Psych 100A – Intro to Stats

1. Psych 100A – Intro to Stats Adi Jaffe, Ph.D.

2. What you need to know • Book– http://www.statstext.com/ • Homework – 6 assignments, 2 points each (lowest dropped) • Exams – 3 Midterms (25 points each), 1 Final (55 points) • Grades – There is a curve (pause for applause) set up only to help, never hurt, your grades.

3. Name 3 important life decisions What you want to do with your life? Who do you want to spend it with? (marriage) How many kids will you have?

4. How do you decide? Why not test the whole country to see: Whose happier? Parents of 1 (K1) Parents of 2 or more (K1+) Impossible (too many people to test) Kids: How Many? 1 2 3 15

5. How can we make a good guess about the whole population without measuring everybody? Answer: measure some of the people and try to generalize that measurement to whole population Statistics – the way to truth

6. Guesses (inferences) we make from samples are not perfect but have ERROR Why? Because we are not measuring everybody so we might be wrong in our guess (inference) Statistics – the way to (mostly) truth

7. Error comes from Variability The error in the subjects we choose is: Between Subjects Variability Statistics – the way to (mostly) truth

8. Other sources of variability? Psychological processes and behavior is performed ina brain that fluctuates “Remembering the Stone” Statistics – the way to (mostly) truth

9. Within subjects variability Depends on what is measured and how often Memory – considerable at times Height – not much Weight - considerable Statistics – the way to (mostly) truth

10. Within subjects variability Depends on task and time Between subjects variability Depends on which subjects chosen Also depends on size of sample Summary of variability

11. Amount of error depends on size of sample. Guess average height of all students in class. Given - 200 students w/average height of 5’5” Statistics – the way to (mostly) truth

12. Sample (n=2) people and average (mean) of scores Pretty easy to get sample mean of 5’10” or 5’2”. Sample (n=100) people and average (mean) of scores. Very difficult to get sample mean of 5’10” or 5’2”. Statistics – the way to (mostly) truth

13. Analyzing data From samples In order to makeguesses (inferences) about characteristics of populations This is called Inferential Statistics So statistics leads to TRUTH by:

14. How do we measure DATA concerning how number of kids affects happiness? Are you happy? How happy are you? (1-10) Give yourself 1 point for each of 100 questions that make up happiness Statistics – the way to truth

15. Take mean of sample (n=100) of parents with K1 & K1+ Make a statement about population. Sample means K1 = 7.7 K1+ = 7.3 Can we generalize this 0.4 difference to whole population? Statistics – the way to truth

16. Can we generalize this 0.4 difference to whole population? Depends on not only on the size of this 0.4, but also how much variability there is in the data Statistics – the way to truth

17. Generalizability of results from sample depend on Mean difference Variability Most likely true in population if High mean difference in sample Low variability in sample Statistics – the way to truth

18. Inferential statistics are always Guesses You can never be 100% sure Statistics – the way to truth

19. Discover “Truth”? Never absolute “proof”, just Evidence supporting likelihood Critical thinking – no lemmings allowed Understand research literature Why Statistics

20. Due to ignorance about the true nature of things P(X) = Number of “X” outcomes ---------------------------------- Number of total outcomes What is Probability

21. Flip a coin P(H) = Number of “H” outcomes (1) ---------------------------------- = 1/2 Number of total outcomes (2) What is Probability

22. Number of outcomes depends on observer’s knowledge of the world (NOT the world itself) With perfect knowledge of all forces acting upon a coin flipped, number of total outcomes changes P(H) = Number of “H” outcomes (1) ---------------------------------- = 1 Number of total outcomes (1) What is Probability

23. 3 doors available (car is behind 1 of them) You choose a door at random (Example 2) Monty Hall Problem

24. Monty Knows where the car is and opens another door (example 1) and shows you no car behind it Gives you an opportunity to switch to the other door (example 3) Should you switch? Monty Hall Problem

25. YD = Your chosen door P(YD) = Number of “Car” outcomes (1) -------------------------------------- = 1/3 Number of total outcomes (3) Your Door Probability

26. OD = Any of the other doors P(OD) = Number of “Car” outcomes (1) -------------------------------------- = 1/3 Number of total outcomes (3) Other Door Probability

27. P(YD) = 1/3 --- No change? Why? Because Monty KNOWS where the car is and can always reveal an empty door More precisely – your total outcomes do not change. Total possible outcomes (You chose door #2) 1– you chose correctly (2) 2– you chose incorrectly (Car is #1) and Monty reveals 3 3– you chose incorrectly (Car is #3) and Monty reveals 1 Your Door Probability After Revealed Door

28. RD = Revealed door P(RD) = Number of “Car” outcomes (0) -------------------------------------- = 0/3 Number of total outcomes (3) Revealed door after revelation

29. SD = Revealed door P(SD) = Number of “Car” outcomes (2) -------------------------------------- = 2/3 Number of total outcomes (3) Because car has to be behind OD, YD or SD P(OD)(0)+P(YD)(1/3)+P(SD)=1 P(SD)=2/3 “Switch” door after revelation

30. If you choose 1 door then P(SD)=1-P(YD) Switch Door Probability After Revealed Door

31. DESCRIPTIVE What data looks like INFERENTIAL Testing Hypothesis (guesses) About populations from samples In order to do inferential statistics we need some background