You are about to take the AP Stats test and…

MAKE SURE YOU HAVE…

MULTIPLE PENCILS… 1 OR 2 CALCULATORS… EXTRA BATTERIES…

EAT A FULL MEAL BEFOREHAND!

Statistics is about…

Models A model is an attempt to represent reality…

…but we know it’s not perfect.

Models

“All models are wrong, but some are useful.”

(George Box)

Models

Common models: Regression lines Simulations

AND MORE…

Avoid confusion …• known vs unknowable• samples vs populations• statistics vs parameters

THINK about Models

Probability Models: Normal Model Geometric & Binomial

t - Models Chi-Square Models

THINK about Models

The calculator…

… can’t TELL what it

all means.YOU have to do that, too!

Remember …

Answers are not numbers,

answers are sentences in

context.

The 68, 95, 99.7 Rule

Only works for Normal Distributions.

When describing Univariate Data (1 variable)

Shape! Center! Spread!

Range is…

A way to measure the “spread” of data

It is a single number, such as 40. (not 30-70)

Variance, standard deviation, IQR are other ways to measure the “spread” of data.

Mean or Median is…

A way to measure the location of data (center)

They are a single number

Adding a constant to every value in a data set…

Changes the central location of the data (such as mean or median)

Does NOT change the spread of the data (such as standard deviation, variance, IQR)

Multiplying by a constant to every value in a data set…

Changes the central location of the data (such as the mean or the median)

DOES CHANGE the spread of the data (such as standard deviation, variance, IQR)

When describing bivariate quantitative data… Form! Strength! Direction!

This is when describing a scatterplot, linear regression, or the like...

A residual is… The vertical distance from point to

LSRL It is calculated as

Observed Y – Predicted Y

All points ABOVE the LSRL have positive residuals!

All points BELOW the LSRL have negative residuals!

An Exponential Model is best fit when…

Log Y vs X is linear Variable is in the exponent

xy ab

A Power Model is best fit when…

Log Y vs. Log X is linear Variable is in the base

by ax

Interpreting Slope…

“For every [unit] increase in [x], we expect an [? unit] increase in [y]

Interpreting Y Intercept

When [x] is 0 [units], we expect [y] to be [? units]

You will see the word “COMPARE” at least once…

So COMPARE!!! Don’t list attributes… use

comparative words!

Lurking variable (Common Response)

x y

z

Confounding Variable

x y

z

“Correlation does not imply causation!”

Be careful with the word “cause”. The only way to prove causation is a properly designed experiment.

R is called the… “Correlation Coefficient”

Or just…. “Correlation”

It measure the strength and direction of a linear relationship (no context for nonlinear relationships)

R-squared is called…

“Coefficient of Determination”

And is interpreted as “the % of the variation in [y] that is explained by [x]”

It can also be thought of as sum of explained error/sum of total error

If r squared is .64

Then r = .8 OR r= -.8

Figure it out by looking at the direction of the scatterplot!

Simpson’s Paradox is…

When combining the data from 2 groups results in a reversal of direction of the conclusion.

Placebo Effect

Giving a person a sugar pill and telling them it will make them feel better

Double Blind

Neither the subjects nor the experimenter know which treatment the subject is receiving

Disjoint

Both cant occur simultaneously

Mutually Exclusive

One or the other must occur

Checks for Independence

P(A and B)=p(A)p(B)

Or

P(B)=p(B|A)

Rules for Means and Variances of Discrete Random Variables

P420

a bx xa b 2 2 2a bx xb

Central Limit Theorem

As sample size increases, the shape of the sampling distribution

gets more and more normal, regardless of the shape of the parent distribution.

The center (mean) of the sampling distributions stays exactly the same.

The variability in the sampling distribution (standard deviation) decreases.

Law of Large Numbers

As sample size increases, the mean, Xbar, tends to get closer and closer to u.

DON’T FORGET TO…

Use the proper NOTATION.

P(x>2)=….

Notation is communication

a, b, n, p, q, r, s, t, x, y, z, E, H, P, π, , all have special meanings…

…and “hats” or “bars” change those meanings.

You are not free to substitute another letter even though it looks like algebra.

4 Requirements of a Binomial Setting are…

Independence Success/Failure for each trial Equal probability of success for

each trial Fixed number of trials

The only difference between binomial setting and geometric setting is…

Geometric does not have a fixed number of trials, it is waiting for the first success…

The mean of a geometric distribution is…

1/p

(this is not on your formula sheet, but you should know it)

To calculate a geometric probability, use a tree diagram

Undercoverage Bias

When some groups are systematically left out of the sampling process (like people without phones in a phone survey)

Voluntary Response Bias

When a sample consists of volunteers (like calling in to a radio survey)

Nonresponse Bias

When an individual cant be contacted or refuses to cooperate

P of your “Phantoms” is “Define the parameter”. So Define your parameter (either p or u) as specifically as possible.

The grader of your test…

Doesn’t know what “PANIC” and “PHANTOMS” are… they are simply for your own organization.

Your hypotheses must…

Be about the PARAMETERS. Why make a hypothesis about the

sample? (X bar and p hat shouldn’t ever be

in the Hypotheses).

When you do inference…

You hypothesize about what the value of a single number is (that number is usually u, or p).

What IS an Assumption?

an underlying hypothesis about the situation required by the mathematical justification for the statistical method.

WE WILL PROBABLY NEVER KNOW

IF AN ASSUMPTION IS TRUE.

Draw the graph if you are given the data set! An outlier/skewness can dramatically affect your Test Statistic.

Your sample should be an SRS of the POPULATION OF INTEREST.

Be specific.

If the sample is randomly selected and unbiased, then we can generalize the findings to the population

We rarely know the population standard deviation, so the only time you do z-tests will probably be when using proportions.

Don’t Forget…

Degrees of Freedom! -for all t-statistics and Chi-Square statistics. ***(r-1)(c-1) for Chi-Square Tests for

Homogeneity and Chi-Square Tests for Independence

***n-2 for LinReg T Test *** n-1 for all others.

Can you find and interpret critical values?

1-sided or 2-sided? Draw a picture! Degrees of freedom?

Critical values interpret to be the number of std. devs. away from the mean, usually in order to reject a hypothesis

Your Calculations in PHANTOMS should…

Include equation and values you are plugging in…

Normal curves will earn you a PLUS (but don’t draw a normal curve for Chi-Square Distributions, they are ALWAYS skewed.

Interpretation of Confidence Interval:

“We are 95% confident that _____ falls within the interval _________”

Interpretation of Confidence Level

“If we repeated this sampling and calculation process many times, 95% of all calculated intervals will correctly contain ______.”

Interpretation of the P-Value

“A p-value of ______ indicates that if Ho is true, then we would obtain a sample statistics as extreme as ours less than (more than) ____% of the time due to random chance alone.”

The communication rubric:

Your conclusion should be …

Clear,Concise,Complete, andin Context!

You will be given an essay question that asks you to describe an experiment… Be thorough!

Your answer must include Repetition, Randomization, Control, and Comparison.

Don’t abbreviate “R.A.” Spell it out! – They will assume you don’t know what you are doing, but you do!

SAY WHAT YOU ARE COMPARING!

When describing an experiment or simulation…

Simply stating one of these things is not enough… “use a random number generator…” “use a table or random digit table…” “use a coin to randomly select…”

YOU MUST DESCRIBE YOUR PROCEDURE IN DETAIL

Describing random assignment using a RDT…

Label subjects to digits Peel digits Assign subjects to treatments

If you are asked to simulate something…

Include a stopping rule as well

Type 1 error is…

The probability of incorrectly rejecting the Null Hypothesis.

Type 2 error is…

The probability of incorrectly failing to reject the null hypothesis.

1- Power

How will each of these affect the power of a test?…

Using a larger alpha? Using a larger sample size? Using a smaller sigma? Choosing an alternative that is further

from the population mean? Increasing Type 1 error? Decreasing Type 2 error? ……They all will Increase the Power!!!

Medians…

Are resistant! Means are not!

IQR…

Is a measure of spread!

The 1.5 IQR Rule…

Adds or subtracts from Q1 and Q3!!! Not the median…

A Five Number Summary is

Min, Q1, Med, Q3, Max 0%, 25%, 50%, 75%, 100%

Variance is

Std. dev squared!

Show all your work, even for little calculations!

AND WRITE NEATLY! Even show your work if the answer

is 2+2 = 4

If you erase on your scantron sheet, erase thoroughly!

Please use…

All 90 minutes of each section…

It cant hurt you and you cant go anywhere…

Once you think you are done, go back and try to find at least 1 problem to change/correct/improve.

The Investigative Task…

Will be difficult- but it will be difficult for everybody.

Even if you can get a 2 on it, you are ahead of the game.

If you don’t know an answer to part A of a question…

Say “Suppose Part A is 3.6”… just so you can go on to part B…

You can still get full credit for Part B if Part A is incorrect.

Every answer…

Should be in context

If you want to review one more thing….

Review mean and variance of a discrete random variable (last pages in your review packet)

The answers and explanations are included in the packet.

And the most important thing I can tell you…

READ CAREFULLY and ANSWER THE QUESTION!

THEY LIKE TO ASK MULTIPLE QUESTIONS AT ONCE… SO ANSWER COMPLETELY!