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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
one-sample t-test
H0: The true mean equals µ0.

HA: The true mean does not equal µ0.
df for one-sample t-test
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 real-number 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.

p-hat = 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[B|A]
Law of total probability
Example:

Pr[egg is male] = Pr[host already parasitized] x Pr[egg is male|host already parasitized] + Pr[host not parasitized]Pr[egg is male|host 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 Goodness-of-Fit 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 = (r-1)(c-1)
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)