1. Lab IV: Outline, Part 1  Use of correlated versus independent t- tests – Sample Experiment  Introduction to a web-based stats program: Vassarstats  How to graph Ms and SDs, an example

2. Independent and Correlated (Paired) t-tests The Terrible t’s

3. I pity the fool who doesn’t know when to use correlated vs. independent t-tests!

4. Sample Experiment: t-test Examples  Hypothesis 1: Exposure to bright light will increase gill flare in male Betta splendens.  Hypothesis 2: Male Betta splendens exposed to bright light will have longer gill flare durations than those not exposed to bright light.

5. Sample Experiment: t-test Examples  Subjects: 4 adult male Betta splendens (A, B, C, D) A

6. Exposed fish to each other for 10 min, recorded gill flare B A C D Trial 1

7. Trial 1 Gill Flare (/10 min.) ABCD 100 s120 s90 s115 s = baseline duration of gill flare

8. Exposed Fish A & Fish C to bright light for 5 min. B A C D (no light)

9. Exposed fish to each other for 10 min, recorded gill flare B A C D Trial 2

10. Trial 2 Gill Flare (/10 min.) AB (no light) CD (no light) 200 s130 s185 s125 s = duration of gill flare after light/no light

11. Hypothesis 1: Exposure to bright light will increase gill flare in male Betta splendens. FishNo Light (Before) Light (After) A100 s200 s C90 s185 s *We want to compare each fish’s score on one condition (“before exposure”) to its score on another condition (“after exposure”)

12. Correlated (or Paired) t-test  Scores between conditions are for same subject  i.e., Fish A has a score for both “light” and “no light”, and Fish B has a score for both conditions  Hence, scores are said to be “paired” or “correlated”) FishNo Light (Before) Light (After) A100 s200 s C90 s185 s

13. How to use Vassarstats for t-tests  http://faculty.vassar.edu/lowry/VassarStats.html http://faculty.vassar.edu/lowry/VassarStats.html t-tests and procedures

15. = Number of rows 2

16. Row 1 = Fish A’s scores Row 2 = Fish C’s scores Xa = before light exposure Xb = after light exposure

19. Because our hypothesis was unidirectional (meaning we predicted change in a single, specific direction), we can use the one-tailed value.

20. Now just copy and paste

21. How to Report Results: Examples  “Exposure to bright light significantly increases gill flare duration in male Betta splendens (t = -39, df = 1, p <.05).” Must also include Ms and SDs in a table or graph.  “Gill flare duration after light exposure (M = 192.5, SD = 10.61) was significantly greater than before light exposure (M = 92.5, SD = 7.07); t(1) = -39, p <.05.”

22. Hypothesis 2: Male Betta splendens exposed to bright light will have longer gill flare durations than those not exposed to bright light. SubjectLightSubjectNo Light A200 sB130 s C185 sD125 s *Across conditions, we are comparing the scores of two different fish; hence, the scores are independent of each other

23. Independent t-test  The scores between the two conditions are from different subjects, which makes them independent  The scores in the “Light” condition are not correlated with scores in the “no light” condition SubjectLightSubjectNo Light A200 sB130 s C185 sD125 s

25. How many scores are in each column? (If unequal, pick larger.) 2

26. Xa = Light Xb = No Light

28. How to Report Results: Examples  “Male Betta splendens that were exposed to bright light (M = 192.5, SD = 10.61) flared their gills for longer durations than those not exposed to bright light (M = 127.5, SD = 3.54); t(2) = 8.22, p <.05.”  Or, can give Ms and SDs in a table or graph.

29. How to graph Ms and SDs for Duck Lab

30. Mean for C1 Mean for C2 SD for C1 SD for C2 HINT: The columns correspond to those used for your t-test…