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48 Cards in this Set
- Front
- Back
- 3rd side (hint)
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compare the mean of a single sample with the population mean proposed in a null hypothesis
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one-sample t-test
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H0: The true mean equals µ0.
HA: The true mean does not equal µ0. |
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df for one-sample t-test
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df = number of independent data points - 1
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µ
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Population Parameter − a quantity describing a population (truth)
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Precision
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the spread of estimates resulting from sampling error.
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Bias
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systematic discrepancy between estimates and the true population characteristics.
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Random sample
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each member of a population has an equal and independent chance of being selected.
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the different categories have no inherent order
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Nominal Categorical
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variables that can be ordered, despite lacking magnitude on the numerical scale.
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Categorical Ordinal
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can take on any real-number value within some range
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Numerical Continuous
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numerical data with indivisible units
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Numerical Discrete
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Experimental study
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the researcher assigns different treatment groups or values of an explanatory variable randomly to the individual units of study.
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Observational study
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the assignment of treatments is not made by the researcher.
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graph categorical data
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Bar graph
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graph numerical data
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Histogram
Cumulative frequency distribution |
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graph two categorical variables
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Grouped bar graph
Mosaic plot |
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graph one numerical variable and one categorical variable
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Grouped histogram
Cumulative frequency distribution Line plot (ordinal categories only) |
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First quartile
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the middle value (median) of the measurements lying below the median.
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Second quartile
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the median
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Third quartile
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the middle value (median) of the measurements larger than the median.
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Extreme values
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those lying farther from the box edge than 1.5 times the interquartile range; displayed by dots.
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Proportion
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most important descriptive statistic for a categorical variable.
p-hat = number in a category/n |
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95% confidence interval for the mean
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We are 95% confident that the population mean falls between ____ and ____.
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2SE Rule of Thumb
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A rough approximation to the 95% confidence interval for a mean can be found from the sample mean plus and minus two standard errors.
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Addition rule
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if two events A and B are mutually exclusive, then Pr[A or B] = Pr[A] + Pr[B]
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Generalized addition rule
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works for both mutually exclusive and not mutually exclusive events.Pr[A or B] = Pr[A] + Pr[B] - Pr[A and B]
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Multiplication rule
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if two events A and B are independent, then Pr[A and B] = Pr[A] x Pr[B]
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General multiplication rule
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finds the probability that both of two events occur, even if the two are dependent.
Pr[A and B] = Pr[A] Pr[B|A] |
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Law of total probability
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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 |
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Baye's theorem
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Type I error
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rejecting a true null hypothesis
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Type II error
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failing to reject a false null hypothesis
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binomial distribution assumptions
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The number of trials (n) is fixed. Separate trials are independent. The probability of success (p) is the same in every trial.
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n choose X
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test whether a population proportion (p) matches a null expectation(p0) for the proportion.
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Binomial test
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H0: The relative frequency of successes in the population is p0.
HA: The relative frequency of successes in the population is not p0. |
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test statistic for binomial test
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observed number of successes
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Adjusted Wald Method
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used to calculate an approximate confidence interval for a proportion.
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measures the discrepancy between an observed frequency distribution and the frequencies expected under a simple random model serving as the null hypothesis.
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X2 Goodness-of-Fit Test
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Degrees of Freedom for X2
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df = (number of categories) − 1 − (number of parameters estimated from the data)
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X2 Specific Assumptions
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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. |
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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.
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Poisson Distribution
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Degrees of Freedom for Poisson
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df = number of categories - 1 - 1
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variance is greater than the mean
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distribution is clumped
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variance is less than the mean
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distribution is dispersed
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estimates and tests for an association between two or more categorical variables.
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X2 contingency test
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H0: categorical variable 1 and 2 are independent.
HA: categorical variable 1 and 2 are not independent. |
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degrees of freedom for the X2 contingency test
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df = (r-1)(c-1)
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Standard normal distribution
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a normal distribution with mean 0 and standard deviation 1.
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Student's t
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the difference between the sample mean and the true mean (Y̅ − µ), divided by the estimated standard error (SEY̅)
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coefficient of variation
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CV = 100% (standard deviation/mean)
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