An example of an independent t-test is examining whether there's a significant difference in first-year graduate salaries between male and female graduates.
Here's a breakdown:
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Purpose: The independent t-test compares the means of two independent groups to determine if there's a statistically significant difference between them. It helps determine if an intervention or condition has a different effect on one group compared to another.
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Scenario: We want to investigate if gender influences first-year graduate salaries.
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Variables:
- Independent Variable: Gender (categorical variable with two levels: male and female). This is the grouping variable.
- Dependent Variable: First-year graduate salaries (continuous variable). This is the variable we are measuring.
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Hypothesis:
- Null Hypothesis (H0): There is no significant difference in the average first-year graduate salaries between males and females.
- Alternative Hypothesis (H1): There is a significant difference in the average first-year graduate salaries between males and females.
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Data Collection: You would collect salary data from a sample of male and female first-year graduate students.
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Performing the T-Test: Statistical software (like SPSS, R, or Python) is used to conduct the independent t-test. The test calculates a t-statistic and a p-value.
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Interpreting Results:
- The p-value indicates the probability of observing the data (or more extreme data) if the null hypothesis were true.
- If the p-value is less than a pre-determined significance level (alpha, typically 0.05), we reject the null hypothesis and conclude that there is a statistically significant difference in first-year graduate salaries between males and females.
- If the p-value is greater than alpha, we fail to reject the null hypothesis, suggesting there is no statistically significant difference.
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Example Result: Suppose the t-test yields a p-value of 0.03. Since 0.03 < 0.05, we reject the null hypothesis. We conclude there is a statistically significant difference in first-year graduate salaries between male and female graduates. Further analysis (examining the means for each group) would be needed to determine which group earns more.
