Midterm Flashcards
(114 cards)
1
Q
data
A
observations collected from field notes, surveys, experiments, etc
2
Q
what is the backbone of statistical investigation
A
data
3
Q
statistics
A
study of how to collect, analyze, draw conclusions, analyze the data, form a conclusion
4
Q
classic challenge in statistics
A
evaluating the efficacy of medical treatment
5
Q
summary statistic
A
a single number summarizing a large amount of data
6
Q
variables
A
characteristic
7
Q
data matrix
A
a way to organize data
8
Q
numerical variable
A
wide range of numerical values, sensible to add/subtract/take averages
9
Q
types of numerical variables
A
discrete, continuous
10
Q
discrete
A
can only take numerical values with jumps (eg number of siblings)
11
Q
continuous
A
can take numerical values without jumps (eg height)
12
Q
categorical
A
responses are categories
13
Q
types of categorical
A
ordinal, nominal
14
Q
ordinal variable
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categorical but have a natural ordering (eg Likert scale)
15
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nominal variable
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categorical and no natural ordering (eg favourite ice cream
16
Q
negative, positive, independent association
A
bleh
17
Q
population vs sample
A
bleh
18
Q
anecdotal evidence
A
data collected in haphazard fashion from individual cases, usually composed of unusual cases that we recall based on their striking characteristics
19
Q
random sampling
A
avoid adding bias
20
Q
simple random sample
A
most basic random sample, using raffle; every case in population has equal chance of being included
21
Q
non response bias
A
response rates can influence bias from a random sample
22
Q
convenience sample
A
individuals who are easily accessible are more likely to be included in the sample
23
Q
explanatory variables
A
independent variable
24
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response variables
A
dependent variable
25
observational studies
collection of data in way that doesn't directly interfere with how the data arises
eg: collecting surveys, ethnography, etc
26
randomized experiment
when individuals are randomly assigned to a group
27
confounding variable
variable correlated with both the explanatory and response variables
aka: lurking variable, confounding factor, confounder
28
prospective study
identifies individuals and collects information as events unfold
eg: medical researchers may identify and follow a group of similar individuals over many years
29
retrospective study
collects data after events have taken place
| eg: researchers may review past events in medical records
30
simple random sampling
every case in population has equal chance of being included
31
stratified sampling
divide-and-conquer; population is divided into strata (which are chosen so similar cases are grouped together), then a second sampling method (usually simple random) is employed within each stratum
eg: who in Canada goes to theme parks? intentionally oversampling PEI because if we didn’t, most of the respondents would probably be from other provinces like Ontario, and PEI might be skipped entirely
32
when is stratified sampling useful?
when cases in each stratum are very similar with respect to the outcome of interest
33
cluster sample
break up population into clusters, then sample a fixed number of clusters and include all observations from each of the samples
eg: surveying Saskatchewan children by sampling Saskatchewan schools randomly, then simple random sampling kids from the selected schools
34
multistage sample
like cluster sample, but collect random sample within each selected cluster
35
pros and cons of cluster and multistage sample
+cluster/multistage can be more economical than alternative sampling techniques
+most useful when there's a lot of case-to-case variability within cluster but clusters themselves don't look very different from one another
eg: neighbourhoods when they are very diverse
-more advanced analysis techniques are typically required
36
scatter plots (and it's strength)
provides case by case view of two numerical variables
| +helpful in quickly spotting associations relating variables, trends, etc
37
dot plots
provides most basic of displays for one variable; like a one-variable dot plot
38
mean
common way to measure centre of distribution of data
- add up and divide by n
- often labeled as x-bar
39
μ
population mean
40
μx
used to represent which variable to population mean refers to
41
histograms
doesn't show value of each observation
each value blongs to bin
binned counts are plotted as bars on histogram
provide view of data density
42
pros and cons of histogram
convenient for describing shape of data distribution
| doesn't show mode
43
skewness
```
right skew (longer right tail)
left skew (longer left tail)
symmetric (equal tails)
```
44
one, two, three prominent peaks
unimodal, bimodal, multimodal
45
two measures of variability
varaince, standard deviation
46
variance
the average squared deviation
| σ2, standard deviation squared
47
standard deviation
σ
| describes how far way the typical observation is from the mean
48
deviation
distance of an observation from its mean
49
box plots
•summarizes data set using five statistics while also plotting unusual observations
•step 1: draw dark line denoting the median, which splits data in half
•step 2: draw rectangle to represent the middle 50% of the data
⁃aka interquartile range aka IQR
⁃measure of variability in data
⁃the more variable the data, the larger the standard deviation and IQR
⁃two boundaries are called first quartile and third quartile
⁃Q1 and Q3 respectively
⁃IQR = Q3 — Q1
•step 3: whiskers attempt to capture data outside of the box
⁃reach is never allowed to be more than 1.5 x IQR
•step 4: any observations beyond the whiskers are identified as outliers
•robust estimates: extreme observations have little effect on value
⁃median and IQR are robust estimates
50
Mapping Data
colours are used to show higher and lower values of a variable
not helpful for getting precise values
helpful for seeing geographic trends and generating interesting research questions
51
contingency tables
summarized data for two categorical variables
| -each value in table represents number of times a particular combination of variable outcomes occurred
52
row totals
total counts across each row
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column totals
total counts down each column
54
relative frequency table
replace counts with percentages or proportions
55
row proportions
computed as counts divided by row totals
56
segmented bar plot
graphical display of contingency table information
57
mosaic plot
graphical display of contingency table information
| -use areas to represent number of observations
58
probability
proportion of times the outcome would occur if we observed the random process an infinite number of times
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law of large numbers
as more observations are colelcted, the proportion p^n occurences with a particular outcome converges to the probability p of that outcome
60
disjoint outcomes
aka mutually exclusive
| when two outcomes cannot happen at the same time
61
probability distributions
table of all disjoint outcomes and their associated probabilities
62
complement of an event
all outcomes not in the event
63
sample space
set of all possible outcomes
64
independence
when knowing the outcome of one process provides no useful information about the outcome of the other
65
marginal probability
if a probability is based on a single varaible
66
joint probability
probability of outcomes is based on two or more variables
67
defining conditional probability
two parts: outcome of interest and condition
68
condition
information we know to be true
69
conditional probability
the outcome of interests A given condition B
70
tree diagrams
organize outcomes and probabilities around the structure of data
71
when are tree diagrams most useful?
when two or more processes occur in a sequence and each process is conditioned on its predecessors
72
expected value of X
average outcome of X
| denoated by E(X)
73
deductive
reasoning
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inductive
experience and rasong
75
wheel of science
/\ deduction
| theory |
| / \ |
| / \ |
| empirical hypothesis |
| generalizations / |
| \ / |
| \ / |
| observations |
induction \/
76
measurement
downward part of wheel of science
77
conceptualization vs operationalize
"lack of money" vs "lack of opportunity" are two conceptualizations of poverty
"do you have enough money to feed your family?" operationalizes the conceptualization of poverty
different conceptualizations often require different operationalizations
78
quantitative vs qualitative
a little about a lot of people vs a lot about a few people
79
administrative data
growing source
digitial data that is collected in process of administering other social goals
everything from information attached to social health number to credit card number
hard to make generalizations beyond the population
eg using database dealing with health cards is hard to generalize to all of Canada because people who didn't use health cards would be completely ignored
80
survey research
designed to ask research questions
responses distilled into data that we work with
measurement necessitates some simplification because we need to compare across different groups of people
81
population vs sample
group we want to make a generalization about vs the group we actually have information about
82
census
rare kind of sample that covers an entire population, can be very expensive
basically the opposite of an annecdote
83
snowball sampling is often used for?
vulnerable communities like illegal immigrant workers in America
84
experiments
typicaly create artificial situtions that are designed to isolate variables of interest and their effects
85
R
increasingly popular open source client
| accessible because it's free
86
SPSS
popular for undergrads and certain fields
| designed for doing experiment research
87
Stata
popular among sociologists and economists
88
stacked dot plot
higher bars represent areas where there are more observations
makes it easier to judge the centre and shape of the distribution
89
questionaire
contains actual phrasing of question and options for the responses
90
codebook
summarize the data set; tells us what the dataset names mean like dictionary
91
CANSIM
micro data, summary statistics (overall estimates)
92
ODESI
contains confidential information
we can use the public-use parts of ODESI, in which everything is anonymized and variables have been "tweaked" a little in order to make sure that information can't be traced back to respondents
93
Rsearch Data Centres
stuff you can't find on PUMFs
94
measures of central tendency
mode, median, mean
95
pros and cons of mode
+can be used for all types of measures, relatively quick/simple measure
-doesn't ues much information, most common doesn't necessarily mean typical (eg: 53 year old is mode, but there are plenty of people who aren't other ages)
96
how to calculate median
odd: middle observation
even: average of two middle observations
97
pros and cons of mode
+capture actual centre of distribution, less suceptible to outliers
-computationally awkward, cannot be estimated for unordered categorical variables
98
percentiles
general concept, closely related to median (median = 50th percentile)
100 percetniles
99
interquartile range
between 25th and 75th
100
90th percentile
90% of observations are lower, 10% are higher
101
25th percentile
25% of observation are lower, 75% are higher
102
mean cons
more susceptible to outliers
103
measures of dispersion
aim to give us a sense of breath of distribution
104
range
interval between smallest and largest values
105
pros and cons for range
+good for quick check
| -only takes into account two observations, very sensitive, only useful for numeric variables
106
pros and cons of SD
+variance and SD take into account all scores, accurately describes "typical" deviation, easily interpreted
-sensitive to outliers, can only be calculated for numerical variables
107
proportions
frequencies are convoluted, make comparisons difficult, so proportions standardize frequency by number of cases
108
frequency cons
working with them is tough when trying to conceptualize comparisons
-this can be fixed by changing them into percentages
109
cumulative percentage
the percentage in the category + the category under it
| only works for ordinal variables
110
random process
a process where we know what outcomes can happen, but we don’t know which particular outcome will happen
111
rules for probability distribution
1. outcomes listed are disjoint
2. each probability must equal between 0 and 1
3. all probabilities must total 1
112
algebra of possibility
if we know the possibility of their component outcomes, we can know the probability of two events
113
continuous distribution
another way of summarizing information
-more advanced mathematical concept than bar graph
the line is called probability density function
-describes information in graph
-has interesting properties
-can be used to infer probability of any outcome
-never loops back (line only moves from left to right)
-always less than one
-the area under the curve adds up to 1
114
the area equals P
the area under the curve gives the probability of people falling in that range
