Podcast
Questions and Answers
What is the primary purpose of hypothesis testing?
What is the primary purpose of hypothesis testing?
Which step is NOT part of the four steps of a hypothesis test?
Which step is NOT part of the four steps of a hypothesis test?
What does a Type I error indicate in hypothesis testing?
What does a Type I error indicate in hypothesis testing?
Which of the following best defines the alpha level in hypothesis testing?
Which of the following best defines the alpha level in hypothesis testing?
Signup and view all the answers
When calculating the z-score for a sample mean, which values are essential?
When calculating the z-score for a sample mean, which values are essential?
Signup and view all the answers
What is a Type II error in hypothesis testing?
What is a Type II error in hypothesis testing?
Signup and view all the answers
In hypothesis testing, what is meant by the critical region?
In hypothesis testing, what is meant by the critical region?
Signup and view all the answers
What is primarily focused on in a hypothesis test?
What is primarily focused on in a hypothesis test?
Signup and view all the answers
Which factor can increase the power of a statistical test?
Which factor can increase the power of a statistical test?
Signup and view all the answers
What must be determined to evaluate a hypothesis using sample data?
What must be determined to evaluate a hypothesis using sample data?
Signup and view all the answers
What does a significant treatment effect not necessarily imply?
What does a significant treatment effect not necessarily imply?
Signup and view all the answers
What relationship does the alpha level have with the power of a test?
What relationship does the alpha level have with the power of a test?
Signup and view all the answers
Which measure is used to estimate the real standard error when the value of σ is unknown?
Which measure is used to estimate the real standard error when the value of σ is unknown?
Signup and view all the answers
Which of the following statements is true regarding one-tailed and two-tailed tests?
Which of the following statements is true regarding one-tailed and two-tailed tests?
Signup and view all the answers
What does the degrees of freedom represent in a sample?
What does the degrees of freedom represent in a sample?
Signup and view all the answers
What does measuring effect size provide insight into?
What does measuring effect size provide insight into?
Signup and view all the answers
What does a Type II error indicate in hypothesis testing?
What does a Type II error indicate in hypothesis testing?
Signup and view all the answers
Which factor is NOT considered when determining the boundaries of the critical region?
Which factor is NOT considered when determining the boundaries of the critical region?
Signup and view all the answers
What happens to the standard deviation when a constant is added or subtracted from a dataset?
What happens to the standard deviation when a constant is added or subtracted from a dataset?
Signup and view all the answers
What is represented by the symbol β (beta) in hypothesis testing?
What is represented by the symbol β (beta) in hypothesis testing?
Signup and view all the answers
What does a significant result in a statistical test imply about the null hypothesis?
What does a significant result in a statistical test imply about the null hypothesis?
Signup and view all the answers
Which of the following is a characteristic of independent observations?
Which of the following is a characteristic of independent observations?
Signup and view all the answers
Which of the following best describes a one-tailed hypothesis test?
Which of the following best describes a one-tailed hypothesis test?
Signup and view all the answers
What does a Type I error represent in hypothesis testing?
What does a Type I error represent in hypothesis testing?
Signup and view all the answers
Which of the following assumptions is crucial for conducting hypothesis tests with z-scores?
Which of the following assumptions is crucial for conducting hypothesis tests with z-scores?
Signup and view all the answers
How does higher variability of scores influence a hypothesis test's outcome?
How does higher variability of scores influence a hypothesis test's outcome?
Signup and view all the answers
In hypothesis testing, what does it mean if sample data fall within the critical region?
In hypothesis testing, what does it mean if sample data fall within the critical region?
Signup and view all the answers
What is the purpose of measuring effect size in hypothesis testing?
What is the purpose of measuring effect size in hypothesis testing?
Signup and view all the answers
Which factor would lead to a larger value for the z-score in hypothesis testing?
Which factor would lead to a larger value for the z-score in hypothesis testing?
Signup and view all the answers
According to Cohen's criteria, how can effect size be standardized?
According to Cohen's criteria, how can effect size be standardized?
Signup and view all the answers
In hypothesis testing, what does it mean if a result is said to be statistically significant?
In hypothesis testing, what does it mean if a result is said to be statistically significant?
Signup and view all the answers
What may cause a decrease in the chance of finding a significant treatment effect?
What may cause a decrease in the chance of finding a significant treatment effect?
Signup and view all the answers
What does the term 'effect size' refer to in the context of treatment variability?
What does the term 'effect size' refer to in the context of treatment variability?
Signup and view all the answers
What is the purpose of calculating a confidence interval?
What is the purpose of calculating a confidence interval?
Signup and view all the answers
Which of the following correctly states the null hypothesis in a one-tailed t-test with the alternative hypothesis suggesting a decrease?
Which of the following correctly states the null hypothesis in a one-tailed t-test with the alternative hypothesis suggesting a decrease?
Signup and view all the answers
How is the critical value for a two-tailed test determined?
How is the critical value for a two-tailed test determined?
Signup and view all the answers
In a t-test with 9 samples, what is the appropriate degree of freedom (df) to use?
In a t-test with 9 samples, what is the appropriate degree of freedom (df) to use?
Signup and view all the answers
What is the critical value of t for a one-tailed test at α = 0.01 with 8 degrees of freedom?
What is the critical value of t for a one-tailed test at α = 0.01 with 8 degrees of freedom?
Signup and view all the answers
What does the term 'critical region' refer to in hypothesis testing?
What does the term 'critical region' refer to in hypothesis testing?
Signup and view all the answers
Which statement about hypothesis testing is false?
Which statement about hypothesis testing is false?
Signup and view all the answers
Study Notes
Statistical Inference and Hypothesis Testing
- Every sample mean (M) has a z-score indicating its position within the distribution of sample means.
- Hypothesis: Predicts the relationship between variables; serves as a scientific guess.
- A hypothesis test evaluates a hypothesis about a population using sample data.
- Hypothesis testing employs statistical analysis to address research questions.
Steps in Hypothesis Testing
- Step 1: State the hypothesis.
- Step 2: Set criteria for making decisions based on data.
- Step 3: Collect data and compute sample statistics.
- Step 4: Make a decision regarding the null hypothesis.
Types of Errors in Hypothesis Testing
- Type I Error (False Positive): Rejecting a true null hypothesis, indicating treatment effect where none exists.
- Type II Error (False Negative): Failing to reject a false null hypothesis, missing a real treatment effect.
- Critical region determined by alpha level, which defines extreme sample values unlikely if the null hypothesis is true.
Z-Scores
- Z-score for Population: Reflects an individual score's position in the entire score distribution.
- Z-score for Sample: Reflects a sample mean's position within the distribution of sample means.
Assumptions for z-Score Hypothesis Tests
- Random Sampling: Ensures sample is representative of the population.
- Independent Observations: The occurrence of one event does not affect another.
- Value of σ remains unchanged by treatment, affecting only the mean, not standard deviation.
Reporting Results in Statistical Tests
- A significant result indicates the null hypothesis is rejected, unlikely to occur by chance alone.
- Directional (One-Tailed) Hypothesis Tests specify expected direction of effect (increase/decrease).
Measuring Effect Size
- Effect size quantifies the magnitude of a treatment effect, independent of sample size.
- Cohen (1988) suggested standardizing effect size by measuring mean difference relative to standard deviation.
Factors Influencing Hypothesis Test Outcomes
- Score Variability: Higher variability may decrease likelihood of significant results due to reduced z-score value.
- Sample Size: Larger samples provide smaller standard errors and larger z-scores, increasing power.
- Alpha Level: Lowering alpha level reduces test power but decreases Type I error risk.
Power of a Statistical Test
- Probability of correctly rejecting a false null hypothesis increases with larger sample sizes.
- Parametric tests generally have greater power than non-parametric counterparts.
- Power calculations help determine if the sample size is sufficient.
t-Statistic in Hypothesis Testing
- Used when population parameters are unknown, forms the basis of t-tests.
- Critical region locations depend on the degrees of freedom (df) determined by sample size.
Confidence Intervals
- Represent a range of values around a sample statistic, predicting the population parameter.
- Confidence intervals provide insight into where the true population parameter likely falls.
T-Test for Related Samples
- Hypotheses must clearly define expected differences between conditions (e.g., swearing and pain tolerance).
- Specify the alpha level to determine critical values for decision-making in hypothesis testing.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
This quiz covers key concepts from Module 2 of Psychological Statistics, focusing on hypothesis testing, effect size, and types of errors. It explores the relationship between sample means and z-scores, providing a comprehensive assessment of your understanding of statistical inference.