Midterm Flashcards
1
Q
Disjoint (mutually exclusive)
A
- events cannot happen at the same time
ex) rolling a die
2
Q
Independent
A
- one event does not affect the probability of the other
ex) tossing 2 coins
3
Q
Disjoint addition rule
A
P(AUB) = P(A) + P(B)
4
Q
proving independence
A
if P(A)*P(B) = P(A and B), A and B are independent
5
Q
conditional probability
A
P(A|B) = P(A and B) / P(B)
6
Q
Multiplication Rule
A
P(A and B) = P(A) * P(B|A)
7
Q
Bad samples
A
- convenience samples
- introduces bias
- over/under estimation
- x reflect population - bias
- systematically favoring certain outcome
- under/over estimation - voluntary response
- people who choose to answer a general appeal
- people with strong emotion
8
Q
Good samples
A
- simple random sample
- ensures everyone has an equal chance of selection
- preferred when there are smaller data sets. - stratified random sample
- ensures all subgroups are represented
- more precise - cluster
- create cluster by location
- save money and time - systematic random sample
- randomly select k individual and count every kth individual
- preferred when population is ordered
- easier to conduct
9
Q
What can go wrong?
A
- undercoverage
- members of the population have less of a chance of being chosen or left out - nonresponse
- chosen individuals cannot be contacted or refuse to participate –> big issue - response bias
- individuals lie or answer a question they don’t know - question wording bias
- they way a question is worded or asked influences the response from an individual
10
Q
Observational study vs. experiment
A
observational study
- x treatment
experiment
- treatment (need experiment to know causation)
11
Q
confounding variable
A
other possible variables other than explanatory variable that affects response variable
12
Q
4 principles of experimental design
A
- random assignment
- replication
- control
- comparison
13
Q
placebo effect
A
dummy treatment
14
Q
purpose of control group
A
provides a baseline for comparison
15
Q
purpose of single and double blind experiments
A
reduce placebo and favoring
16
Q
purpose of random assignment
A
- creates roughly equivalent groups
- helps control confounding variables
17
Q
purpose of replication
A
use enough subjects/experimental units so the outcome of the experiment can have meaning
18
Q
statistically significant
A
- the results most likely did not happen by chance.
- convincing evidence with simulation
19
Q
blocking
A
- stratified sampling in experiments
- blocks should be homogeneous
- use a confounding variable
20
Q
purpose of blocking
A
- controls confounding variables
- increases chance of finding convincing evidence if the effect is real
21
Q
matched pairs design
A
blocks only include 2 experimental units
1. 2 similar units
2. 1 unit that gets both treatment
(randomly assign treatments or randomly assign the order of treatment)
22
Q
interference
A
using information from our sample/experiment to draw conclusions about the population
23
Q
sampling variability
A
different samples from the same population will give different results
24
Q
categorical graphs
A
side by side bar graph
segmented bar graph
mosaic plot
pie chart
25
quantitative graphs
histogram
stem and leaf plot
dot plot
box plot
26
marginal relative frequency
prob of margins.
int: proportion of all who are _________.
27
joint relative frequency
prob of inner over total
int: the proportion of all who are ________ and ________.
28
conditional relative frequency
prob of inner over small total
int: the proportion of _______s who are _________.
29
describe a distribution
Shape
Outlier
Center
Spread
+
context
30
resistant measure
yes
- median
- IQR
no
- mean
- range
- standard deviation
- variance
31
problem of range
ignores all values in the data set except the max and the min
non-resistant to outliers
32
standard deviation
how far, on average, the values of the distribution are from the mean
- greater than 0 (s=0 => no variability)
- large value = more variability
- not resistant to outliers
- measures variance about the mean
int: the (context) differes by (s.d. unit) from mean (mean), on average.
33
+/- of boxplot
+ -- can know how spread the data are
- -- can't see peaks/gaps in the data
34
comparison of symmetric and skewed graph
symmetric (no outliers)
- center: mean
- spread: standard deviation
skewed (yes outliers)
- center: median
- spread: IQR
35
transforming data
linear transformation
--> if add/subtract
- mean = add/subtract
- standard deviation = same
- shape = same
--> if multiply/divide
- mean = multiply/divide
- standard deviation = multiply/divide
- shape = same
36
density curve
a curve that
- is always on or above the horizontal axis
- has area exactly 1 underneath it
- describe the overall pattern of a distribution
37
normal curve
1. symmetric and bell shaped
2. the mean = median, both located at exact center
38
empirical rule
- 68-95-99.7 rule
39
describing scatterplot
Direction
Unusual features
Form
Strength
+
context
40
correlation
measures strength and direction of a linear association
- indicates direction by sign
- both variables need to be quantitative
- does not rely on units of measure
- has no unit of measurement
- does not measure form
- only for linear relationship
- not resistant measure of strength
int: the linear association between (x-context) and (y-context) is (strength) and (direction)
41
extrapolation
using regression line to predict outside the x-values that were used to calculate the line
42
residual
actual y - predicted y
+ = underprediction
- = overprediction
int: the actual (y-context) was (residual) (above/below) the predicted value when (x-context = #)
43
least squares regression line
the line that makes the sum of the squared residuals as small as possible
- distinction between x and y is essential
- r and slope has same sign
- not resistant to unusual point
44
residual plot
a scatterplot that shows the residual as the y-value and the explanatory as x-value
if it doesn't have pattern, the regression model is good.
45
standard deviation of residuals (s)
measures the typical distance between the actual y and predicted y
int: the actual (y-context) is typically about (s) away from the value predicted by the LSRL.
46
coefficient of determination (r^2)
measures the percent reduction in the sum of squared residuals when using the LSRL to make prediction, instead of just using the mean of the y-values
int: about (r^2 %) of the variation in (y-context) can be explained by the linear relationship with (x-context)
47
outlier, high leverage, and influential points
outlier - pt that does not follow the pattern of data (has large residual)
high leverage - much larger/smaller x-values than other pts
influential points - any pt that, if removed, substantially chances {slope, y-int, r, r^2, s}
48
expected value (mean) of discrete random variable
int: if the random process of (context) is repeated many, many times, the average number of (x-context) we can expect is (expected value).
49
standard deviation of a discrete random variable
int: the (context) typically vary by (standard deviation) from the mean of (mean)
50
adding/subtracting random variables X and Y
mean = mu x +/- mu y
standard deviation = sqrt (mu x^2 + mu y^2) --> X and Y must be independent random variables
