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4
Statistics

Statistics

By Will
Published May 30
76 cards
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This is a published deck. Feel free look around, review cards, or make changes, but you'll need to clone it to save your progress.
What is the formula for a mean-derivation score?
x−xˉ x - \bar{x}
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What is the formula for a z-score?
z=x−xˉs z = {x - \bar{x} \over s}
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Which type of t-test would you use if you only wanted to see if two normal distributions were different?
a two-sided t-test, OR
a two-tailed t-test
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How does a linear transformation affect the relationship between values?
The relationship between values does not change because the process changes each value in the same way.
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What happens to the intercept if you center the independent variable in a linear model?
It becomes the predicted value for the mean of the independent variable.
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What is a mean-derivation score?
It is a form of centering where each value in a distribution is subtracted from the mean.
x−xˉ \mathrm{x} - \bar{x}
Values above the mean are positive and values below the mean are negative.
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Why is it useful to have the intercept be the mean?
Because in many cases, an independent variable value of zero doesn't make sense and focusing on values above and below the mean is more productive.
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What is the most common example of centering in statistical transformations?
subtracting out the mean of a distribution, or a mean-derivation score
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What type of transformation is centering and why is it used?
It is the application of a linear transformation to give a particular meaning to the value of 0.
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What is a linear transformation?
It is a transformation involving addition, subtraction, multiplication, or division using a constant value.
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The intercept of a null model is equivalent to what parameter of which variable?
xˉ \bar{\mathrm{x}}
of the dependent variable
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What does a given
R2 \mathrm{R}^2
value imply?
That much of the variation in the
y \mathrm{y}
distribution can be explained by
x \mathrm{x}
. Conversely, that
1−R2 1 - \mathrm{R}^2
of the
y \mathrm{y}
distribution is not explained by
y \mathrm{y}
. This is also called its effect size.
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Why is
R2 \mathrm{R}^2
useful?
It allows us to compare the magnitude of residuals (SSE) of models in a standardized manner.
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What does
R2 \mathrm{R}^2
measure?
It measures how well a model fits the data.
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What is the formula for
R2 \mathrm{R}^2
?
R2=1−SSE1SSE0 R^2 = 1 - {{SSE_{1}\over {SSE}_{0}}}
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Why is a null model useful?
It lets you compare a model to a standard which allows us to calculate a standardized measure of fit (
R2 \mathrm{R}^2
).
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Why are squared errors useful?
It removes negative values and prevents them from canceling out positive values in a sum operation.
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What is a null model, or zero-slope model?
It is a model that assumes there is no relationship between the two variables.
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Why is it important for residuals to have the same variance throughout the range of
x \mathrm{x}
values?
Because otherwise would imply that the effect or slope is stronger for certain intervals of
x \mathrm{x}
and a linear regression model cannot tell us how or why that strength of relationship changes.
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Why is it important for consecutive residuals to be independent from one another?
Because it lowers the accuracy of the model and implies that there is some other linear relationship that the model is not capturing.
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What can you do if there is a clear relationship between two variables but they are not linear?
Apply a non-linear transformation to the independent or dependent variables; such as the log or square root.
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What four assumptions must be true about the data in order to safely interpret a linear regression model?
  • the two factors have a linear relationship
  • the residuals are independent from each other
  • the residuals should also be normally distributed
  • the residuals must have constant variance throughout the regression line
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What is the technical term for the the state in which the residuals of a linear regression model have constant variance?
homoscedasticity
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In what way does adding a residual error term to the linear regression model,
y=b0+b1x+e \mathrm{y} = \mathrm{b}_0 + b _{1}x + e
, stochastic?
In the sense that it will not always return the same
y \mathrm{y}
-value for any given
x \mathrm{x}
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In what way is the linear regression formula,
y=b0+b1x \mathrm{y} = \mathrm{b}_0 + b_{1}x
(without residuals), deterministic?
In the sense that it will always return the same
y \mathrm{y}
-value for any given
x \mathrm{x}
value.
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What do residuals in a linear regression model represent?
the information left over after removing the effect of the independent variable, OR
the parts of
y \mathrm{y}
that cannot be explained by
x \mathrm{x}
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What does it mean if a linear regression model predicts a dependent variable value for an independent variable value that is not possible?
It just means that the model can't be used for independent variable values outside of its trained range. That is normal.
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In the context of linear regression models, what does the term extrapolation mean?
the prediction an independent variable outside the range of the trained model.
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In the context of linear regression models, what does the term interpolation mean?
the prediction of an independent variable within the range of the trained model.
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In the regression model formula
y=b0+b1x+e \mathrm{y} = \mathrm{b}_0 + b_{1}x + e
Which term is the residuals?
e e
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In the regression model formula
y=b0+b1x+e \mathrm{y} = \mathrm{b}_0 + b_{1}x + e
Which term is the dependent variable?
y \mathrm{y}
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In the regression model formula
y=b0+b1x+e \mathrm{y} = \mathrm{b}_0 + b_{1}x + e
Which term is the independent variable?
x \mathrm{x}
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In the regression model formula
y=b0+b1x+e \mathrm{y} = \mathrm{b}_0 + b_{1}x + e
Which term is the slope?
b1 \mathrm{b}_1
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In the regression model formula
y=b0+b1x+e \mathrm{y} = \mathrm{b}_0 + b_{1}x + e
Which term is the intercept?
b0 \mathrm{b}_0
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What is the formula for a linear regression model?
y=b0+b1x+e \mathrm{y} = \mathrm{b}_0 + b_{1}x + e
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What are the coefficients of a linear regression model?
the intercept and the slope
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What is the intercept of a linear regression model?
It is the predicted
y \mathrm{y}
-value for
x=0 \mathrm{x} = 0
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How is slope defined in terms of variables x and y?
The slope is the change in
y \mathrm{y}
for each unit in
x \mathrm{x}
.
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If we believe that the variable
GPA \mathrm{GPA}
is affected by the variable
Family income \mathrm{Family\ income}
;
is
Family income \mathrm{Family\ income}
dependent or independent?
independent
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If we believe that the variable
GPA \mathrm{GPA}
is affected by the variable
Family income \mathrm{Family\ income}
;
is
GPA \mathrm{GPA}
dependent or independent?
dependent
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What word describes analyses that consider the relationship between two variables?
bivariate
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What word describes analyses that only consider one variable?
univariate
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When presenting a boxplot, what detail needs to be specified and reported?
the interpretation of the whiskers; i.e., they can represent the minimum and maximum values or they can represent an additional 1.5 times the IQR.
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What point does the edge of the left or lower whiskers of a boxplot usually represent?
the first quartile minus 1.5 times the interquartile range
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What point does the edge of the right or upper whiskers of a boxplot usually represent?
the third quartile plus 1.5 times the interquartile range
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What is the interquartile range?
the difference between the third quartile and the first quartile
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What percentage of data points does the area of a boxplot cover?
the middle 50 percent
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What percentage of data points are higher than the right or top edge of a box plot?
the top 25 percent
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What percentage of data points are lower than the right or top edge of a box plot?
the bottom 75 percent
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What percentage of data points are higher than the left or bottom edge of a box plot?
the top 75 percent
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What percentage of data points are lower than the left or bottom edge of a box plot?
the lower 25 percent
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What does the symbol
s \mathrm{s}
represent in statistics?
It represents the observed standard deviation of a distribution.
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What symbol is used to show the standard deviation of an observed distribution?
s \mathrm{s}
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What does the symbol
xˉ \bar{\mathrm{x}}
represent?
the observed mean of a distribution
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What symbol is used to represent the observed mean of a distribution?
xˉ \bar {\mathrm{x}}
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What does the symbol
σ \sigma
represent in statistics?
the theoretical standard deviation of a population
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What symbol is used to show the theoretical standard deviation of a population?
σ \sigma
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What does the symbol
μ \mu
represent in statistics?
the theoretical mean of a population
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What symbol is used to show the theoretical mean of a population?
μ \mu
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Why would we use the median instead of the mean, or vice versa?
The median is less affected by extreme values whereas the mean is easily pulled higher or lower.
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What should be reported when we write about a normal distribution?
the mean, standard deviation, and number of observations
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What percentage of the middle section of a normal distribution is within 2 times the standard deviation of the mean?
95%
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What percentage of the middle section of a normal distribution is within 1 standard deviation of the mean?
68%
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What is the formula for a mean of a distribution?
xˉ=∑xN \bar x = {\sum{x} \over N}
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What does this formula describe?
xˉ=∑xN \bar x = {\sum{x} \over N}
the mean of a distribution
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What are the two parameters of a normal distribution?
the mean and the standard deviation
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What does discrete mean in statistics?
It means there is a limited number of responses or outcomes.
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This is an example of what kind of distribution?
a discrete uniform distribution
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The output of rolls of a dice would be an example of which kind of distribution?
a discrete uniform distribution
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How is a discrete uniform distribution different from a discrete normal distribution?
In a discrete uniform distribution, all elements of a finite set are equally probable; for example, a coin toss or dice roll. In a discrete normal distribution, elements are centered around the mean.
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