1. Independent-Sample T-Test Lab16_10.14 Download two files from Canvas: 1. Excel data file: The link->lab files-> October 14th > lab16_data lab16_data 2. Document file: 10.14 1

2. Z Test 1.Double the dataset 2.Creating a second column for just the population mean 1.Creating a second column for just the population mean 1.Delete the entire row if the observation don’t have pairs. 2.Create a new column of the difference between v1 and v2 Single Sample T Paired Sample T Independen t Sample T

3. T-Test: Paired Sample Used when Don’t have any population information, and samples are dependent on each other Prepare the data in Excel Delete the entire row if the observation don’t have pairs. Excel Add- ins T-Test: Paired Two Samples for Means

4. T-Test: Paired SampleT-Test: independent Sample Used when -Don’t have any population information, and samples are dependent on each other -(within-groups design) -every participant is in both samples -Don’t have any population information, and samples are independent of each other - (between-groups design) - each participant is assigned to only one condition Prepare the data in Excel Delete the entire row if the observation don’t have pairs. Excel Add-ins T-Test: Paired Two Samples for Means T-Test: Two Samples for Assuming Equal Variance

5. The scenario_1 ( Math small sample) Ling’s high school math teacher wanted to know how female students in the school could perform differently compared to males students. She administered a math test among 9 randomly selected students (4 females vs. 5 males).  Independent variables: female: 1. Female, 2. Male  Population 1.Math scores for female students 2.Math scores for male students  Assumptions 1.Dependent variable, 2. normally distribution, 3. randomly selection

6.  NH: On average, math achievements do not differ between female and male students.  RH: on average, there are disparities between boys and girls in math achievements.

7. Females o N = 4, M = 82.25, SD =17.02 Males o N = 5, M = 82.6, SD = 17.60

8. Sample size: 9 Mean for difference: -.35 Pooled variance: 301.14 Pooled SD: 17.35 Pooled SE: 11.64

9. t (7) = -.03, t-critical = 2.365 and - 2.365 Fail to reject the null hypothesis. Effect size: (82.25-82.6)/17.35= -.02

10. Confidence level Calculating the confidence interval Lower: -t crit (S mp ) + (difference between mean) Upper: t crit (S mp ) + (difference between mean) t-critical = 2.365 and - 2.365 S mp =11.64 Confidence interval: [-.27.88,.27.18]

11. Interpretations The two sample means are only.02 standard deviation apart. In detail, on average that any females student’s math score will be 0.02 a standard deviation lower than males student’ math score. This is a tiny effect. Interval tells us that if we repeated the study 100 times, 95 of the times the true population difference would fall within the confidence interval, which in this case is between -.27.88 and 27.18. This interval contain zero so it confirms our decision to fail to reject the null hypothesis.

12. The scenario_2 Over the past five years, people relied more and more on their phone. Phone is not only mean calling any more, but also it means social media, reading, healthy recorder, etc. You would like to know if heavy smartphone users sleep less than basic smartphone users. Type 1.I use my smartphone for basic function 2.I use my smartphone for basic function and some application 3.I use my smartphone for all the functions. It’s my life

13. NH: Heavy smartphone users sleep more than, or the same as basic smartphone users. RH: Heavy smartphone users sleep less than basic smartphone users.

14. Independent variable: Basic smartphone user, Heavy smartphone user Level: degree of using smartphone

15. Basic smartphone user o N = 31, M = 7.39, SD = 1.45 Heavy smartphone user o N = 35, M = 7.17, SD = 1.37

16. Sample size:66 Mean for difference:.22 Pooled variance: 1.97 Pooled SD: 1.40 Pooled SE:.35

17. t (64) =.62, t-critical = 1.67 Fail to reject the null hypothesis, Heavy smartphone users is not sleep less than basic smartphone users. Effect size: 0.15

18. Confidence level Confidence interval: [-.48,.91]

19. Interpretations We can expect that on average that any basic smartphone user’s sleeping hour will increase by 0.15 of a standard deviation above heavy smartphone user’s sleeping hour. This is a small effect. Interval tells us that there is a 95% chance that the true population mean for basic smartphone user’s sleeping hour is either.48 lower or.91 higher than the heavy smartphone user. This interval contain zero so it confirms our decision to fail to reject the null hypothesis.