Stats 2

Lower quartile

¼ (n+1)th value

Upper quartile

¾ (n+1)th value

Slope

If points are higher than one I calculated by hand, choose the higher slope; if they’re lower, choose the lower slope

Most efficient point estimator

Has lower variance

Poisson Distribution

! = n to 1

Plug in all values for x

Add results

1 - sum

Wilson Estimator variance

np(1-p)/(n+1)^2

Expected number of good items

Np; p is probability of success

Z-scores and probability

1 - value for that percentage’s z-score; 68 is one standard deviation to left of norm

or

Standard deviation: subtract mean from each value, square each difference, add squared differences, divide by n (population) or n-1 (sample), square root

Calculate standard error: standard deviation/ sqrt n

Z-score formula: Y- mu/standard error

First number of z score is on the left and second number of z-score is on the top

Do 1- number in the box

Bernoulli random variable

1 (times first value) + 0(times second value)

Independent and dependent events

If probability is same = independent; if different = not independent

Standard deviation of mean

Decreases as n increases

t-score

Sample mean - population mean / standard deviation over sqrt of n

Disjoint events

No outcomes in common; P(X and Y) = 0, so subtract

Nondisjoint events

Outcomes in common; P(X and Y) ≠ 0, so add

Binomial distribution equation

n!/k!(n-k)! p^k(1-p)^n-k

Standard error equation for proportions

Sqrt (entire thing) of p-hat(1 - p-hat)/n; p-hat equals number of people in that group/total

Standard error equation for mean

Sx (std. dev.) / sqrt n

Wilson Estimator

Biased but asymptotically unbiased

Central limit theorem

Mean of sample is same as mean of individual events; standard deviation is standard deviation of individual events divided by square root of sample size

Sample variance

Sample standard deviation squared

Standard deviation equation

Subtract mean from each value

Square each difference

Add squared differences

Divide by n (population) or n-1 (sample)

Square root

Stratified sampling

Divides a population into subgroups (strata)

Convenience sampling

Who is available

Cluster sampling

Select clusters and every individual in cluster is included

Systematic sampling

Select using fixed starting point in larger population and then constant interval between samples is used to select samples to include in survey

How to make sample size smaller

Reduce nonresponse rate and stratify population; stratifying population reduces variation within groups, allowing smaller sample size to adequately represent population

Number of affected people is random

(1-p)^(X-1) times p

Adjusting probability

Desired probability times x = original number of that item

Total - x = answer

Percent change

100 times (end - start/start)

Inferential statistics

P-value

Empirical rule

68-95-99 rule

z population

Control group

Clinical significance

Conversion between health care providers and patient and their families

Inference

P-value in relationship to the a priori p-value

Pearson correlation

Bivariate analysis test to determine linear regression