1. PAVLOVIAN PARADIGM unconditional stimulus unconditional response elicits UCR UCS elicits CR CS conditional stimulus conditional response But what does mean?

2. Respondent Contingencies • Standard Procedure • P(UCS|CS) = 1 ; P(UCS|~CS) = 0 • Partial Reinforcement • 0 < P(UCS|CS) < 1 ; P(UCS|~CS) = 0 • Random Control • 0 < P(UCS|CS) = P(UCS|~CS) • Inhibitory CS • 0 < P(UCS|CS) < P(UCS|~CS) Pavlovian Conditioning

3. Contingency Table UCS ~UCS #UCSCS = A # CS = A + B P(UCS|CS) = A / (A+B) CS B A+B A ~CS D C+D C A+C B+D N |AD - BC| (A+B)(C+D)(A+C)(B+D)  = Pavlovian Conditioning

4. Staddon’s Data Pavlovian Conditioning

5. Contingencies and Staddon’s Data SH ~SH = 20/30 = 2/3 = 10/30 = 1/3 = 10/30 = 1/3 = 20/30 = 2/3 P(S) P(~S) P(SH) P(~SH) 10 20 S 10 012 011 10 ~S 10 0 022 021 30 10 20 Pavlovian Conditioning

6. Contingencies and Staddon’s Data If S and SH were independent (“random control”): P (SH|S) = P (SH) or P (SH  S) = P (SH) P(S) By definition: P (SH|S) = P (SH  S) = #(SH and S) P(S) #S = 10/20 = 1/2 But: P (SH) = 10/30 = 1/3 So: P (SH|S) ≠ P (SH). Also, P (SH  S) ≠ P (SH) P(S) 10/30 = 1/3 ≠ (1/3)(2/3) = 2/9 Pavlovian Conditioning

7. = X²1df= │011022 – 012021│ • N (011 + 012)(021 + 022)(011 + 021)(012 +022) Recall X² test for independence in contingency table with observed frequencies 0ij rc i=1 j=1  Where the Eij’s are the Expected Frequencies X²1df = (0ij – Eij) ² Eij  For a 2 x 2 Table X²1df = N │011022 – 012021│² (011 + 012)(021 + 022)(011 + 021)(012 +022) Pavlovian Conditioning

8. For a 2 x 2 Table Χ²1df = N │011022 – 012021│² (011 + 012)(021 + 022)(011 + 021)(012 +022) SH ~SH E11 = (011 + 012)(011 + 021) N E12 = (011 + 012)(012 + 022) N E21 = (021 + 022)(011 + 021) N E22 = (021 + 022)(012 + 022) N S 011 + 012 012 011 021 022 021 + 022 ~S N 012 + 022 011 + 021 Pavlovian Conditioning

9. X1² = (13.33 – 10)² + (10 - 6.67)² 13.33 6.67 + (10 – 6.67)² + (3.33 -0)² 6.67 3.33 = 7.486 ≈ 7.5 X².95 = 3.84 1df  = │(10(0) – (10)(10) │= 100 = 0.5 (20)(10)(20)(10) (20)(10) ² = 0.25 = X1² / 30, so X1² = 7.5 as above. S and Shock are not independent • For Staddon’s Data, the table is: 011 = 10 E11 = 13.33 012 = 10 E12 = 6.67 20 022 = 0 E22 = 3.33 021 = 10 E21 = 6.67 10 30 10 20 Pavlovian Conditioning

10. cs S = Rcs Rcs+ Rcs cs cs S = 0.0 S = 0.5 Pavlovian Conditioning

11. P(UCS|CS) = P(UCS|~CS) = P(UCS~CS) = # (UCS~CS) P(~CS) # ~CS [P(CS) > 0] ~CS E UCSCS UCS~CS ~CS = E – CS = Context P(UCS|CS) = 1- P(~UCS|CS) P(UCS|~CS) = 1- P(~UCS|~CS) ~UCS Pavlovian Conditioning

12. RESCORLA-WAGNER MODEL

13. What are some characteristics of a good model? Variables well-described and manipulatable. Accounts for known results and able to predict non-trivial results of new experiments. Dependent variable(s) predicted in at least relative magnitude and direction. Parsimonious (i.e., minimum assumptions for maximum effectiveness).

14. STEPS IN MODEL BUILDING • IDENTIFICATION: WHAT’S THE QUESTION? • ASSUMPTIONS: WHAT’S IMPORTANT; WHAT’S NOT? • CONSTRUCTION: MATHEMATICAL FORMULATION • ANALYSIS: SOLUTIONS • INTERPRETATION: WHAT DOES IT MEAN? • VALIDATION: DOES IT ACCORD WITH KNOWN DATA? • IMPLEMENTATION: CAN IT PREDICT NEW DATA?

15. PRINCIPAL THEORETICAL VARIABLE: ASSOCIATIVE STRENGTH, V

16. RESCORLA-WAGNER MODEL

17. ASSUMPTIONS 1. When a CS is presented its associative strength, Vcs, may increase (CS+), decrease (CS-), or remain unchanged. 2. The asymptotic strength () of association depends on the magnitude (I) of the UCS:  = f (UCSI). 3. A given UCS can support only a certain level of associative strength, . 4. In a stimulus compound, the total associative strength is the algebraic sum of the associative strength of the components. [ex. T: tone, L: light. VT+L =VT + VL] 5. The change in associative strength, V, on any trial is proportional to the difference between the present associative strength, Vcs, and the asymptotic associative strength, .

19. R-W Accounts for the Following • Acquisition • Extinction • Overshadowing • Blocking • Conditional Inhibition • and more.

20. Contiguity in R-W Model If P(UCS|CS) = P(UCS|~CS), we really have CS = CS + CTX and ~CS = CTX. Then: P(UCS|CS + CTX) = P(UCS|CTX) V (CS + CTX) = VCS + VCTX (R-W axiom) V CS = V (CS +CTX) = VCS + VCTX but: V CTX = V ~CS so: V (CS + CTX) = V CS + V~CS = 0  No significant conditioning occurs to the CS Pavlovian Conditioning