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
Independent and Correlated (Paired) t-tests

3. I pity the fool who doesn’t know when to use correlated vs
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 flareB A C D
Trial 1

7. Trial 1 Gill Flare (/10 min.)B C D
100 s
120 s
90 s
115 s
= baseline duration of gill flare

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

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

10. Trial 2 Gill Flare (/10 min.)B
(no light) C D
200 s
130 s
185 s
125 s
= duration of gill flare after light/no light

11. Hypothesis 1: Exposure to bright light will increase gill flare in male Betta splendens.
Fish
No Light (Before)
Light (After) A
100 s
200 s C
90 s
185 s
To evaluate this hypothesis, we want to look at the data for the fish that experienced both light and no-light conditions, that is, Fish A, and C. Note that we want to compare…
*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”)
Fish
No Light (Before)
Light (After) A
100 s
200 s C
90 s
185 s

13. How to use Vassarstats for t-tests
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

18. Because our hypothesis was unidirectional (meaning we predicted change in a single, specific direction), we can use the one-tailed value.
Our hypothesis was that bright light would increase gill flare, thus we predicted that our “after light” scores to be higher than our “before light” scores. Had we only hypothesized that the gill flare under light and no light conditions would differ, we would have to allow for the possibility that bright light could either increase or decrease gill flare. If we had not predicted the direction of the change, we would have to use the two-tailed value.

19. Now just copy and paste

20. 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.”

21. Hypothesis 2: Male Betta splendens exposed to bright light will have longer gill flare durations than those not exposed to bright light.
Subject
Light
No Light A
200 s B
130 s C
185 s D
125 s
To evaluate this hypothesis, we need to compare the data for the fish that were exposed to light with the data for the fish that were not exposed to light, so we will use the data from Trial 2 only. Note that, across conditions…
*Across conditions, we are comparing the scores of two different fish; hence, the scores are independent of each other

22. 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
Subject
Light
No Light A
200 s B
130 s C
185 s D
125 s

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

25. Xa = Light
Xb = No Light

27. 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.

28. How to graph Ms and SDs for Duck Lab

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