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Tags and Description

Statistics

103 Terms

1

population

the entire group of individuals that is the target of our interest; generally too big to actually measure or observe

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2

sample

subgroup of the population which we can examine or observe, measure and collect data from

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3

individual

single entity that is being observed

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4

variable

characteristic measured on each individual

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5

quantitative variable

variable whose possible values are meaningful numbers

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6

categorical variable

variable whose possible responses are non-quantitative categories (words/labels/attributes)

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7

measurement

value of a variable for an individual

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8

data

measurements for a set of individuals (Goal of Statistics: convert this to useful information)

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9

data set

data identified with contextual information (who was observed, what was measured, why is study done) often given in a table

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10

EDA (exploratory data analysis) goals

  • organize and summarize data

  • discover features, patterns and striking deviations

  • interpret patterns in context

  • include visual displays and numerical values

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11

single variable pattern

distribution of a variable: summary of data one variable at a time (all the possible values and how often they occur)

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12

process of statistical problem solving

  1. Collect data

  2. Summarize data

  3. Interpret data

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13

parameter

numerical fact about the variable in the population

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14

statistic

numerical fact about the variable in the sample

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15

convenience sampling

select individuals in the easiest possible way

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16

volunteer response sampling

individuals select themselves

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17

quota sampling

force the sample to meet specified quotas

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18

simple random sample (SRS)

every possible set of a specified size has an equal chance of being selected

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19

cluster sampling

a random sample of clusters is taken and all individuals in selected clusters are included in sample

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20

stratified random sample

select a random sample (SRS) from each stratum and combine these SRSs together

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21

multi-stage sample

take a sample at each hierarchical level of the population

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22

treatment

the condition applied to a subject in an experiment (one of the subcategories/values of the explanatory variable)

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23

lurking variables

variables that affect both the explanatory and response variables but are not measured or included as a planned factor in the study

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24

control

an effort to reduce the effects of lurking variables

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25

confounding

situation in which effects of lurking variables cannot be distinguished from effects of factors

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26

historical comparison experiments

study involving only one treatment, where treated subjects are compared to untreated subjects from some external source

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27

unreplicated experiments

assigns one subject only to each treatment

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28

confounded experiments

treatment groups are handled differently in some way OTHER than the treatment

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29

undercoverage

some individuals have no possibility of being selected

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30

non-response

some selected individuals choose not to be in the sample because they refuse to provide information or cannot be contacted

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31

misleading response

people lie or give inaccurate answers (often about sensitive issues)

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32

interviewer effect

person asking questions influences responses (for in-person/phone surveys)

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33

question order effect

the order that questions are asked promotes certain responses

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34

question wording

the way a question asked leads, misleads or confuses

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35

open questions

allow for almost unlimited possible responses (short answer), less restrictive but more difficult to analyze

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36

closed questions

limit response options (multiple choice), easier to analyze but may be biased by the options provided. should include "other/unsure" option

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37

observational studies

individuals are not assigned to treatments, are self selected, cannot conclude causation

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38

experiment

study where individuals are assigned to treatments, causation okay if valid

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39

subject

individual to which treatment is applied

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40

response variable

characteristic measure on each subject; outcome of interest

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41

explanatory variable

characteristic/measurement that is use to predict or explain changes in the response variable; variable we think could help us know about the response (measured earlier or more easily); independent variable

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42

factor

planned explanatory variable

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43

comparison

two or more groups; controls lurking variables by including comparison treatments

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44

randomization

randomly assign subjects to groups; neutralizes effects of lurking variables by assigning subjects to treatments using a random device

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45

replication

two or more subjects in each group; assign more that one subject to each treatment to detect important effects

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46

double blinding

neither subjects nor the researchers in direct contact with the subjects know which treatment is received

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47

placebo effect

favorable response of a human subject to a placebo because of trust in the medical provider or belief that the treatment will work

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48

diagnostic bias

diagnosis of subjects is biased by preconceived notions about the effectiveness of the treatment (person administering treatments expects certain responses)

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49

lack of realism

realism is compromised by the conditions of the study

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50

hawthorne effect

people in experiment behave differently than they would normal behave, not like real life

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51

non-compliance

subjects fail to submit to the assigned treatment or refuse to follow the protocol of the experiment

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52

principles of data ethics

• safety and well-being of the subjects must be protected • all individuals must give their informed consent before data are collected • individual data must be kept confidential

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53

randomized controlled experiment

randomly assign subjects to treatments, grouped by treatment

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54

randomized block design

randomly assign to treatments within blocks, grouped by treatment or by block

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55

benefits of randomized block design (RBD)

  • removes confounding of lurking variables

  • reduces chance variation by removing variation associated with the blocking variable

  • yields more precise estimates of chance variation

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56

matched pairs

two treatments; matched individuals or two measurements per subject

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57

three principles of experiments

  • randomly assign two treatments to two individuals or randomize the order of treatment application to each individual

  • replication = number of pairs

  • compare the two treatments

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58

analysis of distribution of quantitative data

  • always plot data first

  • look for an overall pattern and for striking deviations

  • look at shape, center, spread of distribution

  • add numerical summaries to supplement graph

  • if pattern is regular, use mathematical model to describe data

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59

symmetric and bell shaped distribution examples

blood pressure, IQ, biological factors

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60

symmetric and bell shaped distribution

mean, median, and mode are the same

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61

right skewed distribution

concentration of data on left, tail extends to the right; mean > median

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62

right skewed distribution examples

salary, home price, children, economic variables

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63

left skewed distribution

concentration of data on right and the tail on the left; median > mean

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64

left skewed distribution examples

test scores, olympic high jump

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65

bimodal distribution

a distribution with two modes

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66

bimodal distribution examples

speed limits, restaurant patrons

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67

flat or uniform distribution

relatively equal across graph

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68

flat or uniform distribution examples

rolling a die, day of the month born

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69

center

typical, middle value; half of data to each side

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70

spread

consistency/inconsistency of data; look for maximum and minimum

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71

outliers

values that are far outside most of data

  • is data point miscoded?

  • unusual conditions?

  • should data point be excluded?

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72

mode

most frequently occurring score, corresponds to a peak

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73

median

the middle score in a distribution; half the scores are above it and half are below it

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74

mean

center of gravity; the arithmetic average of a distribution, obtained by adding the scores and then dividing by the number of scores

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75

mean vs median

  • construct graph to evaluate skewness and outliers

  • use median if distribution is markedly skewed or outliers are present

  • use mean if distribution is roughly symmetric

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76

range

maximum - minimum

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77

interquartile range (IQR)

the difference between the first and third quartiles

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78

standard deviation

average distance of values from the mean

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79

first quartile (Q1)

a number for which 25% of the data is less than that number; same as the median of the data which are less than the overall median

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80

second quartile (Q2)

median

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81

third quartile (Q3)

a number for which 75% of the data is less than that number; same as the median of the part of the data which is greater than the median

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82

5 number summary vs 2 number summary

use 5 number for skewed, and 2 number for symmetric

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83

5 number summary

minimum, Q1, median, Q3, maximum

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84

random phenomenon

individual outcome unpredictable, but outcomes from large number of repetitions follow regular pattern

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85

sample space

the set of all possible outcomes

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86

event

a collection of possible outcomes

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87

probability of an outcome

The proportion of times that an outcome occurs in many, many repetitions of the random phenomenon

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88

probability rules

  • 0<P(A)<1

  • summation of all probabilities is 1

  • if two events cannot occur simultaneously, the probability of one or the other equals the sum of separate probabilities

  • probability of event not occurring equals one minus the probability of event occurring

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89

theoretical probability

number of favorable outcomes divided by total number of possible outcomes

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90

empirical probability

number of outcomes divided by total of repetitions

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91

law of large numbers

As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the theoretical probability of the outcome

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92

probability

the long-run relative frequency with which an event will occur

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93

probability distribution

all possible events and their associated probabilities

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94

random variable

a variable whose value is a numerical outcome of a random phenomenon

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95

continuous random variable

a variable that can take on any possible value, all values cannot be listed

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96

discrete random variable

variable whose possible values are a list of distinct values

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97

𝜇

mean of a population

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98

x-bar

mean of a sample

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99

s

standard deviation of a sample

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100

𝜎

standard deviation of a population

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