psych 100a – intro to stats

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