psych 100a – intro to stats
DESCRIPTION
Psych 100A – Intro to Stats. Adi Jaffe, Ph.D. 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) - PowerPoint PPT PresentationTRANSCRIPT
Adi Jaffe, Ph.D.
Psych 100A – Intro to Stats
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.
What you need to know
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?
Kids: How Many?
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)
1 2 3 15
Statistics – the way to truth
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 (mostly) truth
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
Error comes from Variability
The error in the subjects we choose is:Between Subjects Variability
Statistics – the way to (mostly) truth
Other sources of variability?
Psychological processes and behavior is performed in a brain that fluctuates
“Remembering the Stone”
Statistics – the way to (mostly) truth
Within subjects variability
Depends on what is measured and how often
Memory – considerable at timesHeight – not muchWeight - considerable
Summary of variability
Within subjects variabilityDepends on task and time
Between subjects variabilityDepends on which subjects
chosenAlso depends on size of sample
Statistics – the way to (mostly) truth
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
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”.
So statistics leads to TRUTH by:
Analyzing data From samples In order to make guesses (inferences) about characteristics of populations
This is called Inferential Statistics
Statistics – the way to truth
How do we measure DATA concerning how number of kids affects happiness?
1) Are you happy?2) How happy are you? (1-10)3) Give yourself 1 point for each of 100
questions that make up happiness
Statistics – the way to truthTake 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
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
Generalizability of results from sample depend on
Mean differenceVariability
Most likely true in population if High mean difference in sample Low variability in sample
Statistics – the way to truth
Inferential statistics are always Guesses
You can never be 100% sure
Why StatisticsDiscover “Truth”?
Never absolute “proof”, just Evidence supporting likelihoodCritical thinking – no lemmings allowed
Understand research literature
What is ProbabilityDue to ignorance about the true nature of things
P(X) = Number of “X” outcomes ---------------------------------- Number of total outcomes
What is ProbabilityFlip a coin
P(H) = Number of “H” outcomes (1) ---------------------------------- =
1/2 Number of total outcomes (2)
What is ProbabilityNumber 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)
Monty Hall Problem3 doors available (car is behind 1 of them)
You choose a door at random (Example 2)
Monty Hall ProblemMonty 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?
Your Door Probability YD = Your chosen door
P(YD) = Number of “Car” outcomes (1)
-------------------------------------- = 1/3
Number of total outcomes (3)
Other Door Probability OD = Any of the other doors
P(OD) = Number of “Car” outcomes (1)
-------------------------------------- = 1/3
Number of total outcomes (3)
Your Door Probability After Revealed DoorP(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
Revealed door after revelation
RD = Revealed door
P(RD) = Number of “Car” outcomes (0)
-------------------------------------- = 0/3
Number of total outcomes (3)
“Switch” door after revelationSD = Revealed doorP(SD) = Number of “Car” outcomes (2)
-------------------------------------- = 2/3 Number of total outcomes (3)
Because car has to be behind OD, YD or SDP(OD)(0)+P(YD)(1/3)+P(SD)=1P(SD)=2/3
Switch Door Probability After Revealed Door
If you choose 1 door thenP(SD)=1-P(YD)
In order to do inferential statistics we need some background
DESCRIPTIVE What data looks like
INFERENTIAL Testing Hypothesis (guesses) About
populations from samples