T-test Presentation by Gilbert Bentulan.

T-test presentation

1. T TEST - Statistics By: GILBERT E. BENTULAN, MPA

2. A t-test is a kind of inferential and hypothetical statistical test. It is done under the  null hypothesis .  It is used to compare whether the means of two groups are significantly distinct or not, even when some particular features/characteristics might be related. The T-test helps us estimate the difference between the averages of two sets of data, combined with the certainty that they are from the same population. For example, if we were to take samples of students from two different schools and expect the means and  standard deviation  to be the same, then it is not possible. There should be a slight distinction between the average and standard deviation. 

3. ​A t-test is a statistical tool that helps researchers figure out if two groups of data are different from each other. It's commonly used to compare things like test scores, product performance, or customer preferences. There are two main types of t-tests: the independent samples t-test and the paired samples t-test. The independent samples t-test is used when the two groups being compared are separate and unrelated to each other. The paired samples t-test is used when the two groups being compared are related to each other.

4. Types of T-tests

5. The t-test calculates a t-value, which is then compared to a critical value based on the size of the groups and the level of significance chosen by the researcher. If the calculated t-value is larger than the critical value, it means that there is a statistically significant difference between the two groups. If the calculated t-value is smaller than the critical value, it means that there is not enough evidence to suggest that the groups are different. There are three types of t-tests. 

6. If all of the groups come from one single population (like measuring before and after an experimental treatment), then we perform a  paired t-test . If the groups under consideration come from two different populations (like two different species, or people from two separate cities), then we perform a  two-sample t-test  or  independent t-test ). If there is one group being compared against a standard value (like comparing the acidity of a liquid to a neutral pH of 7), then we perform a  one-sample t-test .

7. T-Test formula

8. The t-test is any statistical hypothesis test in which the test statistic follows a Student’s t-distribution under the null hypothesis. It can be used to determine if two sets of data are significantly different from each other, and is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. T-test uses means and standard deviations of two samples to make a comparison. The formula for T-test is given below:

9. Where, = Mean of first set of values = Mean of second set of values = Standard deviation of first set of values = Standard deviation of second set of values = Total number of values in first set = Total number of values in second set.

10. Where, x  = Values given = Mean n  = Total number of values. The formula for standard deviation is given by:

11. T-Test Solved Examples

12. Question: Solution: Formula for mean: Formula for standard deviation:  Find the t-test value for the following two sets of values: 7, 2, 9, 8 and 1, 2, 3, 4? Number of terms in first set:  = 4 Mean for first set of data: = 6.5

13. Construct the following table for standard deviation:

14. Standard deviation for the first set of data: S 1  = 3.11 Number of terms in second set: n 2  = 4 Mean for second set of data: Standard deviation for second set of data:

15. Construct the following table for standard deviation:

16. Formula for t-test value:

17. n 1 + n 2 – 2 4+4 = 8-2 = 6

18. t comp.= 2.38 < t tab = 2.447

19. “There is no significant difference between the two sets of data.” it means that there is not enough evidence to suggest that the groups are different.

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21. Paired t-test Dependent t-test

22. Also known as dependent sample t-test, within groups t-test, at t-test for correlataed /related samples. - Ginagamit ang paired t-test upang ikumpara ang dalawang grupo o set ng scores na nanggaling sa isang grupo ng tao . - Hal. Religiosity ng mga tao bago at pagkatapos ng spiritual retreat. What is Paired t-test?

23. Kumuha tayo ng 8 na tao na sasali sa isang spiritual retreat. Pinasagutan natin sa kanila ang isang religiosity measure bago ang retreat at pagkatapos nito Research Problem

24. Ito ang mga hypotheses natin: Ho: There is no significant difference in the pretest and posttest religiosity scores. Ha: There is a significant difference in the pretest and posttest religiosity scores. Hypotheses

25. Do you have any questions? Verifications Violent Reactions Thanks!