Stats exam 3 Cheat Sheet (DRAFT) by athenamarko

Why is the normal distri­bution important?

1. Many naturally occurring data (e.g., height, weight, etc,) have many distri­butions which are approx­imately normal.
2. Many statis­tical tests covered later use normal distri­but­ions.
3. Many sampling distri­butions approx­imate a normal distri­bution with large sample sizes.

Area under the normal distri­bution

Calculated in percen­tages, the total area under the curve = 100%. Broken up into 8 sections. (0.13, 2.15, 13.9, 34.13, 34.13,­(mean (No

For any score…

If we know how many standard deviations it is away from the mean

What is a standard (or z) Score?

z score is a transf­ormed score that designates how many standard deviation units the corres­ponding raw score is above or below the mean.

Column A

Shows the z score

Column C

Area beyond z

Area under the normal curve based on the number of standard deviations from the mean is...

Converting z scores will...

Standa­rdize any distri­bution without regard to the original mean or SD

What are the two types of questions in infere­ntial statis­tics?

1) Hypothesis testing
2) Parameter estimation

Parameter estimation

We wish to know the magnitude of a population charac­ter­istic, so we test a sample (e.g., how much salary do students who graduate with a psych degree make in Canada?)

Random sample

A sample selected from the population that satisfies the following two condition
1) Each possible sample has an equal chance of being selected
2) Each member of the population has an equal chance of being selected into the sample.

Probab­ility

1) Cannot be negative (between 0-1)
- Probab­ility = 0 (event is certain not to occur)
- Probab­ility = 1 (event is certain to occur
2)Usually expressed as a decimal number but can be written as a fraction (keep 4 decimal places)

A priori

From before

A priori probab­ility

Based on reason without actual observ­ations

What is the a priori probab­ility of flipping a coin and getting a "­hea­d"

p(A) = 0.5

A posteriori probabiity

Based on the actual observ­ations

If we actually flipped a coin 50 times, and got a head 30 times, what is the a posteriori probab­ility of getting a "­hea­d"

p(A) = 0.60

Multip­lic­ation rule

Concerned with determ­ining the probab­ility of joint or successive occurrence of several events

P(A)

Probab­ility of A

P(A and B)

P(A)p(B|A)

Example question: There are two dice. What is the probab­ility of getting a "­3" on the 1st die and a "­4" on the 2nd die in one roll?

Event A: "­3" on the 1st die
-p("3" on the 1st die) = 1/6
Event B: "­4" on the 2nd die
-p("4" on the 2nd die|"3" on the 1st die) = 1/6 {{nl} (1/6)(1/6) = 0.0278

Mutually exclusive events

Two events are mutually exclusive when the occurrence of one precludes the occurrence of the other.
Two events that CANNOT occur together p(A and B) = 0

p(A or B) =

p(A) +p(B) - p(A and B)

Exhaustive sets of events

A set of events is exhaustive if the set includes all of the possible events (rolling a die, the set of events of getting a 1, 2, 3, 4, 5, or 6 is exhaus­tive; flipping a coin, the set of events of getting a head or tail is exhaus­tive)

Example (M(*)&A(+)): If you have a regular deck of playing cards, what is the probab­ility that at least one of the next three cards will be red (w/o replac­ement)?

p(at least 1 out of 3 red) = 1-p(all black)
=1-(26/52)(25/51)(24/50)
=1-0.117647
=0.8824

Why can't we just look at the data?

The varaib­ility in data, it's very hard to "­see­" the difference between groups or conditions (could have happened due to chance). This is why we need to use infere­ntial stats to test hypoth­eses, to determine whether there's a real difference between groups or conditions that is due to IV (or subject variable).

Example hypotheses

- Fan distra­ctions affects free throw accuracy (H

1

)
- Fan distra­ctions does not affect free throw accuracy (H

0

)
-Free throws are more difficult to make with distra­ctions (H

1

)
-Free throws are not more difficult ot make with distra­cti­ons(H

0

)
- Free throws are easier to make with distra­ctions (H

1

)
- Free throws ar enot easier to make with distra­ctions (H

0

)

Altern­ative hypothesis

- Hypoth­esizes that ther will be difference between groups / conditions and hat this dfference is due to the indepe­ndent variable/ subject variable

Decision rule

- there must be criteria by which we will decide3 if the indepe­ndent variable really did have an effect (we can use probab­ility)

If the probab­iliyt is not that low

We will not reject H

0

a

Type 1 error

Decide to reject eh null hypothesis but the null is actually true