T-Test.pdf T-Test.pdf T-Test.pdf T-Test.pdf
- 1. T - Test By: Huda Ahmed
- 2. What is a T-Test? A statistical method used to determine if there is a significant difference between the means of two groups. “It is particularly useful when the sample sizes are small and the population standard deviations are unknown”.
- 3. Types of T-Tests one Sample T- Test Compares the mean of a single sample to a known population mean. Compares the means of two independent groups. Compares means from the same group at different times Independent Samples T-Test Paired Samples T-Test
- 4. Assumptions of T-Tests For a t-test to be valid, certain assumptions must be met: The data should be approximately normally distributed. The samples should be independent (for independent t- tests). Variances in the two groups should be equal (homogeneity of variance), although some versions of the t-test (like Welch's t-test) can handle unequal variances.
- 5. Hypotheses in T-Tests In hypothesis testing using t-tests, two hypotheses are formulated: Null Hypothesis (H0 ): Assumes no difference between the group means. Alternative Hypothesis (Ha): Assumes a difference exist. The outcome of the t-test will either reject or fail to reject the null hypothesis based on the calculated t-value and corresponding p-value.
- 6. 1. One-Sample T-Test Formula: Calculation ot T-Test
- 7. 2. Independent Samples T-Test Formula: Calculation ot T-Test
- 8. 3. Paired Samples T-Test Formula: Calculation ot T-Test
- 9. Read Critical T value Calculate P-value Null hypothesis testing We can use the T-Test in two ways; 1 2
- 11. Critical Values 1 Key Features of the T-Test Table The t-test table lists critical values of the t-statistic, which are used to determine the threshold for rejecting the null hypothesis in hypothesis testing. Critical values vary based on the chosen significance level (commonly 0.05 for a 95% confidence level) and the degrees of freedom (df), which depend on the sample sizes involved in the test.
- 12. Key Features of the T-Test Table Degrees of Freedom (df) 1 Degrees of freedom are typically calculated as the sample size minus one (for one-sample tests) or as the total number of observations across both groups minus two (for independent samples). The left column of the t-table indicates different degrees of freedom, allowing users to find corresponding critical values easily.
- 13. Key Features of the T-Test Table One-Tailed vs. Two-Tailed Tests 1 One-Tailed Test: Used when testing for an effect in one direction (either greater than or less than). Two-Tailed Test: Used when testing for any significant difference, regardless of direction.
- 14. What is P value? The p-value indicates the probability of obtaining results at least as extreme as those observed, given that the null hypothesis (which typically states that there is no effect or no difference) is correct A smaller p-value suggests stronger evidence against the null hypothesis. 1
- 15. Common Thresholds The conventional threshold for significance is often set at 0.05. If the p-value is less than this value, the result is considered statistically significant; if it exceeds 0.05, it suggests insufficient evidence to reject the null hypothesis. So if there is only a five percent chance then we have enough evidence to assume that we reject the null hypothesis. 2
- 16. Thank you