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STA261 Prof. Swart > Exam 1 > Flashcards

Exam 1 Flashcards

1
Q

Data file

A

the format in which statistical format is organized, typically in spreadsheet form. Rows contain measurements for a particular subject, columns contain measurements for a particular characteristic

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2
Q

Simulation

A

use of a computer to mimic what would actually happen if you selected a sample and used statistics in real life. These are done when it is not practical to physically perform an experiment. Probability sampling is used in designing simulations

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3
Q

Response variable

A

variable we are interested in measuring

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4
Q

component

A

what you are simulating through use of a random device

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5
Q

trial

A

One repetition of a simulation/experiment

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6
Q

Steps for building simulations

A
  1. Identify component to be repeated/simulated
  2. Explain how you will model the component’s outcome
  3. State response variable clearly
  4. Explain how to combine the components into a trial to model the response variable
  5. Run several trials
  6. Collect and summarize the results of the trials
  7. State your conclusion
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7
Q

3 reason for studying stats

A
  1. being informed
  2. making good decisions
  3. evaluate decisions that affect you
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8
Q

Definition of statistics

A

The science of learning from data in the presence of variability. variability is everywhere

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9
Q

Statistical problem solving process

A
  1. formulate a statistical research question
  2. collect data
  3. analyze data
  4. interpret results
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10
Q

Main components of statistics

A
  1. design: plan on how to obtain data to answer the question
  2. description: summarize and analyze the data
  3. probability: determine how sample differs from population
  4. Inference: make decisions and predictions
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11
Q

Variable

A

any characteristic observed in a study

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12
Q

data

A

the values of a variable for one or more people or things

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13
Q

Observation

A

(subject) an individual piece of data

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14
Q

data set

A

the collection of all observations for a particular variable

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15
Q

Categorical variable

A

(qualitative) Non-numerical variable with different categories, can still be a number depending on what that number represents

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16
Q

Quantitative variable(and types)

A

a numerical variable

Types
1. Discrete: values form a set of separate numbers. Typically something we count

  1. continuous: values form a continuum of values, infinite number of possible values. Typically something we measure
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17
Q

Reasons for identifying different data types

A
  1. Choose appropriate graphical display

2. Choose correct statistical method for inferential procedures

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18
Q

W’a and H for data

A

How, What, Where, When, Why, Who

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19
Q

Frequency distribution

A

A listing of distinct categories and their frequencies

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20
Q

Relative frequency distribution

A

A listing of distinct values and their relative frequencies(proportions and percentages). Used to compare samples of unequal size

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21
Q

Joint event

A

Event with two or more characteristics

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22
Q

How to tell if there is an association or not?

A

Association: relative frequencies differ

No association: relative frequencies are similar

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23
Q

Dot plots

A
  • easy to make
  • useful for comparing 2 or more data sets
  • display individual values of data set
  • good for smaller data sets
  • shows raw data
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24
Q

Stem plots

A
  • not useful with large data sets
  • Usually displays more info than histograms
  • include raw data
  • useful for comparing 2 or more data sets
  • Have “stem”(can have more than one digit) and “leaf” can not have more than one digit
  • arranged in ascending order
  • must have a key
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25
Q

Histogtams

A
  • analogous to bar charts
  • horizontal axis has classes of quantitative data
  • frequency, relative frequency or percent
  • bars touch
  • good for larger data sets
  • good if you need more flexibility
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26
Q

Time plots

A
  • show changes over time
  • vertical axes show each observation
  • horizontal axes show time when observation was measured
  • trends can be seen by connecting points
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27
Q

what does “n” usually indicate?

A

sample size

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28
Q

Which measures of center are resistant to the outliers and which arent?

A
  • Resistant: Median

* Not resistant: Mean

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29
Q

Which measures of center are useful with quantitative data and which are useful with qualitative/categorical data?

A

Mean and median can only be used with quantitative data. Mode can be used with both

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30
Q

What can you know about the distribution if the mean is greater than median? What about if the is less than the median?

A

Mean is greater: right skewed

Mean is less than: left skewed

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31
Q

Measures of variation(purpose and types)

A

Indicate amount of spread in a distribution

types
1. Range: if you dont know this youre screwed
2. standard deviation: accounts for all
observations, indicates how far on average observations lie from the mean, not resistant to outliers
3. Interquartile range(IQR): Quartiles of data, used with boxplotd

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32
Q

which types of graphical displays are for quantitative data?

A
  1. dot plots
  2. stem and leaf plots
  3. histograms
  4. time plots
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33
Q

Graphical displays for categorical data

A
  1. Frequency distribution
  2. Relative frequency distributions
  3. Pie charts: use relative frequencies, aka circle graph, difficult to construct by hand, best for data sets for few categories
  4. Bar charts: easiest way to graph, horizontal axis is distinct values of categorical data, vertical axis is frequencies or relative frequencies
  5. Pareto charts: bar graph with bars from tallest to shortest
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34
Q

Response variable

A

measured to make comparisons between groups

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35
Q

Explanatory variable

A

(predictor) explains the value of response values

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36
Q

Association

A

relationship between 2 variables

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37
Q

Contingency table

A

Frequency distribution for bivariate data, also called a two way or cross tabulation table

38
Q

Conditional proportions

A

Proportions based on the explanatory variable for categories of the response variables

39
Q

Empirical rule

A

Applies to bell shaped distributions

68% of data falls within 1 standard deviation the mean

95% falls within 2 standard deviations

99.7% falls within 3

40
Q

Percentile

A
  • measure of relative standing
  • indicate the below which a certain percentage of observations fall
  • resistant to outliers
  • often preferred over mean and STD
  • Divides data into 100 equal parts, there are 99 percentiles
41
Q

Types of percentiles

A
  1. Deciles: divide data into tenths
  2. Quartiles: divide data into fourths
    •1st quartile: aka lower quartile, median of lower half of data, divides lower 25% and upper 75%
    •Second quartile: median
    •Third quartile: divides bottom 75% from top 25%
42
Q

5 number summary and it’s graph

A
  1. Minimum
  2. Q1
  3. Median
  4. Q3
  5. Maximum
    represented by a boxplot
43
Q

Interquartile range

A
  • Preferred measure of variation when median is used
  • IQR=Q3-Q1
  • more resistant to outliers
44
Q

Finding potential outliers with IQR

A
  1. less than Q1-1.5•IQR

2. greater than Q3+1.5•IQR

45
Q

Difference between potential outlier and outliers

A

and outlier is far removed from the rest of the data

46
Q

SOCS

A
  • Acronym for Shape, Outliers, center, spread

* Use to describe distributions of quantitative data

47
Q

Components of graph shape

A

Modality: #of peaks, can be unimodal, binodal or multimodal

Skewedness and symmetry

48
Q

Outlier criterion using z scores

A

z>|3|

49
Q

How to know whether to use mean or median for measure of center

A
  • Use mean of possible because it takes into account of actual observations
  • mean is good for symmetric observations with a small number of discrete values
  • median is good for skewed distributions when potential outliers are oresent
50
Q

What is report with the mean? median?

A

Mean and standard deviation are reported together while IQR and range are reported with median

51
Q

Probability

A

The science of uncertainty, used to evaluate and control the likelihood that a statistical inference is correct. It quantified uncertainty

52
Q

Types of probability

A
  1. Subjective: guessing a probability based off personal judgement
  2. Theoretical: Based on formulas
  3. Experimental/empirical: results of a random experiment
53
Q

Common cutoff values for an event to be considered “unusual”

A

1%, 5%, 10%(mainly 5%)

54
Q

Law of large numbers

A

The probability of an event is the proportion of times it occurs in a large number of repetitions in an experiment. Aka frequentist interpretation. Ignores black swan events. Helps understand and visualize meaning of probability

55
Q

Sample space

A

all possible outcomes for an experiment

56
Q

Ways to visualize a sample space

A

Tree diagram or venn diagram

57
Q

Event

A

A subset of the sample space. A collection of 1 or more outcomes

58
Q

Complement of an event

A
  • Event that does not occur
  • denoted as A^c
  • P(A^c)=1-P(A)
59
Q

Disjoint events

A
  • aka mutually exclusive events
  • events that do not have any outcomes in common
  • events that cant happen at the same time
  • compliment events are disjoint
60
Q

Intersection

A
  • consists of outcomes that are in both events, the overlap

* disjoint events: P(A and B)=0

61
Q

Union

A
  • A or B

* Out comes that are in one or the other

62
Q

P(A or B)

A

Disjoint: = P(A)+P(B)

Not disjoint: = P(A)+P(B)-P(A and B)

63
Q

Conditional probability

A

The probability of an event occurring when you know that another event has occurred

P(A|B)=P(A and B)/P(B)

Probability that event A will occur given that B has occurred. We are conditioning event B, meaning it occurred first

64
Q

Formula for intersection of two events using conditional probability

A

P(A and B)= P(A)•P(B|A)

P(A and B)=P(B)•P(A|B)

65
Q

Methods for determining if events are independent

A
  1. P(A|B)=P(A)
  2. P(B|A)=P(B)
  3. P(A and B)=P(A)•P(B)
66
Q

Sensitivity

A

The probability that the test will give a positive result, given that the condition tested for is present

P(Positive result|condition present)

67
Q

Specificity

A

The probability that the test will give a negative result, given that the condition tested for is not present

P(Negative result|Condition isnt present)

68
Q

Parameter

A
  • Numerical summary of a population
  • Numerical summary of a probability distribution
  • Denoted by greek letters
69
Q

Random variable

A

A numerical measurement of the outcome of a random event

70
Q

Expected value

A

the mean

71
Q

Mean of a discrete probability distribution

A

mean=x•p(x)

repeat “x•p(x)” for each sample

72
Q

What type of graph represents continuous distributions?

A

A curved graph

73
Q

Normal distribution

A
  • used for continuous random variables

* symmetric and bell shaped

74
Q

Properties of empirical rule

A
  1. Data must be unimodal and approximately bell-shaped

2. Probabilities are approximate

75
Q

Rounding rules when working with normal distributions

A

Round to 4 decimal places

76
Q

Conditions for binomial dostribution

A
  1. Fixed number of trials(n)
  2. each trial has 2 possible outcomes
  3. the probability of success (p) is the same for each trial
    4: Trials are independent
77
Q

What happens to a binomial distribution if p isnt 0.50?

A

p<0.5: right skewed

p>0.5: left skewed

78
Q

How do you know if n is large enough in a binomial distribution?

A

np> or equal to 15

and

1-p=15

79
Q

Mean and standard deviation formulas for binomial distributions

A

Mean=np

Std=/np(1-p)

80
Q

Ways to obtain information

A

census, sampling, experimentation

81
Q

Mean and median in symmetric distributions

A

Mean and median can be used, they should be close in value

82
Q

What is spread measured by?

A

Standard deviation and IQR

83
Q

How to gage symmetry

A

Look at how different the mean and median are

84
Q

What type of statistics is probability?

A

Inferential

85
Q

How do you measure spread for discrete random variables?

A

Range

86
Q

What is used to find the center of probability distributions?

A

Mean

87
Q

Purpose of descriptive statistics

A

Reduce the data to simple summaries without distorting too much information

88
Q

Types of proportion distributions

A
  1. Population distribution: almost never observed, we learn about it from sample distributions
  2. Sample distribution: aka data distribution, consists of sample data you observe and analyze, should resemble population distribution if good sampling techniques were used
  3. Sampling distributions: Describes long run behavior of the statistic, specifies probabilities for all possible values of the statistic for a sample in a given sizr
89
Q

How to tell if a sampling distribution is normal?

A

n•p and n(1-p) are at least 15

90
Q

Central limit theorem assumptions and conditions for the sampling distribution of p

A
  1. Randomization condition: values are randomly obtained
  2. Independence assumption: Sampled values are independent
  3. 10% condition: n is no more than 10% of the population
  4. Sample size assumption: n has to be large enough to expect at least 15 successes and failures
91
Q

Central limit theorem assumptions and conditions for the sampling distributions of the mean of observations

A
  1. Randomization condition: values are sampled randomly
  2. Independence assumption: sampled values are independent
  3. 10% condition: n is no more than 10% of the population
  4. Sample size assumption: There is no one size fits all rule, small samples work if population is unimodal and symmetric, large sample is need if skewed

STA261 Prof. Swart (3 decks)

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