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Questions and Answers
What is one assumption for parametric tests?
The distribution is approximately normally distributed.
What should be checked and removed if assumptions are not met?
Outliers
Which of the following transformations can be applied to data? (Select all that apply)
Non-parametric tests make assumptions on the distribution.
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What does ANOVA stand for?
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What is the main purpose of hypothesis testing?
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Match the following probability distributions:
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Which of the following characterizes a discrete random variable?
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In the context of random variables, what does the symbol 𝑌 represent?
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What type of random variable is characterized by a sample space of $𝑌 = {𝑦 ≥ 0}$?
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When a die is thrown until a 5 occurs, which characteristic of the random variable is exhibited?
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What is a defining feature of continuous random variables compared to discrete random variables?
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What is a key characteristic of non-parametric tests?
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Which of the following statements is true regarding the power of non-parametric tests?
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In which experimental design is the use of non-parametric tests particularly appropriate?
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Which of the following is NOT a type of probability distribution mentioned?
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Which of the following is an example of a non-parametric test?
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What is a main disadvantage of non-parametric tests compared to parametric tests?
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Which analysis is most suitable for comparing two populations when data do not meet parametric test assumptions?
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In experimental design, what principle must be adhered to for effective results?
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What is necessary for a distribution to meet the assumptions of parametric tests?
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What is one method to address violations of assumptions in parametric tests?
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Which transformation method is used to address violations of assumptions by altering scale?
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Which statement is true regarding the equality of variance assumption?
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What is a potential cause of an outlier in a dataset?
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What can be a characteristic of distributions that violate parametric test assumptions?
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What type of transformation involves taking the reciprocal of each data point?
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If a dataset is not normally distributed, what should be the first step in addressing this issue?
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What term describes the set of all entities or individuals under consideration in statistics?
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Which of the following correctly defines a qualitative variable?
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In the context of statistical inference, what is the purpose of estimation?
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What statistical method would be appropriate for comparing two independent parametric samples?
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Which of these phases of statistical inference involves generating a specific numerical value estimate of a parameter?
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What type of design would be most appropriate for an experiment with two treatment factors?
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Which term is used to define values (measurements or observations) that the variables can assume?
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Which of the following tests is used for related samples when the data is parametric?
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What is the relationship between a sample and a population?
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Which statement best defines a random variable?
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What does the summation notation Σ represent?
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What does the sample mean ($ar{y}$) represent?
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What does the probability mass function describe?
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How is sample variance ($s^2$) calculated?
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Which of the following describes an interval estimate?
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What does the sample standard deviation ($s$) indicate?
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Study Notes
Week 2: AMAT 131 Statistical Methods and Experimental Design
- Covers introduction to statistics, hypothesis testing, parameter estimation, correlation analysis, regression analysis, and chi-square tests.
- Includes probability and counting rules, discrete probability distributions, the normal probability distribution, and the central limit theorem.
- Contains three long exams.
Assumptions for Parametric Tests
- Data should be approximately normally distributed.
- Some tests require equal variances (homogeneity of variance).
Addressing Violations of Parametric Test Assumptions
- Outlier Management: Identify and remove outliers which may arise from measurement variability, novel data points, or experimental errors.
- Data Transformation: Apply transformations such as logarithmic (log x), square root (√x), reciprocal (1/x), or power (xk) transformations.
- Non-parametric Alternatives: Utilize non-parametric tests if assumptions are not met. These tests are distribution-free, performing rank transformations but are less powerful than parametric tests.
Choosing Statistical Models
- Selection depends upon the data's characteristics and the research question.
Probability Distributions and Comparison of Two Populations
- Topics include a review of basic statistics and an introduction to probability distributions (binomial, multinomial, Poisson, and normal distributions).
- Covers methods for comparing two populations, focusing on independent samples.
Experimental Design
- Introduces experimental design principles, including single-factor experiments, analysis of variance (ANOVA), and completely randomized designs (CRD).
- Discusses ANOVA assumptions, their violations, and potential remedies.
- Includes the Kruskal-Wallis test, a non-parametric alternative to ANOVA.
Relationships and Associations
- Covers simple and multiple linear regression analysis, examining relationships between variables.
- Explores simple correlation analysis using parametric and non-parametric approaches.
Introduction to Statistics
- Covers introductory concepts, methods of data presentation, descriptive statistics, probability and counting rules, discrete and continuous probability distributions, the normal probability distribution, and the central limit theorem.
- Includes three long exams.
Assumptions for Parametric Tests
- Data should be approximately normally distributed.
- Some tests require the assumption of homogeneity (equality) of variance.
Handling Violations of Parametric Test Assumptions
- Check for and remove outliers (potential causes: measurement variability, novel data, experimental error).
- Transform data using logarithmic, square root, reciprocal, or power transformations.
- Consider non-parametric alternatives, which are distribution-free but less powerful than parametric tests. They use rank transformations.
Choosing Statistical Models
- The course will cover model selection criteria.
Probability Distributions and Comparison of Two Populations
- Reviews basic statistics and introduces probability distributions (binomial, multinomial, Poisson, other, normal).
- Covers the comparison of two populations using parametric and non-parametric methods for independent and related samples.
Experimental Design
- Covers single-factor experiments, principles of experimental design, ANOVA, assumptions of ANOVA, and remedies for violations.
- Includes completely randomized designs (CRD), randomized complete block designs (RCBD), Latin square designs (LSD), and factorial designs (two-factor, split-plot).
- Non-parametric alternatives like the Kruskal-Wallis test and Friedman test are also discussed.
Relationship and Association
- Covers simple and multiple correlation and regression analysis (parametric and non-parametric).
Course Navigation on UVLE (University Virtual Learning Environment)
- Access UVLE at uvle.upmin.edu.ph.
- Log in using your UP email address.
- Find AMAT 131.
- Explore platform features.
Free Statistical Software
- R and RStudio are recommended.
Basic Statistical Terms
- Universe: The entire set of entities or individuals under consideration.
- Variable: A characteristic or attribute with varying values (qualitative or quantitative).
- Data: The values assumed by variables.
- Random variable: Represents outcomes of a non-deterministic process.
- Statistical inference has two phases: estimation (point and interval) and hypothesis testing.
- Population: All subjects being studied; the set of all possible values of the variable.
- Sample: A subset of the population.
Summation Notation
- Σ denotes summation.
- First Constant Theorem: Σᵢ₌₁ⁿ k = nk
- Second Constant Theorem: Σᵢ₌₁ⁿ kXᵢ = k Σᵢ₌₁ⁿ Xᵢ
- Third Constant Theorem: Σᵢ₌₁ⁿ (aXᵢ + bYᵢ) = a Σᵢ₌₁ⁿ Xᵢ + b Σᵢ₌₁ⁿ Yᵢ
Example Calculation (Wheat Yield)
- Given a sample of wheat yields (7, 9, 6, 12, 4, 6, 9 tons), the mean, sample variance, and sample standard deviation can be calculated using standard formulas.
Probability Distributions
- Describes the probability structure of a random variable.
- For discrete variables, it's the probability mass function (PMF).
- For continuous variables, it's the probability density function (PDF).
Random Variables
- Numerical variables whose values depend on random experimental outcomes.
- Associate numerical values with sample space outcomes.
- Classified as discrete (whole numbers, finite or countably infinite values) or continuous (can assume any value within an interval).
Examples of Random Variables
- Number of defective components in a sample (discrete).
- Number of die throws until a 5 appears (discrete).
- Height difference before and after taking a supplement (continuous).
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Description
This quiz covers the fundamentals of statistical methods including hypothesis testing, correlation analysis, and regression analysis. It also explores the assumptions for parametric tests and how to address violations through methods like outlier management and data transformations. Prepare to test your understanding of both parametric and non-parametric alternatives.
