1. Dr. C. Ertuna1 Hypothesis Testing 2 Samples (Chapter - 04/D)

2. Dr. C. Ertuna2 2-Sample Hypothesis Testing Parameters of two samples are different population-I sample-A population-II sample-B Parameters of two samples are not different population-II sample-A sample-B

3. Dr. C. Ertuna3 2-Sample Hypothesis Test for Means To determine whether two populations have the same or different means, one can use 2-Sample Hypothesis for means The test is based upon 3 important assumptions: 1.Sample selected from populations are independent, 2.Each population has normal distribution, 3.Un/Equality of population variances.

4. Dr. C. Ertuna4 2-Sample Hypothesis Test for Means 1.Independence within this setting (hypothesis testing) means that one observation does not affect another observation (pre and post test) 2.If observations are not independent than paired mean test could be used. 3.Independence could have a different meaning in other settings such as regression

5. Dr. C. Ertuna5 2-Sample Hypothesis Test for Means (SPSS) Analyze / Compare Means / Independent Samples T-test / Test Variable (s): Enter Stacked Data Grouping Variable: Enter Grouping variable and Define it To change Confidence Level click on Options

6. Dr. C. Ertuna6 2-Sample Hypothesis Test for Means (SPSS) The output is in the “Independent Samples Test”

7. Dr. C. Ertuna7 If Levene’s test is a 2-sample variance test. If p_value of the test is less than alpha then that means variances of two groups are different. So check the significance level of the t-test for “Equal variances not assumed” 2-Sample Hypothesis Test for Means (SPSS)

8. Dr. C. Ertuna8 No distiction between upper tail or lower tail p_value p_value for 2-tailed test / 2 = p_value for 1-tailed test 2-Sample Hypothesis Test for Means (SPSS)

9. Dr. C. Ertuna9 2-Sample Hypothesis Test for Means (SPSS) If the Hypothesis test is 1-tailed test (upper tail or lower tail; no distinction) Then If 1-tailed p_value is greater than alpha that tells us that there is NO DIFFERENCE between the means of two samples. If 1-tailed p_value is less than alpha that tells us that there is DIFFERENCE between the means of two samples.

10. Dr. C. Ertuna10 2-Sample Hypothesis Test for Means (SPSS) Decision: If there is a difference between the two samples then (obviously) the sample with higher mean value is greater than the other one.

11. Dr. C. Ertuna11 2-Sample Hypothesis Test for Means 1.In 2-Sample mean testSample-1 is the one that comes first in Ha:, 2.In 2-Sample mean test equality of variance is determined by using 2-sample 2-tailed variance test. 3.For 2-Sample mean test use Excel’s Tools / Data Analysis / t-Test Two sample: Un/Equal Variance

12. Dr. C. Ertuna12 Related Samples Related (Paired) samples are samples that selected such that each data value from one sample is matched with a corresponding data value from the second sample. The paired samples are used to control for sources of variation that might otherwise distort the conclusion of a study. Example: Engine oil – mileage relation: Different cars, different drivers.

13. Paired Samples - SPSS Assumption is that both samples are normally distributed. Enter each related sample as separate variable 1.Analyze / Compare Means / Paired Sample T test 2.Bring each variable to the right pane Dr. C. Ertuna13

14. Dr. C. Ertuna14 Paired Samples - SPSS

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17. Paired Mean Test - Excel Dr. C. Ertuna17

18. Dr. C. Ertuna18 Paired Mean Test - Excel

19. Dr. C. Ertuna19 Paired Mean Test - Excel

20. 2-Sample Proportion Test Dr. C. Ertuna20

21. Dr. C. Ertuna21 2-Sample Proportion Test - Excel

22. Dr. C. Ertuna22 2-Sample Proportion Test - Excel

23. Dr. C. Ertuna23 2-Sample Proportion Test - Excel

24. Dr. C. Ertuna24 Next Lesson ANOVA

25. Dr. C. Ertuna25 2 Methods of F-Test The hypothesis testing for variability could be done using one of two methods: 1.Compare p with . for upper tail test: Numerator > Denominator for lower tail test: Numerator < Denominator 2. Compare F Current with F  /tails p = FDIST(F Current, (n 1 -1), (n 2 -2))

26. Dr. C. Ertuna26 2-Sample Variance Test The hypothesis testing for 2-sample variance (or Standard Deviation) could be done as follows: 1.Detemine Sample-1 Sample-1 is the one with largest Standard Deviation 2.State Ha: (and Ho:) which should start with Sample-1 3.Run PhStat for 2-Sample Variance test