AP Stats Vocab Review

When only those that choose to participate do participate. Those that choose to participate usually feel very strongly one way or the other.

voluntary response bias

to reduce bias- the use of chance or probability during the selection process

Randomization

when participants are put in position that makes them uncomfortable to respond truthfully.

response bias

when certain groups are left out of a survey often due to the difficulty in including them

undercoverage bias

when one group is more heavily studied than any other group.

selection bias

A sample where n individuals are selected from a population in a way that every possible combination of n individuals is equally likely. The best possible method.

Simple Random Sample (SRS)

A sample in which simple random samples are selected from each of several homogeneous subgroups of the population, known as strata.

stratified random sample

A method of sampling in which sample elements are selected from a list or from sequential files, with every nth element being selected after the first element is selected randomly within the first interval

systematic random sampling

A probability sampling technique in which clusters of participants within the population of interest are selected at random, followed by data collection from all individuals in each cluster.

cluster sampling

Stratified random sampling guarantees that each of the strata will be represented. When strata are chosen properly, a stratified random sample will produce better (less variable/more precise) information than an SRS of the same size.

Advantage of using a Stratified Random Sample Over an SRS

A control group gives the researchers a comparison group to be used to evaluate the effectiveness of the treatment(s). (context) (gauge the effect of the treatment compared to no treatment at all)

Why use a control group?

P-arameters: Define them mu, p, or Beta

A-ssumptions and Conditions

N-ame the interval (1,2 prop z; 1, 2 paired sample t; LinReg)

I-nterval (Find it)- on formula sheet

C-onclusion in Context

5-Step Process Confidence Intervals

P-arameters: Define them (mu, , or beta)

H-ypothesis: Ho = ; Ha:

A- ssumptions and Conditions (RILT, RILC, LINER)

N-ame the test (1, 2 prop z; 1, 2 paired sample t; LinReg; x^2 GOF, 2 Way)

T-est Statistic

O-btain p value

M-ake decision (pval < a Reject Ho; pval >= a fail to Reject Ho)

S-tate conclusion in context (If Reject H)

8-Step Process Significance Tests

The systematic favoring of certain outcomes due to flawed sample selection, or question wording, under coverage, nonresponse, etc.

Bias

Exactly 5: P(X = 5) = Binompdf(n, p, 5)

At Most 5: P(X 5) = Binomcdf(n, p, 5)

Less Than 5: P(X < 5) = Binomcdf(n, p, 4)

*At Least 5: P(X 5) = 1-Binomcdf(n, p, 4)

*More Than 5: P(X> 5) =1-Binomcdf(n, p, 5)

*with our Inspire Calc, we can just use LB= & UB=

Remember to define X, n, and p!

For CDF -> LB & UB

Binomial Distribution (Calculator Usage)

Binomial

S) Success/Failure

P) Probability the same

I) Independent Trials

T) Trial a set number

Mr. Bernoulli S(S/F) I(Ind) P(Prob Same) his tea in his GEOMETRIC cup until he saw it was *PISS (Stop at 1st success) and his wide BINOMIAL said *SPIT (TRIAL set #) it out before you go on TRIAL for sipping someone's pee

*SIP = PIS = SPI

Binomial Distribution (Conditions)

Yes, if: A large random sample was taken from the same population was hope to draw conclusions about.

Can we generalize the results to the population of interest?

We do/(do not) have enough evidence to reject H0: μ = ? in favor of Ha: μ≠ ?at the α = 0.05 level because ? falls outside/(inside) the 95% CI.

α = 1 - confidence level

Carrying out a Two-Sided Test from a Confidence Interval

1. Goodness of Fit:

Df= # of categories -1

Expected Counts: sample size times hypothesized proportion in each category.

2. Homogeneity or Association?Independence: df= (# of rows -1)(# of columns -1)

Expected Counts: (row total)(column total)/ (Table total)

Chi-Squared Test df and Expected Counts

Two mutually exclusive events whose union is the sample space.

Ex: Rain/Not Rain,

Draw at least one heart / Draw NO hearts

complementary events

CUSS & BS

(C)enter, (U)nusual features, (S)hape, (S)pread.

Only discuss outliers (unusual features) if there are obviously outliers present. Be sure to address SCS in context!

(B)e (S)pecific: State Context.

If it says "compare" then YOU MUST USE comparison phrases like "is greater than" or "is less than" for Center and Spread

Describe the Distribution OR Compare the Distributions

Association is NOT Causation!

An observed association, no matter how strong, is not evidence of causation. Only a well-designed, controlled experiment can lead to conclusions of cause and effect.

Does ___ CAUSE ___?

1.CRD (Completely Randomized Design) - All experimental units are allocated at random among all treatments

2. RBD (Randomized Block Design) - Experimental units are put into homogeneous blocks. The random assignment of the units to the treatments is carried out separately within each block.

3. Matched Pairs-A form of blocking in which each subject receives both treatments in a random order or the subjects are matched in pairs as closely as possible and one subject in each pair receives each treatment, determined at random.

experimental design

A study is an experiment ONLY if researchers IMPOSE a treatment upon the experimental units.

In an observational study researchers make no attempt to influence the results.

Experiment or Observational Study?

Assuming that the null is true (context) the P-value measures the chance of observing a statistic (or difference in statistics) (context) as large as or larger than the one actually observed.

Explain a P-value

Using a LSRL to predict outside the domain of the explanatory variable.

(Can lead to ridiculous conclusions if the current linear trend does not continue)

extrapolation

1. Sample Size: To increase power, increase sample size.

2. Increase α: A 5% test of significance will have a greater chance of rejecting the null than a 1% test.

3. Consider an alternative that is farther away from μ0: Values of μ that are in Ha, but lie close to the hypothesized value are harder to detect than values of μ that are far from μ0.

Factors that Affect Power

For one mean m=z*(Ơ/√n)

For one proportion: m= z*√(pq/n)

If an estimation of p is not given use 0.5 for p. Solve for n.

Finding the Sample Size (For a given margin of error)

Geometric

P) Probability the same

I) Independent Trials

S) Success/Failure

S) STOP at first success

Mr. Bernoulli S(S/F) I(Ind) P(Prob Same) his tea in his GEOMETRIC cup until he saw it was *PISS (Stop at 1st success) and his wide BINOMIAL said *SPIT (TRIAL set #) it out before you go on TRIAL for sipping someone's pee

*SIP = PIS = SPI

Geometric Distribution (Conditions)

The goal of blocking is to create groups of homogeneous experimental units.

The benefit of blocking is the reduction of the effect of variation within the experimental units. (context)

Goal of Blocking

Benefit of Blocking

Random: Data from a random sample(s) or randomized experiment

Large Sample Size:All expected counts are at least 5