Intro Stats Exam 1

observation

each row in a data set (represents one result)

variable

each column in a data set (represents a characteristic of all datasets)

tidy data

data frame where each row is a unique case, each column is a variable, and each cell is a single value

numerical variable

takes a wide range of numerical values, and it makes sense to add/subtract or take averages with those values

discrete variable

numerical; can only take on a finite number of outcomes

continuous

numerical; can take any outcome to any degree of exactness

categorical variable

where the variable takes on a certain category

ordinal variable

categorical; has a natural order or rank

population

the full number of a representative group

sample

a fraction of a population

parameter

a calculation using an entire population

statistic

a calculation using a sample of a population

simple random sample

each case in a population has an equal chance of being included in the sample & are not purposely related to each other

bias

a cause of a skewed, disproportionate, or non-representative sample

non-response bias

when a small portion of cases from a sample respond, it is unclear whether the results are representative of the population

convenience sample

where individual cases who are easily accessible are more likely to be included in a sample

volunteer response sample

when all responses are gathered from willing volunteers

response bias

an individual’s tendency to provide inaccurate answers to self-reported questions

a good sample is one that is ___ ___ ___ ___.

representative of the population

the best way to achieve a representative sample is to take a ___ sample from the population.

random

randomized experiment

when researchers assign treatments to cases using randomization

observational study

a study where no treatment has been explicitly applied or withheld

explanatory variable

a label for a variable that is suspected to affect another

response variable

a label for a variable that is suspected to be affected by another

confounding variable

a variable associated with an explanatory and response variable that prevents the study from concluding that the explanatory caused the response variable

when randomly sampling, conclusions (may/may not) generalize to a population

may

when not randomly sampling, conclusions (may/may not) generalize to a population

may not

when describing data, always remember to include ___.

context

two categorical variables are (independent/dependent) if the relative frequency of a level in the first variable does not change depending on the level of the second

independent

two categorical variables are (independent/dependent) if the relative frequency of a level in the first variable does change depending on the level of the second

dependent

what does it mean for an observation to be in the 50th percentile?

the observation is higher than 50% of all variables in the dataset

formula (upper AND lower fence) for determining outliers

upper: Q₃ + 1.5 (IQR)

lower: Q₁ - 1.5 (IQR)

formula for determining the interquartile range

Q₃ - Q₁

when describing or comparing distributions, mention ___, ___, ___, and ___ in ___.

shape, center, spread, outliers, context

list 3 examples of shape

• skew (left or right skew)

• symmetry

• modality (uni, bi, multi)

list 2 examples of center

• mean

• median

list 2 examples of spread

IQR, standard deviation

explanatory variable is denoted as

x

response variable

y

equation of the least squares regression line/line of best fit

ŷ = b₀ + b₁x

the denotation of predicted/fitted value

ŷ

description and formula of residual

leftover variations in data after finding the fitted model; denoted as

e = y_i - ŷ_i

least sqares regression line

minimizes the sum of the squared residuals (how far points are from the line of best fit)

when interpreting the least squares regression line, provide ___, including that the regression line is a ___.

context,

prediction

correlation coefficient

describes the strength and direction of the linear relationship between two variables; denoted as

r

1 ≥ r ≥ -1

coefficient of determination

measures the percentage of variability in the outcome “y” that can be explained by the linear model with predictor “x;” denoted as

R²

“the variability of y is _% affected by factor x.”

the red point has leverage because it falls ___ ___ from the center of the cloud of points and influences the ___ of the line.

horizontally away,

slope

the red point is an influential point because it influences the ___ of the line.

slope

interpret standard deviation

typical deviations from z (the mean) would be s (standard deviation) above or below the mean