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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)