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### Assumptions for the t-test:

**Normality**
- The data for each group should be approximately normally distributed.
- This assumption can be checked using various methods, such as histograms, Q-Q plots, or statistical tests like the Shapiro-Wilk test.

**Homogeneity of Variances**
- The variances of the two groups should be equal.
- This is especially important for the independent two-sample t-test.
- Can be checked using the Levene’s test.

**Independent Observations**
- The observations (or data points) in each group should be independent of each other.
- This typically means that one observation in a group should not influence another observation.

**Random Sampling**
- Data should come from a random sample, ensuring that every individual has an equal chance of being included in the study.

**Scale of Measurement**
- The t-test is appropriate for continuous (interval or ratio) data.
- The dependent variable should be continuous, while the independent variable should be categorical with two levels/groups.

**Absence of Outliers**
- Outliers can significantly affect the mean and standard deviation, which in turn can affect the t-test results.
- It’s important to check for outliers and decide how to handle them before conducting the t-test.