STATS EXAM

Frequency table

number of individuals with each value

relative frequency table

proportion of each individuals value

What method should you use when asked to describe the shape of a graph?

SOCS(shape, outliers, center, spread)

How to find the fence of the data in which any value outside of the fence is an outlier in the box plot?

IQR = Q3-Q1 Q3 = median of second half Q1 = median of first half IQR(1.5) = fence on both sides(add/subtract from Q1 and Q3)

What is the equation for a z score?

Value - mean/Standard deviation

Do you use the symbol for sample mean or population mean when calculating z-score?

Population mean

In an approximately normal distribution, how much of the data is within 1 standard deviation from the mean?

68%

In an approximately normal distribution, how much of the data is within 2 standard deviations from the mean?

95%

In an approximately normal distribution, how much of the data is within 3 standard deviations of the mean?

99.7%

Explanatory Variable

may help predict/explain changes in response variable

Response variable

measures outcome of study

-1<r<1 description

the closer r value is to -1 or 1, the higher the association is(both variables have to be quantitative

Equation for least squares regression line and meaning

y = a + bx —> y=mean b= r(Sy/Sx) x=mean a— SOLVE FOR

r² meaning

measures proportion of variation in response variable accounted for by explanatory value

s meaning

size of typical residual

What would you do when asked to describe the shape of a scatter plot?

Direction, form(linear or non-linear), strength, outliers

How would the LSRL of the graph be affected if a point was added higher vertically than the other points?

The y-intercept would increase

How would the LSRL be affected if a point was added far away from the others but aligned with the line?

r would be closer to one and r² would increase, s would decrease

How would the LSRL be affected if a point was added far away and farther down than the other points?

the y-intercept would increase

How to take a SRS?

1. # everyone

2. Randomize them

3. Collect data

How to take a stratified random sample?

Split the population into strata of alike characteristics, take SRS of each strata

How to take a systematic random sample?

Line up subjects, random start, count every nth subject

How to take a cluster random sample?

Divide a population into clusters and select random clusters to collect data from entire cluster(eg. cliuster each house into its own neighborhood, select five neighborhoods and take data from all houses in those neighborhoods)

What is the problem with question wording?

leads to bias

How to do a randomized block design?

Block subjects together by shared traits to test multiple treatments

How to do a matched pairs design?

Pair people off into two and test different treatments on each

Difference between randomized block design and stratified random sample?

stratifies random sample is an observational survey while randomized block design gives treatments in an expiriment

What is the law of large numbers?

The larger sample size leads to a smaller deviation or variability of data

Conditional probability

P(AIB) = (PA and B)/P(B) P(A)= new event P(B)= given event

Conditional probability if independent

P(AIB) = P(A)

General multiplication rule

P(A and B) = P(A) * P(BIA)

General addition rule:

P(A or B) = P(A) + P(B) - P(A and B)

Discrete random variable

takes a countable set of values with gaps between

What is another word for expected value?

Mean

How to find the expected value in a data set?

x1(P(x)) + x2(P(x))…..

median

smallest value for which cumulative probability reaches or exceeds 0.5

Conditions for a confidence interval for proportion

1. random

2. Large counts - np>10, n(1-p)>10

3. 10% Rule

Equation for proportion confidence interval

p^ ± z* sqroot(p^ (1-p^)/n)

what is the margin of error equal to in a proportion confidence interval?

z* * SE

How to increase power?

increase sample size, increase confidence level(alpha), lower the standard error

What does it mean to have more power?

less type 2 error → Power = 1- P(type 2 error)

How to find percentile given the subjects position on a graph or data set?

1. IF YOU HAVE MEAN AND SD - find z score - value-mean/SD → look for z-score on table -→ match z score with percent

2. IF YOU ONLY HAVE SCATTER PLOT - Count the persons position from left to right on the graph → divide by total amount → make percentage

How to find the value given the percentile?

1. IF YOU HAVE SD AND MEAN - search for z-score that matches percent given —> plug in z score to z score equation → solve for x

2. IF YOU ONLY HAVE SCATTER PLOT - Multiply percent by total amount(n) —> use number to find position on scatter plot(if you got 60, count sixty dots) → find x value based on position in scatter plot(horizontal axis value based on where the last dot is)

Interpret the z score

The value is ____ standard deviations above/below the mean

Can you always use z scores to find percentiles?

NO, only for approx normal graphs

Interpret percentile

The subject is at a level equal to or below ____% of the population

How to find percentile based on a cumulative relative frequency graph?

y axis - percentile values

x axis - x value

If given x-value, look for its corresponding percentile on the vertical axis and vise versa if given percentile

How to find IQR given a cumulative relative frequency graph?

Q1 is at the 25% mark → look for value on x-axis

Q3 is at the 75% mark → look for value on x-axis

Q3-Q1 = IQR

If a value is multiplied to every value in the data, what variables will be affected? Shape, center, or variability?

The center will increase by the multiplied value, measures of variability will also increase by the multiplied value

When should you say the distribution is “normal” rather than “approximatly normal”?

NEVER, always say appox

Mean and standard deviation of a z-score?

ALWAYS-

mean = 0

SD = 1