main types of statistical tests?
What are the two main types of statistical tests?
Parametric tests assume that the data follows a normal distribution, among other assumptions.
Parametric tests assume that the data follows a normal distribution, among other assumptions.
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What is an example of a parametric test?
What is an example of a parametric test?
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Non-parametric tests assume that the data follows a specific distribution.
Non-parametric tests assume that the data follows a specific distribution.
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What are some examples of non-parametric tests?
What are some examples of non-parametric tests?
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What are the assumptions that need to be met by the data in parametric tests?
What are the assumptions that need to be met by the data in parametric tests?
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What does the assumption of Normality mean for parametric tests?
What does the assumption of Normality mean for parametric tests?
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What does the assumption of Homogeneity of Variance mean for parametric tests?
What does the assumption of Homogeneity of Variance mean for parametric tests?
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What does the assumption of Independence mean for parametric tests?
What does the assumption of Independence mean for parametric tests?
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What does the assumption of Outliers mean for parametric tests?
What does the assumption of Outliers mean for parametric tests?
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What are Degrees of Freedom?
What are Degrees of Freedom?
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What is a t-test?
What is a t-test?
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What are the two types of t-tests?
What are the two types of t-tests?
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What determines the appropriate t-test to be used?
What determines the appropriate t-test to be used?
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Study Notes
Parametric and Non-Parametric Tests
- Statistical methods used to reject or not reject a null hypothesis
- Based on probability distributions
- Can be one-tailed or two-tailed, depending on the research hypotheses
Parametric Tests
- Statistical tests assuming data approximately follows a normal distribution
- Include z-tests, t-tests, and ANOVA
- Crucial assumption: the entire population, not just the sample, follows a normal distribution.
Non-Parametric Tests
- Statistical tests not assuming any specific distribution for the data
- Also called distribution-free tests
- Examples include Chi-square tests, Mann-Whitney U tests
- Based on ranks of data points
Parametric Test Examples
- Paired t-test
- Unpaired t-test
- One-way ANOVA
- Pearson's correlation coefficient
Non-Parametric Test Examples
- Wilcoxon signed-rank test
- Mann-Whitney U test
- Kruskal-Wallis H test
- Spearman's rank correlation coefficient
Parametric Test Focus
- Analyzing and comparing the mean or variance of data.
- Mean is a common measure of central tendency, but it's sensitive to outliers.
- Data analysis should consider outliers when using means.
Parametric Test Assumptions
- Normality: Sample data originates from a normally distributed population.
- Homogeneity of variance: Sampled data comes from populations with equal variances.
- Independence: Observations are independent of each other.
- Outliers: Absence of extreme outliers in the sample.
Degrees of Freedom
- Essentially the number of independent values that can differ within a data set while measuring statistical parameters.
Comparing Means using T-Tests
- One-sample t-test: Compares a sample to a population standard value. Does the sample behave differently than the population?
- Two-sample t-test: Compares two separate samples. Both samples must be randomly selected from the population, with independent observations.
Choosing Between Z-test and T-test
- Known Population Variance and Large Sample: Use z-test (sample size ≥ 30).
- Known Population Variance and Small Sample: Use either z-test or t-test.
- Unknown Population Variance and Small Sample: Use t-test.
- Unknown Population Variance and Large Sample: Use t-test.
T-test for Independent Samples
- Used to determine if there's a difference between two independent groups' means.
- Data should be normally distributed, have equal variances, and be in interval or ratio form.
- Sample size should be less than 30.
T-test Usefulness
- More powerful than other tests for evaluating differences between independent groups.
Example Data and Problem
- Provided data tables show hours of overtime per week for male and female nurses. The goal is to determine if there's a significant difference in their overtime performance.
Steps for Solving a T-Test Problem
- Establish the problem: Determine if there's a significant difference
- Develop Hypotheses:
- Null Hypothesis (H₀): No significant difference in overtime performance between groups.
- Alternative Hypothesis (H₁): A significant difference exists in overtime performance.
- Assess Level of Significance
- Perform Statistical calculations using the formula(s).
- Decide based on computed and critical values if t-computed > t-critical.
- Final result: State the conclusion
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Description
Test your understanding of parametric and non-parametric statistical tests. This quiz covers the assumptions, examples, and applications of both types of tests, including common methods like t-tests and ANOVA. Enhance your statistical knowledge and application skills with these important concepts.
