Unit 5 Key Ideas

Question 1

Univariate analysis

Answer 1

The analysis of a single attribute or variable at a time

Question 2

Standard deviation (SD)

Answer 2

A measure that tells us how spread out observations are from one another.

Question 3

Define five number summary

Answer 3

it is a summary that contains five numbers that statisticians and data scientists use to help understand the various values that different observations have for an attribute

Question 4

What are the five numbers in the five number summary?

Answer 4

Minimum, first quartile, median, third quartile, maximum

Question 5

Define the minimum

Answer 5

The smallest value that any observation has for the attribute

Question 6

Define the first quartile

Answer 6

It is the 25th percentile value.
25% of observations have a value below the first quartile (i.e. this is the point that is a quarter through all your data)

Question 7

Define the median (i.e. the second quartile)

Answer 7

It is the second quartile (aka the 50% percentile value) Half of the values are below the median. It is the point where half of the data is below and half is above.

Half of the values are below the median.

Question 8

Define the third quartile

Answer 8

This point is three quarters into your data. It is the 75th percentile value. 75% of all observations have value below the third quartile.

Question 9

Define the maximum

Answer 9

This is the largest value that any observation has for the attribute

Question 10

Define frequencies

Answer 10

The total number of observations whose response is equal to a particular value
(e.g. if nine of the resondents say they are 7 ft, than the frequency for seven is nine)

Question 11

Relative frequencies (i.e. percentages)

Answer 11

The percentage of all observations without missing values whose value is equal to a particular response

Question 12

What is a dot plot?

Answer 12

A graph where each observation is displayed as one dot on the graph. Looking at the height of a dot plot tells you the frequency for a particular value.

Question 13

What is a density plot (i.e. density curve)?

Answer 13

It is like a dot plot but with a line drawn on top of it. It doesn’t show individual stacks of dots. It shows the concentration of where there are fewer and greater observations.

Question 14

What is a word cloud?

Answer 14

It is meant to graphically depict text data. It shows all the text recorded from all the responses to each observation. The size of the word represents the frequency of it (i.e. how many times someone said it)

Question 15

What is a bar graph?

Answer 15

It is based on a frequency table and has one bar for every response option (typically in order). The bar height is equivalent to each response option’s frequency.

Question 16

Define aggregate characteristics

Answer 16

They are the characteristics of a group of observational units

Question 17

What aggregate characteristics are recorded for text, rating scale, and categorical data?

Answer 17

Frequencies

Question 18

How do you think of the spread of a distribution?

Answer 18

Think of the “middle 95%” and the standard deviation

Question 19

How do you think about the location of a distribution?

Answer 19

Think about the peak/mode and the mean

Question 20

How do you think about the shape of a distribution?

Answer 20

Think about the number of peaks, and the symmetry (asymmetrical? left or right skewed?), and compare it to one of the common distributions (i.e. bell curve, multimodal, uniform distribution, etc.)

Question 21

What aggregate characteristics are recorded for quantitative data?

Answer 21

The shape, location, and spread, of the data

Question 22

Define distribution

Answer 22

The pattern that the responses from all the observational units make

Question 23

What are the different common shapes that we often see in quantitative distributions?

Answer 23

U-Shaped, Uniform distribution, Multimodal, Unimodal, Bell-curve (Normal distribution), Skewed distributions, symmetric

Question 24

Deine U-Shaped distribution

Answer 24

Most of the observational units either have very low values or very high values with hardly any values in-between

Question 25

Define uniform distribution

Answer 25

It is essentially a flat shape. There are approximately the same number of observational units for each of the possible values.

Question 26

Define multimodlal

Answer 26

It has multiple peaks. It is common when there are actually group differences in the attribute.

Question 27

Define unimodal

Answer 27

It has only one peak

Question 28

Define a bell-curve (i.e. normal distribution)

Answer 28

Most of the observational units have a value near the average. Approximately 95% of the values are within two standard deviations of the mean (aka average)

Question 29

What is another word for the mean?

Answer 29

Average

Question 30

What is another word for the median?

Answer 30

The second quartile

Question 31

What is a skewed distribution?

Answer 31

They are distributions that look like they have one side stretched out

Question 32

Define right skew

Answer 32

Distributions look like the right side of a normal distribution has been stretched out (indicating some units have large values "stretching it" out)

Question 33

Define left skew

Answer 33

Distributions that look like the left side of a normal distribution has been stretched out (indicating that some units have very small values)

Question 34

Why does a left skew mean that some units have very small values while a right skew means some units have a very large value?

Answer 34

Think of a left skew (also called negatively skewed) distribution as having a tail that drags to the left. This means that while most of your data points are bunched up on the higher end, there are a few smaller values pulling that tail out to the left. Conversely, a right skew (positively skewed) distribution has a tail that extends to the right, meaning most of your data points are on the lower end, but there are a few larger values dragging that tail out to the right.

Question 35

What is a key to thinking statistically?

Answer 35

Focusing on how each observational unit varies

Question 36

What is a two-way table?

Answer 36

Similar to a frequency, this type of table is a two-dimensional version of this. One attribute's frequencies are presented as different rows in the table, and a second attribute's frequencies are presented as columns.

Question 37

Define conditional relative frequencies

Answer 37

They are relative frequencies based only on the total from a single row or single column

Question 38

Scienticians use what when each column represents a separate group?

Answer 38

Column percentages

Question 39

Define Cramer's V

Answer 39

It is the statistic that quantifies the association between two attributes. Having an association typically means there is a perceived relationship between the two attributes. It is on a scale of 0-1

Question 40

Define a side-by-side bar graph

Answer 40

It is a bar graph that has one bar graph created separately for each of the different response options for the second attribute being considered in the two-way table

Question 41

Define side-by-side density plots

Answer 41

Have one density curve for a quantitative attribute for each group all on the same plot

Question 42

The ratio of standard deviation is equal to what?

Answer 42

The largest standard deviation between the two groups divided by the smallest standard deviation Largest standard deviation in the group/smallest standard deviation in the group

Question 43

What is the effect size queal to?

Answer 43

The difference in the means (averages), divided by the larger standard deviation Difference in means/larger standard deviation in the group

Question 44

What effect sizes indicate a large difference in the averages between the groups?

Answer 44

0.75 or more

Question 45

What effect sizes indicate a small difference in the averages between groups?

Answer 45

0.25 or less

Question 46

What is a scatterplot?

Answer 46

A plot in which each observational unit is placed as a point on a graph according to their value for each quantitative attribute

Question 47

What is a smoothed trend line?

Answer 47

Is a line through the average value of the vertical axis attribute across all values of the horizontal axis attribute. It is a line that shows a general trend or direction of the data without getting caught up in the ups and downs. It's the calm, steady flow in a river of data points.

Question 48

Define Kendall's Tau

Answer 48

Is a correlation measure that can be used even when the trend line is not straight

Question 49

What do the values of the Kendall Tau mean?

Answer 49

If values are close to 0, it means there is no association between the attributes. When values are close to -1 (the trend is going down), it means there is a strong negative association between attributes. When values are close to +1, it means that there is a strong positive association between the attributes (the trend is going up).