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Questions and Answers
What is the purpose of a one sample t-test?
What is the purpose of a one sample t-test?
- To evaluate variances across multiple groups
- To compare two independent sample means
- To assess the correlation between two variables
- To compare a sample mean with a population mean (correct)
When should standard deviation be used instead of standard error?
When should standard deviation be used instead of standard error?
- When estimating the precision of the sample mean
- When comparing two sample means directly
- When measuring the variability within a sample (correct)
- When analyzing the difference between two population means
In a paired t-test, what does it compare?
In a paired t-test, what does it compare?
- A sample mean with a hypothesized population mean
- Different subjects and their responses at two different times
- Two measures from the same subject under different conditions (correct)
- Two independent samples from the same population
What can a p-value of 0.027 in a paired sample t-test indicate?
What can a p-value of 0.027 in a paired sample t-test indicate?
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What is a key characteristic of an independent t-test?
What is a key characteristic of an independent t-test?
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Study Notes
Parametric Tests
- Parametric Tests assume the data follows a normal distribution.
- Specific tests help analyze the difference between means.
Two-Sample t-Tests
- Analyze the difference between two sample means.
- Uses Mean and Variation.
- Requires understanding of Standard Deviation and Standard Error.
Standard Deviation
- Measures the spread of data around the mean.
- Higher standard deviation indicates greater spread.
Standard Error
- Estimates the variability of the sample mean.
- Lower standard error indicates a more precise sample mean estimate.
T-Test Steps
- Calculate the t-statistic, which measures the difference between the means relative to the variability.
- Calculate the p-value, which indicates the probability of observing the obtained difference in means if there is no true difference.
- Determine a significance level (usually 0.05).
- Compare the p-value to the significance level.
- If the p-value is less than the significance level, we reject the null hypothesis and conclude that there's a statistically significant difference between the means.
One-Sample t-Test
- Compares a single sample mean to a known population mean.
Independent t-Test
- Applies when two independent groups are being compared.
Paired or Dependent t-Test
- Applies to paired data, like pre- and post-treatment measurements for the same individuals.
- Involves two measurements for each participant, allowing analysis of changes within individuals.
Paired t-Test Example
- Measures pre- and post-training scores.
- Means: 79.6 vs 82.4
- p-value of 0.027.
- This indicates a statistically significant difference, as the p-value is less than the significance level (0.05).
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