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Questions and Answers
What is the purpose of a paired t-test?
What is the purpose of a paired t-test?
To evaluate the mean difference from same subjects before and after a treatment.
What are the null and alternative hypotheses in a paired t-test?
What are the null and alternative hypotheses in a paired t-test?
H0: Physiotherapy did not produce a difference in recovery (ubefore = uafter), H1: Physiotherapy produced a difference in recovery (ubefore ≠uafter).
What does the t-value represent in a paired t-test?
What does the t-value represent in a paired t-test?
The t-value represents the test statistic, which indicates the difference from the mean due to chance for the null hypothesis to be true.
How is the critical t-value determined in a paired t-test?
How is the critical t-value determined in a paired t-test?
What can be concluded if the t-calculated value is greater than the critical t-value in a paired t-test?
What can be concluded if the t-calculated value is greater than the critical t-value in a paired t-test?
What does a small p-value in a paired t-test indicate?
What does a small p-value in a paired t-test indicate?
What is the purpose of a t-test?
What is the purpose of a t-test?
What are the assumptions of a t-test? (Select all that apply)
What are the assumptions of a t-test? (Select all that apply)
For a t-test, the degrees of freedom (df) for one sample is ___ and for two samples is ___.
For a t-test, the degrees of freedom (df) for one sample is ___ and for two samples is ___.
In a t-test, the null hypothesis assumes no relationship exists between two different groups.
In a t-test, the null hypothesis assumes no relationship exists between two different groups.
Match the t-test type with its description:
Match the t-test type with its description:
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Study Notes
Introduction to t-test
- A powerful inferential statistical tool used to compare if there is a significant difference between the means of two groups or samples
- T-distribution is a continuous probability distribution that arises from an estimation of the mean of a normally distributed population using a small sample size and an unknown standard deviation for the population
Assumptions of t-test
- Normality: The data should follow a normal distribution, i.e., a bell-shaped curve
- Independence: The observations within each group should be independent of each other
- Equal variance: When the standard deviations of the samples are approximately equal
t-distribution
- Used to determine statistical significance of the differences between groups
- A t-distribution is a distribution of the t-statistic, a measure of the difference between the sample mean and the unknown population mean
t-test Procedure
- Formulate hypotheses (H0 & H1)
- Choose the appropriate t-test based on study design and assumptions
- Collect and organize data
- Calculate the t-statistic
- Determine the degrees of freedom (df)
- Find the critical value or p-value
- Make a decision: Reject or fail to reject the null hypothesis
Types of t-tests
- 1-sample t-test: Compares the mean of a single sample to a known population mean
- Independent samples t-test (2-sample unpaired t-test): Compares the means of two independent samples
- Paired t-test (2-sample paired t-test): Compares the means of two related samples or matched pairs
Paired t-test
- Used to evaluate the mean difference from the same subjects before and after a treatment
- Accounts for the correlation between the two samples, making it more powerful than an unpaired t-test in certain scenarios
1-sample t-test Example
- Testing if the mean time for a student athletics team 2 km run is significantly different from a known population mean
- Calculating the t-statistic and comparing it to the critical value
2-sample Unpaired t-test Example
- Comparing the means of two milk formulas on the growth of infants
- Calculating the t-statistic and comparing it to the critical value
Paired t-test Example
- Determining if physiotherapy made a difference in recovery at a significance level of 0.05
- Calculating the t-statistic and comparing it to the critical value
Interpreting t-test Results
- If p-value is less than the chosen significance level (typically 0.05), the difference observed in the data is statistically significant
- Considering the effect size and practical significance is crucial
Limitations of t-test
- Sensitivity to sample size
- Normality assumption
- Homogeneity of variance
- Limited to two groups
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