Module 6-T-tests pdf copy.pdffghdfjfdjdjdj
- 1. MODULE 6:
- 2. t-Tests are used for inferences concerning one or two means.
- 3. • One Sample t-Test • Independent Samples t-Test • Paired Samples t-Test TYPES OF T-TESTS
- 5. ONE SAMPLE T-TEST •Used to test whether the mean of single variable differs from a specified constant.
- 6. ONE SAMPLE T-TEST Example: • A researcher wants to test whether the average IQ score of a group of students differs from 100. • A stats professor wants to determine whether the average grade on Assignment 1 differs significantly from 23 (an A average).
- 7. Step 1: State the Null and Alternate Hypotheses • H₀ = The average grade on Assignment 1 is equal to 23. • Hₐ = The average grade on Assignment 1 is not equal to 23. ONE SAMPLE T-TEST
- 8. Step 2: Input each student’s grade into SPSS. ONE SAMPLE T-TEST
- 9. Step 3: Run the Analysis. a. Analyze Compare Means One Sample T-test Test variable = assign I b. Test value = 23 c. Click OK ONE SAMPLE T-TEST
- 10. N Mean Std. Deviation Std. Error Mean assign 1 15 21.0333 1.54072 .39781 ONE SAMPLE T-TEST ONE SAMPLE STATISTICS
- 11. ONE SAMPLE T-TEST ONE SAMPLE TEST TEST VALUE = 23 t df Sig. (2- tailed) Mean difference 95% Confidence Interval of the Difference Lower Upper Assign 1 -4.944 14 .000 -1.96667 -2.8199 -1.1134
- 12. Step 4: Make a decision regarding the null M = 21.03, SD = 1.54 t (14*) = -4.944 p < .001 ONE SAMPLE T-TEST
- 13. Step 5: Write up your results. ONE SAMPLE T-TEST
- 15. • The independent samples t-test is used to test comparative research questions. • That is, it tests for differences in two group means or compares means for two groups of cases. INDEPENDENT T-TEST
- 16. Step 1: State the Null and Alternate Hypotheses a. Ho = There is no difference between class 1 and class 2 on Assignment 1. b. Ha = There is a difference between class 1 and class 2 on Assignment 1. INDEPENDENT T-TEST
- 17. Step 2: Input each student’s grade into SPSS, along with which class they are in. INDEPENDENT T-TEST Grade Class 20.00 1.00 20.50 1.00 21.00 1.00 20.50 1.00 20.00 1.00 24.50 2.00 23.50 2.00 20.00 2.00 20.00 2.00
- 18. Step 3: Run the Analysis. a. Analyze Compare Means Independent Samples T-test b. Test variable = assign1 c. Grouping variable = class INDEPENDENT T-TEST
- 19. d. Define Groups: Type “1” next to Group 1 e. Type “2” next to Group 2 f. Click Continue g. Click OK INDEPENDENT T-TEST
- 20. Step 4: Make a decision regarding the null Class 1 (M = 21.18, SD = 1.49) Class 2 (M = 21.90, SD = 1.94) INDEPENDENT T-TEST
- 21. Levene’s Test for equal variances • Ho = The variances of the two variables are equal. • Ha = The variances of the two variables are not equal. INDEPENDENT T-TEST Levene's Test for Equality of Variances F Sig. Assign 1- Equal variances assumed Equal variances not assumed 4.519 .044
- 22. Make a decision regarding the null •t (22.5) = -1.086 •p = .289 INDEPENDENT T-TEST
- 23. Step 5: Write up your results. INDEPENDENT T-TEST
- 25. Used to compare the means of two variables for a single group. The procedure computes the differences between values of the two variables for each case and tests whether the average differs from 0. PAIRED SAMPLES T-TEST
- 26. Example: A researcher wanted to know the effects of a reading program. The researcher gave the students a pretest, implemented the reading program, then gave the students a post test. PAIRED SAMPLES T-TEST
- 27. Step 1: State the Null and Alternate Hypotheses Ho = There is no difference in students’ performance between the pretest and the posttest. Ha = Students will perform better on the posttest than on the pretest. PAIRED SAMPLES T-TEST
- 28. REMEMBER: Directional Hypothesis= One-tailed Test Non-Directional Hypothesis= Two- tailed test PAIRED SAMPLES T-TEST
- 29. SPSS (unless given the choice) automatically runs a 2 tailed test, IF you have a directional alternate hypothesis (and a 2-tailed test was run), you MUST divide the p-value by 2 to obtain the correct p-value! PAIRED SAMPLES T-TEST
- 30. Step 2: Set up data PAIRED SAMPLES T-TEST Pre Post 20.00 25.00 21.00 24.00 19.00 23.00 18.00 22.00 20.00 24.00 21.00 25.00
- 31. Step 3: Analyze the Results • Analyze Compare Means Paired Samples t-Test • Paired variables: pre--post PAIRED SAMPLES T-TEST Mean N Std. Deviation Std. Error Mean Pair Pre 1 Post 19.8333 23.8333 6 6 1.16905 1.16905 .47726 .47726 Paired Samples Statistics
- 32. PAIRED SAMPLES T-TEST Paired Sample Test Paired Differences T df Sig. (2- tailed) Mean Std. deviation Std. error mean 95% Confidence Interval of the Difference Lower Upper -15.492 5 .000 Pair 1 Pre-Post -4.00000 .63246 .25820 -4.66372 -4.66372
- 33. Step 4: Make a decision regarding the null • Pretest (M = 19.83, SD = 1.17) • Posttest (M = 23.83, SD = 1.17) • t (5) = -15.49 – p < .001 (two-tailed) .000/2 = 0 p < .001 PAIRED SAMPLES T-TEST
- 34. Step 5: Write up your results. •The null hypothesis stated that there is no difference in students’ performance between the pretest and the posttest. PAIRED SAMPLES T-TEST
- 35. • Suppose: – Ha = Class 1 will score higher on Assignment 3 than Class 2. • Must be based on literature (or prior data/test scores). Directional Hypothesis Example
- 36. • If Ha = Class 1 will score higher on Assignment 3 than Class 2. •SPSS reported a p-value of .08. Directional Hypothesis Example
- 37. SPSS ILLUSTRATIVE EXAMPLE Child No. Age (months) 1 8 2 9 3 10 4 15 5 18 6 17 7 12 8 11 9 7 10 8 11 10 12 11 13 8 14 9 15 12 Data:
- 38. Solution: Step 1: Enter the Data. Enter the Age scores in the first column (VAR00001) of the SPSS Data Editor, beginning with the first score listed above in the first cell of the first column of the Data Editor. SPSS ILLUSTRATIVE EXAMPLE
- 39. Solution: Step 2: Name the Variables. 1. Click the Variable View tab in the lower left corner of the Data Editor. 2. Click VAR00001; the type Age in the highlighted cell and then press Enter. SPSS ILLUSTRATIVE EXAMPLE
- 40. Solution: Step 3: Analyze the data. 1. Click on Analyze; then select Compare Means; then click on One-Sample T-Test… 2. Click the arrow in the middle of the dialog box. SPSS ILLUSTRATIVE EXAMPLE
- 41. 3. In the Test Value: box, replace 0 with 13.0 4. Click OK. SPSS ILLUSTRATIVE EXAMPLE
- 42. Analysis Results: One-sample Statistics: SPSS ILLUSTRATIVE EXAMPLE N Mean Std. Deviation Std. Error Mean Age 15 11.000 3.33809 .86189
- 43. One-sample Test SPSS ILLUSTRATIVE EXAMPLE Test Value = 13.0 95% Confidence Interval of the Difference t df Sig. (2- tailed) Mean Differenc e Lower Upper Age -2.320 14 .036 -2.00000 -3.8486 -.1514
- 44. Data: Before the Campaign After the Campaign (gal/month) (gal/month) Family Group 1 Group 2 A 55 48 B 43 38 C 51 53 D 62 58 E 35 36 F 48 42 G 58 55 H 45 40 I 48 49 J 54 50 K 56 58 SPSS ILLUSTRATIVE EXAMPLE
- 45. Solution: Step 1: Enter the data. 1. Enter scores of Group 1 in the first column (VAR00001) of the Data Editor, beginning with the first Group 1 score the top cell of the first column. SPSS ILLUSTRATIVE EXAMPLE
- 46. 2. Enter the scores of Group 2 in the second column (VAR00002) of the Data Editor, beginning with the first Group 2 score in the top cell of the second column. SPSS ILLUSTRATIVE EXAMPLE
- 47. Solution: Step 2: Name the Variables. 1. Click the Variable View tab in the lower left corner of the Data Editor. 2. Click VAR00001 with Before_C in the highlighted cell and then press Enter. SPSS ILLUSTRATIVE EXAMPLE
- 48. SPSS ILLUSTRATIVE EXAMPLE 3. Replace VAR00002 with After_C and then press Enter.
- 49. Solution: Step 3: Analyze the data. 1. Click Analyze; then select Compare Means; then click Paired-Samples T-Test… SPSS ILLUSTRATIVE EXAMPLE
- 50. 2. Click the arrow in the middle of the dialog box. 3. Click After_C; then click the arrow in the middle of the dialog box. 4. Click OK. SPSS ILLUSTRATIVE EXAMPLE
- 51. Analysis Results SPSS ILLUSTRATIVE EXAMPLE T Df Sig. (2- tailed) Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference Lower Upper Pair 1 Before_C – After_C 2. 91667 3. 47611 1.00347 .70805 5.12528 2.907 11 .014 Paired Samples Test
- 52. SUMMARY