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**Summary**

__One-sample T-Test__

1. The one-sample t-test is used to test whether the population mean is significantly different than a hypothesized value.

2. Proc ttest can be used to perform one-sample t-test, paired t-test and two-sample t-tests.

3. The H0 option specifies the hypothesized value from one-sample t-test.

4. The 95% confidence interval is the basis for accepting or rejecting the null hypothesis.

5. If p-value is less than 0.05, you can generally conclude the result being statistically significant.

__One-sided T-Test__

6. A one-sided t-test is used to test whether the population mean is significantly

*larger or smaller*than a hypothesized value.

7. Use the (SIDED=) option to specify for the three different test:

- 2: 2-sided test (default)
- U: Upper 1-sided test
- L: Lower 1-sided test

__Paired T-Test__

8. Paired t-test is used when comparing population means between two

*dependent*variables. It is generally used to compare "before" and "after" results, where observations come in pairs.

9. The paired statement must be added to proc ttest to perform the paired ttest.

__Two-sample T-Test__

10. The two-sample t-test is used to compare population means between two independent populations.

Common applications include:

- Compare the treatment efficacy between the treatment and placebo group
- Compare the effectiveness of a marketing campaign on two groups of customer
- Compare the income inequity between the two gender

11. There are two p-values from the two-sample t-test:

- Pooled Method
- Satterthwaite Method

The Pooled method is used when the two populations have equal variance.

The Satterthwaite method is used when they don't.

Which one to use depends on the equality of variance test that is generated from Proc ttest.

12. The ODS (Output Delivery System) must be used when creating output data sets from Proc ttest.

13. The chi-square test is used when examining the association and difference between two categorical variables.

Applications of chi-square test include:

- Compare the smoking behavior between Male and Female
- Compare education level by different race group
- Compare the voting preference by income level

14. One of the major assumptions for chi-square test is that each cell count has to be at least 5 or above.

The Fisher Exact test is the more accurate test to use if the assumption is not met.

15. The correlation coefficient (r) is used to measure the strength of association between two variables.

The range of r is between -1 to 1. The closer r to 1 or -1, the stronger the correlation between the two variables.

16. Positive r represents positive correlation between the two variables.

When one variable goes up, the other variable tends to go up as well.

17. Negative r represents negative correlation between the two variables.

When one variable goes up, the other variable tends to go down.