Lesson 3

Question 1

scatterplots

Answer 1

used for identifying explanatory variable

Question 2

Which axis should have response or explanatory variable?

Answer 2

response= y axis
explanatory = x axis
this is only a way to keep track of which one we suspect is which

Question 3

What factors do you use to evaluate the relationship of variables on a scatterplot?

Answer 3

direction (neg/pos)
shape (linear/curved)
strength (strong/weak)
outliers

Question 4

histogram

Answer 4

data are binned into intervals and heights represent number of cases that fall into each interval
provides a view of the data density
useful for describing shape of distribution

Question 5

data density

Answer 5

where the data is relatively more common

Question 6

considerations for outliers

Answer 6

don’t handle “naively” by discarding outliers without careful consideration
check data for data entry mistakes
outliers can be very interesting

Question 7

left skewed

Answer 7

-data sets with longer tail on left
-negative end tail

Question 8

right skewed

Answer 8

-data sets with longer tail on the right
-data trails off to the right
-skewed to the high end
-skewed to the positive end

Question 9

symmetric

Answer 9

data sets with roughly equal trailing off in both directions are called symmetric

Question 10

long tail

Answer 10

when data trail off in one direction the distribution has a long tail

Question 11

define modality and state examples

Answer 11

a mode is represented by a prominent peak in the distribution, if a peak is less prominent or only represented by a few data points-its not counted
1-unimodal
2-bimodal
0-uniform (no prominent peaks)
3+ -multimodal

Question 12

how does bin width alter the story the data is telling in a histogram?

Answer 12

too wide= might loose interesting details
too narrow= might be difficult to get an overall sense of distribution
-ideal width depends on data you are working with

Question 13

dot plot

Answer 13

especially useful when individual samples are of interest but might get too busy with sample size

Question 14

box plot

Answer 14

useful for displaying outliers, median, interquartile range IQR, not good for showing modality

Question 15

intensity map

Answer 15

showing data in context, often geographical, using different layers

Question 16

center of distribution: name and define the 3 types

Answer 16

mean: arithmetic average
mode: most frequent observation
median: midpoint of the distribution(50th percentile)

Question 17

sample statistic

Answer 17

-when mean, median and mode are calculated from a sample
-use letters from latin alphabet

Question 18

point estimate

Answer 18

involves the use of sample data to calculate a single value which is to serve as a “best guess” or “best estimate” of an unknown population parameter (for example, the population mean).

Question 19

are greek or latin letters used to describe population parameters?

Answer 19

greek letters

Question 20

what is a helpful way to think of the mean?

Answer 20

think of the mean as the balancing point in the variance

Question 21

mode

Answer 21

most common value in distribution

Question 22

median

Answer 22

average of middle two observations or middle value of odd number of values

Question 23

range

Answer 23

difference between min and max
not as reliable because uses two most extreme points

Question 24

what are the four measures of spread

Answer 24

range
variance
standard deviation
inter-quartile range

Question 25

variance- describe roughly what this is

Answer 25

roughly the average squared deviation from the mean

Question 26

formula for calculating sample variance (s^2)

Answer 26

1)difference between mean and each observation 2)square each deviation and add them up 3)then divide by sample size by n-1 --answer is squared

Question 27

why do we divide by n-1, rather than n, when computing a sample's variance?

Answer 27

doing this makes the statistics slightly more reliable and useful

Question 28

letters used to describe sample variance and population variance

Answer 28

s^2 = sample variance sigma ^2= population variance

Question 29

why do we square the differences when calculating variance?

Answer 29

-get rid of negatives so that negatives and positives don't cancel each other out when added together -increase larger deviations more than smaller ones so that they are weighted more heavily

Question 30

deviation

Answer 30

distance of an observation from its mean

Question 31

what is the symbol for standard deviation?

Answer 31

lowercase sigma

Question 32

standard deviation

Answer 32

roughly the average deviation around the mean and has the same units as the data formula= square root of the variance

Question 33

Which distribution is more variable, one where more observations are clustered around the center or one where less are centered around the variable?

Answer 33

Distributions where less observations are clustered around the center are more variable.

Question 34

interquartile range

Answer 34

-range of the middle 50% of the data, distance between first quartile(25th percentile) and third quartile (75th percentile) IQR = Q3-Q1 -best to use box plot to visualize -IQR is more reliable in looking at spread because it doesn't look at values which could be outliers

Question 35

robust statistics

Answer 35

measures on which extreme observations have little effect eg data. mean. median 1,2,3,4,5,6 3.5. 3.5 1,2,3,4,5,1000. 169. 3.5 Here the median is more robust.

Question 36

describe which: median, mean, IQR and SD are robust or non-robust and when are they better for describing data

Answer 36

---------- robust. non-robust center. median. mean spread. IQR. SD, range Median and IQR= more robust when looking at data with skewed with extreme observations Mean and SD= best for looking at symmetric observations

Question 37

transformation

Answer 37

-rescaling of the data using a function -when data are very strongly skewed, we sometimes transform them so they are easier to model

Question 38

(natural) log transformation

Answer 38

-often applied when much of the data cluster near zero(relative to the larger values in the data set) and all values are positive -can be easier to analyze because outliers become less extreme, data is more symmetric, less skewed -make the relationship between the variables more linear and easier to model with simple methods

Question 39

square root transformation

Answer 39

plot the square root or the inverse square root

Question 40

goals of transformation

Answer 40

-see data structure differently -reduce skew to assist in modeling -straighten a nonlinear relationship in a scatterplot

Question 41

what greek letter represents the population mean?

Answer 41

mu (micro)

Question 42

what letter represents sample mean?

Answer 42

x bar

Question 43

contingency table

Answer 43

-summarizes data for two categorical variables -shows number of times a particular combination of variable outcomes occurred, along with column totals and rows totals

Question 44

bar plot

Answer 44

way to display single categorical variable -x-axis shows categories

Question 45

difference between histogram and bar plot

Answer 45

bar plot -shows discrete or categorical variables -x-axis shows categories -bars can be rearranged histogram-depicts the frequency distribution of variables in a dataset -x-axis shows numbers -the bars cannot be rearranged

Question 46

row or column proportions

Answer 46

-counts divided by their row totals ie. 3496 renters/8505 total = 0.441 -can be displayed in a contingency table

Question 47

types of bar plots

Answer 47

stacked standardized version of stacked side-by-side

Question 48

when is standardized stacked bar most useful and what is the downside

Answer 48

-useful if the primary variable in the stacked bar plot is relatively unbalanced -downside is that we lose all sense of how many cases each of the bars represents

Question 49

when is side-by-side most useful and what is the downside

Answer 49

- agnostic in their display about which variable if any represents the explanatory and which the response variable -easy to see the number of cases in the group combinations -downside is that it can require more horizontal space -downside is that it can be difficult to to discern if there is an association between two variables if two groups are of very different sizes

Question 50

when is a stacked bar graph the most useful

Answer 50

- when one variable is the explanatory variable and the other is the response

Question 51

mosaic plot

Answer 51

plot suitable for contingency tables that resembles a standardized stacked bar plot with the benefit that we still see the relative group sizes of the primary variable as well - the x-axis shows the width of the columns based on area representing relative proportion -the y-axis can be split into different variables

Question 52

why is a pie chart less useful than a bar plot

Answer 52

it can be difficult to see details in a pie chart which are more obvious in a bar plot, especially for comparing groups

Question 53

side-by-side box plot

Answer 53

good for comparing across groups

Question 54

hollow histograms

Answer 54

compare numerical data across groups -outlines of histograms of each group put on the same plot

Question 55

independence model

Answer 55

a model to test when the variables are independent and any observed result is due to chance

Question 56

alternative model

Answer 56

a model to test when the variables are not independent, the observed result is not due to chance

Question 57

simulation

Answer 57

testing whether a different randomization will affect result eg, take 20 notecards to represent 20 subjects

Question 58

statistical inference

Answer 58

one field of statistics, evaluating whether differences are due to chance