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

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

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!

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.

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

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

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

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

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

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

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”)

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

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

= Number of rows 2

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

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.

Now just copy and paste

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.”

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

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

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

Xa = Light Xb = No Light

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.

How to graph Ms and SDs for Duck Lab

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