Podcast
Questions and Answers
How does the shape of the t-distribution change based on the degrees of freedom?
How does the shape of the t-distribution change based on the degrees of freedom?
- It remains constant regardless of the degrees of freedom.
- It becomes more symmetrical and approaches a normal distribution as the degrees of freedom increase. (correct)
- It becomes less symmetrical as the degrees of freedom increase.
- It becomes skewed to the right as the degrees of freedom increase.
A researcher wants to compare the mean systolic blood pressure of a group of patients to the known population mean. Which statistical test is most appropriate?
A researcher wants to compare the mean systolic blood pressure of a group of patients to the known population mean. Which statistical test is most appropriate?
- Two-sample t-test.
- Independent measures t-test.
- Repeated measures t-test.
- One-sample t-test. (correct)
A researcher is analyzing data with a small sample size and suspects that the population standard deviation is unknown. Which distribution should they use to calculate confidence intervals?
A researcher is analyzing data with a small sample size and suspects that the population standard deviation is unknown. Which distribution should they use to calculate confidence intervals?
- F-distribution.
- T-distribution. (correct)
- Z-distribution.
- Chi-squared distribution.
Why are two-tailed tests generally considered more stringent than one-tailed tests?
Why are two-tailed tests generally considered more stringent than one-tailed tests?
How is Cohen's d calculated, and what does it represent?
How is Cohen's d calculated, and what does it represent?
What is the primary purpose of using an independent measures design (between-subjects design)?
What is the primary purpose of using an independent measures design (between-subjects design)?
In a repeated measures design, what is a key characteristic of the participants?
In a repeated measures design, what is a key characteristic of the participants?
How do individual differences impact the analysis in independent measures designs compared to related samples designs?
How do individual differences impact the analysis in independent measures designs compared to related samples designs?
What does the formula $df = n - 1$ represent in the context of a one-sample t-test?
What does the formula $df = n - 1$ represent in the context of a one-sample t-test?
Which of the following is a key assumption that must be met when using a t-test?
Which of the following is a key assumption that must be met when using a t-test?
Flashcards
What is a t-distribution?
What is a t-distribution?
A distribution of sample means when the population standard deviation (σ) is estimated.
One-sample t-test
One-sample t-test
Compares the mean of a single sample against a known population mean.
t-test statistic formula
t-test statistic formula
t = (Sample Mean - Population Mean) / (Sample Standard Error)
Confidence Interval
Confidence Interval
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Cohen's d (Effect Size)
Cohen's d (Effect Size)
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Independent Measures Design
Independent Measures Design
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Repeated Measures Design
Repeated Measures Design
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Related samples design
Related samples design
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Degrees of freedom (df)
Degrees of freedom (df)
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Two Sample t-Tests
Two Sample t-Tests
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Study Notes
- The T-distribution is a distribution of sample means when σ is estimated using s.
T-Distribution
- Symmetrical with most scores clustered around the mean.
- Its shape changes depending on the degrees of freedom.
- df = n - 1
One-Sample T-Test
- Compares one sample mean against the population mean.
T-Test Statistic
- t = (X̄ - μ) / Sx = (X̄ - μ) / (s/√n)
- Sx = standard error of the sample.
Two-Tailed Tests
- More common to use for more stringent tests
- Generally easier to reject a null hypothesis than one-tailed tests.
Confidence Intervals
- Confidence Intervals = Point estimate ± Margin of Error
- CI(1-α) = X̄ ± tcrit (s/√n)
- Where α is the level of confidence
- XÌ„ is the point estimate
- tcrit (s/√n) is the margin of error
Cohen's d
- Measures effect size
- d = (X̄ - μ) / σ ⇒ d = (X̄ - μ) / s
Two Sample T-Tests
- One sample z-test and one sample t-test allow the comparison of one sample mean to the population mean
Independent Measures Design (a.k.a. Between-Subject Design)
- Compares different treatments where each participant is only in one treatment group.
- Compares samples from different existing populations.
- Samples and groups are independent of one another.
Repeated Measures Design (a.k.a. Within-Subject Design)
- Compares treatments by having each participant undergo every treatment level.
- Individuals in one sample determine the members of the other sample (related samples design).
- Participants go through both treatments.
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