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Which statistical tests rely on assumptions about the population distribution?
Which statistical tests rely on assumptions about the population distribution?
What is a key characteristic of non-parametric tests?
What is a key characteristic of non-parametric tests?
Which factor is not considered when selecting a probability distribution for hypothesis testing?
Which factor is not considered when selecting a probability distribution for hypothesis testing?
What is the purpose of comparing the test statistic to the critical value?
What is the purpose of comparing the test statistic to the critical value?
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Which of the following is a primary source of hypotheses according to the provided information?
Which of the following is a primary source of hypotheses according to the provided information?
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Which type of hypothesis test assumes that the data comes from a normally distributed population?
Which type of hypothesis test assumes that the data comes from a normally distributed population?
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What is a primary characteristic of a non-parametric test?
What is a primary characteristic of a non-parametric test?
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Which of the following is NOT considered a parametric test?
Which of the following is NOT considered a parametric test?
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Which test is specifically used to compare two independent samples?
Which test is specifically used to compare two independent samples?
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What condition must be met to use a Z-test effectively?
What condition must be met to use a Z-test effectively?
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Which non-parametric test is used for comparing paired samples?
Which non-parametric test is used for comparing paired samples?
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What is the main difference between parametric and non-parametric tests?
What is the main difference between parametric and non-parametric tests?
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Which of the following tests is appropriate for analyzing differences across multiple independent samples?
Which of the following tests is appropriate for analyzing differences across multiple independent samples?
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When should a t-distribution be used instead of a normal distribution in hypothesis testing?
When should a t-distribution be used instead of a normal distribution in hypothesis testing?
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What is the consequence of rejecting the null hypothesis when it is actually true?
What is the consequence of rejecting the null hypothesis when it is actually true?
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Which step is NOT part of the hypothesis testing process described?
Which step is NOT part of the hypothesis testing process described?
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In a two-tailed hypothesis test, the value for α when comparing calculated probability must be:
In a two-tailed hypothesis test, the value for α when comparing calculated probability must be:
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What does it mean if the calculated probability is greater than the level of significance (α)?
What does it mean if the calculated probability is greater than the level of significance (α)?
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What risk is associated with accepting the null hypothesis?
What risk is associated with accepting the null hypothesis?
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Which is a correct sequence of steps in hypothesis testing?
Which is a correct sequence of steps in hypothesis testing?
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Why is random sampling important in hypothesis testing?
Why is random sampling important in hypothesis testing?
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What statement accurately describes the significance level (α)?
What statement accurately describes the significance level (α)?
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What is the overall goal of hypothesis testing?
What is the overall goal of hypothesis testing?
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Which test is appropriate for judging the significance of means in small samples when the population variance is unknown?
Which test is appropriate for judging the significance of means in small samples when the population variance is unknown?
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What does the chi-square test primarily compare?
What does the chi-square test primarily compare?
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In what scenario is the paired T-test used?
In what scenario is the paired T-test used?
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Which test would you use to assess the significance of the correlation coefficient?
Which test would you use to assess the significance of the correlation coefficient?
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What is the primary distribution associated with the F-test?
What is the primary distribution associated with the F-test?
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When should the Z-test be used over the T-test?
When should the Z-test be used over the T-test?
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Which test can be used for analysis of variance (ANOVA)?
Which test can be used for analysis of variance (ANOVA)?
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Which of the following is a characteristic of parametric tests?
Which of the following is a characteristic of parametric tests?
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Which statistical method primarily focuses on comparing the variance of two independent samples?
Which statistical method primarily focuses on comparing the variance of two independent samples?
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When is a Z-test typically used?
When is a Z-test typically used?
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Which non-parametric test is specifically designed for analyzing matched pairs?
Which non-parametric test is specifically designed for analyzing matched pairs?
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Which of the following tests can be utilized to compare two independent samples?
Which of the following tests can be utilized to compare two independent samples?
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Which of the following statements about the Kruskal-Wallis H-test is true?
Which of the following statements about the Kruskal-Wallis H-test is true?
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Which method is primarily used to determine the degree of association among multiple sets of ranked data?
Which method is primarily used to determine the degree of association among multiple sets of ranked data?
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What is a critical requirement for conducting a sign test?
What is a critical requirement for conducting a sign test?
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In which scenario would the McNemar test be most appropriately applied?
In which scenario would the McNemar test be most appropriately applied?
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Which non-parametric test would be the most appropriate for assessing the correlation between variables?
Which non-parametric test would be the most appropriate for assessing the correlation between variables?
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What distinguishes the Wilcoxon Mann-Whitney test from the Sign test?
What distinguishes the Wilcoxon Mann-Whitney test from the Sign test?
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Which of the following is NOT a characteristic of non-parametric tests?
Which of the following is NOT a characteristic of non-parametric tests?
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Study Notes
Research Methodology - Hypothesis Testing
- Hypothesis is a key instrument in research, suggesting experiments and observations. Many experiments are deliberately designed to test hypotheses.
- Decision-makers often use hypothesis testing based on available data, before making a decision in social sciences.
- Hypothesis testing is a strategy for deciding if sample data supports generalization about population parameters.
- A hypothesis may not be definitively proven but is accepted if it withstands critical testing.
What is a Hypothesis?
- A hypothesis is a tentative assumption or supposition that's tested or disproved.
- It's a formal question to be resolved, explaining the occurrence of phenomenon, or an explanation supported by existing evidence.
- A research hypothesis is a predictive statement about an independent variable and a dependent variable.
Types of Hypotheses
-
Null Hypothesis (H₀): Represents the assumption that no significant difference or relationship exists between factors.
- Often used as a starting point, assuming no effect is present.
- Alternative Hypothesis (Hₐ): Represents the assumption that a significant difference or relationship does exist between factors.
- In a comparison (e.g., method A vs method B), the null hypothesis suggests both are equally effective.
- The alternative hypothesis posits that one method is more effective than another.
- Symbolically, H₀: μ = μ₀, and Hₐ: μ ≠ μ₀, with μ being a population mean.
Alternative Hypothesis Interpretations
- Hₐ: μ ≠ μ₀: The population mean is not equal to the hypothesized mean.
- Hₐ: μ > μ₀: The population mean is greater than the hypothesized mean.
- Hₐ: μ < μ₀: The population mean is less than the hypothesized mean.
Considerations for Choosing a Null Hypothesis
- Risk avoidance: If rejecting a true null hypothesis carries high risk, it should be the null hypothesis.
- Specific statements: The null hypothesis should make specific statements about a value, not general or close approximations.
Significance Level
- The significance level (often 5%, or 1%) is the risk a researcher is willing to take of incorrectly rejecting a null hypothesis when it's true.
- It's the percentile for making decisions in hypothesis testing.
Decision Rules and Hypothesis Tests
- A decision rule, crucial for hypothesis testing, dictates when to accept or reject a null hypothesis.
- Example: Given a lot of items, to accept Ho it must contain low number of defective items.
Type 1 and Type 2 Errors
- Type 1 error: Rejecting a true null hypothesis.
- Type 2 error: Accepting a false null hypothesis.
- Type 1 error (α) known as significance level.
- Type 2 error (β) is less specific and hard to determine.
Probability of Errors
- Probability of type 1 error is typically set in advance.
- It's a trade-off: reducing one error typically increases the other.
Hypothesis Testing Steps
- Formulating hypotheses: Define the null and alternative hypotheses.
- Choosing the significance level: Set the acceptable risk of error.
- Selecting a distribution: Choose the appropriate probability distribution.
- Sampling randomly: Collect a sample and calculate necessary statistics.
- Calculating probability: Compute the probability of obtaining the sample results if the null hypothesis is true.
- Comparing probabilities: Compare the calculated probability to the significance level.
- Final decision: Reject or accept the null hypothesis.
- Test of Hypothesis Classification: Parametric versus Non-Parametric testing.
Sources of Hypothesis
- Culture: Traditions and contexts.
- Scientific theories: Existing theory, usually affects culture.
- Analogies: Other fields or ideas, providing possible theories.
Parametric Tests
- Based on assumptions about the distribution of the population.
- These tests require a normal distribution.
- Common examples include Z-test, T-test, Chi-square test, and F-test.
Non-Parametric Tests
- Often used when assumptions of normality cannot be made.
- Common examples include sign test, Wilcoxon matched-pairs test, Wilcoxon-Mann-Whitney test, Kruskal-Wallis test, rank correlation, Kendall's coefficient of concordance, McNemar test.
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Description
Explore the critical concepts of hypothesis testing in research methodology. This quiz covers definitions, types of hypotheses, and their applications in decision-making processes. Improve your understanding of how hypotheses influence research outcomes.
