PSYCH-STAT-PPT-GR1-1.pptx dsdsdsdsdsdsdsds

psychology

1. Psychological Statistics INTRODUCTION TO T-TESTS GROUP 1

2. What is t Test? A t-test (also known as Student's t-test) is a tool for evaluating the means of one or two populations using hypothesis testing. A t-test may be used to evaluate whether a single group differs from a known value (a one-sample t-test), whether two groups differ from each other (an independent two-sample t-test), or whether there is a significant difference in paired measurements (a paired, or dependent samples t-test).

3. The one sample t test, also referred to as a single sample t test, is a statistical hypothesis test used to determine whether the mean calculated from sample data collected from a single group is different from a designated value specified by the researcher. 3 The t Test for a Single Sample

4. 4 One Sample t Test Assumptions For a valid test, we need data values that are: Independent (values are not related to one another). Continuous. Obtained via a simple random sample from the population. Also, the population is assumed to be  normally distributed .

5. Example: In the population, the average IQ is 100. A team of scientists wants to test a new medication to see if it has either a positive or negative effect on intelligence or no effect at all. A sample of 30 participants who have taken the medication has a mean of 140 with a standard deviation of 20. Did the medication affect intelligence? Alpha = 0.05 5

6. Define Null and Alternative Hypothesis State Alpha Calculate Degress of Freedom State Decision Rule Calculate Test Statistic State Results State Conclusion 6 One Sample t Test

7. Define Null and Alternative Hypothesis Ho ; µ = 100 H1 ; µ ≠ 100 7 One Sample t Test

8. Define Null and Alternative Hypothesis State Alpha α = 0.05 8 One Sample t Test

9. Define Null and Alternative Hypothesis State Alpha Calculate Degress of Freedom N – 1 = 30 – 1 = 29 9 One Sample t Test

10. Define Null and Alternative Hypothesis State Alpha Calculate Degress of Freedom State Decision Rule 10 One Sample t Test

11. Calculate Test Statistic =140   11 One Sample t Test

12. State Results Decision rule: If t is less than -2.0452, reject the null hypothesis. t = 10.96 Reject: H0 12 One Sample t Test

13. State Conclusion Medication significantly affected intelligence, t=10.96,p=   13 One Sample t Test

14. The t-test for dependent means (also called a paired samples t-test or repeated measures t-test) is used when comparing two sets of related measurements, such as:- The same group of people tested twice (e.g., pre-test and post-test).- Two conditions from a within-subjects design (e.g., participants experience both conditions A and B). 14 t-Test for Dependent Means

15. 15 Key Assumptions: Normality: The differences between paired scores should be approximately normally distributed. Dependent Samples: The data consists of paired measurements (e.g., before and after for the same group). 3. Continuous Data: The data should be interval or ratio. 15

16. 16 Formula Formula: The formula for the t-statistic in a dependent means t-test is:

17. 17 Where: - D is the mean difference between the paired scores. - SD is the standard deviation of the differences. - n is the number of paired scores. t-Test for Dependent Means

18. 18 Steps to perform the t-test: Calculate the differences between the paired measurements. 2. Compute the mean of the differences (D). 3. Find the standard deviation of the differences, ( sD ). 4. Plug the values into the formula and calculate the t-statistic. 5. Determine the degrees of freedom, ( df = n - 1), where ( n ) is the number of paired observations. 6. Compare the t-value to the critical value from the t-distribution table (or use the p-value) to determine statistical significance.

19. 19 Example of paired scores for dependent t-test: Imagine a teacher wants to know if a new teaching method improves student performance. She gives a group of 5 students a math test before and after using the new method. In this example: Student Pre-Test Post-Test Difference (Post-Pre) 1 70 75 2 80 85 3 60 70 4 90 95 5 85 80

20. Effect Size Tells you how meaningful the relationship between variables or the difference between group is. It indicates the practical of a research outcome. Effect Size Formula: 20  

21. 21 The Distribution of Difference Between Means difference between sample means from two independent groups.  

22. It’s the difference between the average (means) of two groups. 22 Example: Group 1 has a mean score of 75, and Group 2 has a mean score of 85. The difference is 85 - 75 = 10. What is the Difference Between Means?

23. 23 Sample mean vs Population Mean Sample means are taken from subsets of the population. Example: Comparing the average scores of students from two different schools. It’s the distribution of all possible differences between two sample means. Sampling Distribution of the Difference Between Means

24. 24 Formula for Difference Between Means Formula Difference = Where: = Mean of sample 1  

25. 25 Standard Error of the Difference Formula: SE   Where: , = variances of the two samples = sample sizes  

26. 26 Hypothesis Testing Example Null Hypothesis : No difference between the means Alternative Hypothesis   Example: Group 1: Mean = 100, SD = 10, n = 30 Group 2: Mean = 95, SD = 12, n = 30 Calculate the Difference between means and test for significance.

27. 27 The t-test for independent means compares the difference between two independent sample means to an expectation about the difference in the population. The Independent Samples t Test can only compare the means for two (and only two) groups. It cannot make comparisons among more than two groups. The t-test for independent means requires that there is no overlap between the two groups in the research design. HYPOTHESIS TESTING WITH THE T-TEST FOR INDEPENDENT MEANS

28. The Independent Samples t Test is commonly used to test the following: •Statistical differences between the means of two groups •Statistical differences between the means of two interventions •Statistical differences between the means of two change scores 28

29. Assumptions of the t-Test for Independent Means Data are Numeric Independence of Observation Normality Equal Variances

30. Thank You 30

31. 31 GROUP MEMBERS Alyssa Vellesco Clarisse Urbano Jaslyn Boday Nickie Aman Danica Aguirre Wella Mae Anta Demilyn Yocte