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48 Cards in this Set
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compare the mean of a single sample with the population mean proposed in a null hypothesis

onesample ttest

H0: The true mean equals µ0.
HA: The true mean does not equal µ0. 
df for onesample ttest

df = number of independent data points  1


µ

Population Parameter − a quantity describing a population (truth)


Precision

the spread of estimates resulting from sampling error.


Bias

systematic discrepancy between estimates and the true population characteristics.


Random sample

each member of a population has an equal and independent chance of being selected.


the different categories have no inherent order

Nominal Categorical


variables that can be ordered, despite lacking magnitude on the numerical scale.

Categorical Ordinal


can take on any realnumber value within some range

Numerical Continuous


numerical data with indivisible units

Numerical Discrete


Experimental study

the researcher assigns different treatment groups or values of an explanatory variable randomly to the individual units of study.


Observational study

the assignment of treatments is not made by the researcher.


graph categorical data

Bar graph


graph numerical data

Histogram
Cumulative frequency distribution 

graph two categorical variables

Grouped bar graph
Mosaic plot 

graph one numerical variable and one categorical variable

Grouped histogram
Cumulative frequency distribution Line plot (ordinal categories only) 

First quartile

the middle value (median) of the measurements lying below the median.


Second quartile

the median


Third quartile

the middle value (median) of the measurements larger than the median.


Extreme values

those lying farther from the box edge than 1.5 times the interquartile range; displayed by dots.


Proportion

most important descriptive statistic for a categorical variable.
phat = number in a category/n 

95% confidence interval for the mean

We are 95% confident that the population mean falls between ____ and ____.


2SE Rule of Thumb

A rough approximation to the 95% confidence interval for a mean can be found from the sample mean plus and minus two standard errors.


Addition rule

if two events A and B are mutually exclusive, then Pr[A or B] = Pr[A] + Pr[B]


Generalized addition rule

works for both mutually exclusive and not mutually exclusive events.Pr[A or B] = Pr[A] + Pr[B]  Pr[A and B]


Multiplication rule

if two events A and B are independent, then Pr[A and B] = Pr[A] x Pr[B]


General multiplication rule

finds the probability that both of two events occur, even if the two are dependent.
Pr[A and B] = Pr[A] Pr[BA] 

Law of total probability


Example:
Pr[egg is male] = Pr[host already parasitized] x Pr[egg is malehost already parasitized] + Pr[host not parasitized]Pr[egg is malehost not parasitized] = (0.2 x 0.9) + (0.80 x 0.05) = 0.22 
Baye's theorem



Type I error

rejecting a true null hypothesis


Type II error

failing to reject a false null hypothesis


binomial distribution assumptions

The number of trials (n) is fixed. Separate trials are independent. The probability of success (p) is the same in every trial.


n choose X



test whether a population proportion (p) matches a null expectation(p0) for the proportion.

Binomial test

H0: The relative frequency of successes in the population is p0.
HA: The relative frequency of successes in the population is not p0. 
test statistic for binomial test

observed number of successes


Adjusted Wald Method

used to calculate an approximate confidence interval for a proportion.


measures the discrepancy between an observed frequency distribution and the frequencies expected under a simple random model serving as the null hypothesis.

X2 GoodnessofFit Test


Degrees of Freedom for X2

df = (number of categories) − 1 − (number of parameters estimated from the data)


X2 Specific Assumptions

None of the categories should have an expected frequency less than one.
No more than 20% of the categories should have expected frequencies less than five. 

probability of getting X successes in a block of time or space, when successes happen independently of each other and occur with equal probability at every point in time or space.

Poisson Distribution


Degrees of Freedom for Poisson

df = number of categories  1  1


variance is greater than the mean

distribution is clumped


variance is less than the mean

distribution is dispersed


estimates and tests for an association between two or more categorical variables.

X2 contingency test

H0: categorical variable 1 and 2 are independent.
HA: categorical variable 1 and 2 are not independent. 
degrees of freedom for the X2 contingency test

df = (r1)(c1)


Standard normal distribution

a normal distribution with mean 0 and standard deviation 1.


Student's t

the difference between the sample mean and the true mean (Y̅ − µ), divided by the estimated standard error (SEY̅)


coefficient of variation

CV = 100% (standard deviation/mean)
