Exam 3 Lecture 4

Question 1

Weird number? Data literacy = asking: Did they have a plan?

Answer 1

With all data, the goal is always to use as much as possible!
- Some people think- if a data point looks weird, chuck it!
BUT ITS NOT THAT SIMPLE!
- Yes, errors add BIAS
- But chucking data can also introduce BIAS
Like in ‘real life’ -> BIAS is bad!

Question 2

To avoid BIAS, you need ______________ about what you are chucking, and why.

Answer 2

A clear plan about what you are chucking, and why.

Question 3

Errors vs. outliers

Answer 3

Errors = not ‘real’ data -> always discard
Outlier = ‘real’ data -> decide/ discard or transform

Question 4

Statisticians have _______ about discarding a data point. They also have multiple ways to ________ a data point to make it more ‘manageable’ but still ‘different’.

Answer 4

Statisticians have rules about discarding a data point. They also have multiple ways to transform a data point to make it more ‘manageable’ but still ‘different’.

Question 5

A good statistician…

Answer 5

Tries to use all available data whenever possible.

Question 6

Just because it’s weird/unexpected…

Answer 6

Rare numbers (at tail end of a range) are rare, so you can’t just say- nah, I doubt it!
Remember: your data are from a SAMPLE that represents a POPULATION. Sometimes a sample represents every possible thing, sometimes it doesn’t.

There is no single rule about what an outlier is.
- All data ‘behave’ differently but you can look at the DISTRIBUTION of your data (that is, look at the list of numbers)

Even if a data point is real and correct, it might be so extreme as to add BIAS to your results- affecting both the mean and the variance- just like as if it was an error. When a data point adds bias, it is called an influential outlier.

Question 7

When a data point adds bias, it is called an

Answer 7

Influential outlier

Question 8

Aren’t you important! The power of outliers example

Answer 8

When a data point is so extreme that it throws off the central tendency, the variance or the distribution, it is called an influential outlier.

Data: The number of students who fail Art History per semester
1+2+3+2+2= 10/5= 2 (average), 0.7 (std dev)
1+2+3+2+22= 30/5= 6 (average), 9.0 (std dev)
Wow! One bad semester and look at the difference!

We need to determine if the 22 is real data. Go back to the source.

IF…
The class size was 20 until the course went online. In the 5th semester, 200 students registered.
Possibly real. Keep. NEED to TRANSFORM data! (% failing) to account for different class sizes.

IF…
The class size was CAPPED at 20 each semester.
Not real. Can’t fail more than took the class! Discard. You lose a data point.
1+2+3+2=8/4=2 (average), 0.8 (std dev)

Question 9

Managing outliers

Answer 9

You get to make a rule about how extreme is too extreme. Some examples:
RULE: discard if >3 std dev from next closest point
RULE: discard if above a specific # (resting HR > 120; drinks per day > 20)

As long as:
- you believe the value is possible (not error)
- other people will agree that this is reasonable
- you have a good rationale AND
- you apply this rule to all data

It can still be good/reliable data.

Question 10

If we don’t look at outliers/errors…

Answer 10

We might mislead people with data.

Question 11

Managing outliers through transformations

Answer 11

You can ‘fix’ the distribution of your data (make it more normal!)
A transformation is an equation that is applied to ALL data points to make the overall data distribution more normal.
A common transformation is a log transformation. By taking the log of all values, you can ‘pull in the tails’, especially a right tail. But, since you can’t take a log of 0, people often first add a constant (x+1)

Takes the data from kurtotic to normal.

Question 12

An equation that is applied to all data points to make the overall data distribution more normal

Answer 12

A transformation

Question 13

What is a log transformation and what does it do?

Answer 13

A log transformation is a type of transformation- an equation that is applied to all data points to make the overall data distribution more normal. By taking the log of all values, you can ‘pull in the tails’, especially a right tail.
By log transforming the values, the outlier is still there, but now manageable.

Question 14

Central tendencies + variability =

Answer 14

A full picture.
Most often research uses mean and standard deviation.

Question 15

How to report mean and standard deviation

Answer 15

We report it like this:
- 300 +/- 10
- 300 +- 10
M: 300, SD: 10
Mean = 300, Std Dev = 10

Standard error of the mean is also a common variance term.

Question 16

State examples of central tendency and examples of variability.

Answer 16

Central tendency: Mean, median, mode
Variability: Range, standard deviation, variance

Question 17

Graph

Answer 17

A graph is a visual representation of a table (or dataset)

Question 18

When and why is graphical data analysis performed?

Answer 18

Often performed early on to determine whether the data “look good”
- Have enough variance (without variance, there is nothing to predict)
- Are normal
- Have no outliers

Often performed prior to (or following) statistical analyses to visualize patterns and relationships
- Commonly reported in research studies to help readers digest what the statistical tests mean

Question 19

What is a line graph?

Answer 19

It uses lines to connect individual data points.
Used mainly to show:
a) change over time (always on x-axis)
b) relationship between two variables

The graph CAN include more than 1 line.
The line CAN be straight or curved.

Line graphs are used to look at the relationship between two variables (what happens to the # on the y-axis as the # of the x-axis gets bigger?)

This type of graph is used when both variables (1 on the x- and 1 on the y-axis) are CONTINUOUS (in other words, no groups!)

This type of graph uses continuous data. To statistically ANALYZE it, we’ll need to do a REGRESSION or CORRELATION

Question 20

Line graphs use ____________ data.

Answer 20

Continuous

Question 21

To statistically analyze a line graph, you need to do a _____________ or a _______________

Answer 21

Regression or correlation

Question 22

Line graphs tell a story
Without knowing anything other than the SLOPE of a line, we can say

Answer 22

• All datapoints belong to a SINGLE GROUP or CONDITION (there is only 1 line)
• Group average ‘STARTING VALUE’ is 150 (y-intercept, the value of y when x=0)
• There is a LINEAR relationship between x and y (it’s a straight line)
• There is a POSITIVE relationship between x and y (as x gets bigger, so does y)

Question 23

Line graphs tell a story:
How many GROUPS/CONDITIONS?
What is ‘STARTING VALUE’?
Is this LINEAR?
Is it a POSITIVE or NEGATIVE (or null) relationship between x and y?

Answer 23

1 Group/condition if there is 1 line
2 Groups/conditions if there are 2 lines
Starting value is the number the line starts at
Yes linear, it is a line
DON’T MISTAKE THIS THOUGH. It is always a line graph, but not always linear. If the line is curved, it is not linear.
Positive if going up, negative if going down
Null if straight line

Question 24

Line graphs tell a story. These groups change the same but start at different places.
Example: 8th versus 12th males (weight), eating same diet.

Answer 24

Our result: 8th graders weighed less than 12th graders at the START of the study, but gained weight at the same RATE across the study period.

Question 25

Line graphs tell a story. These groups start at the same place but change differently.

Answer 25

Example: All participants weighed the same (160lbs) at the beginning of the study. When they were split into a group that did or did not get put on a calorie-restriction diet, their weights diverged (changed differently) over the study period.

Question 26

Protocol: 4 participants added 150 cal/day to diet; no other changes- this is what happened to average weight. What would a line graph tell you?

Answer 26

Tells you how many days to gain 5 lbs.
Also you can see:
- Weight kept increasing for every day that the extra calories were consumed.
- The rate of increase in weight was consistent across all days.

Question 27

What is missing in just line graphs? What doesn’t a line tell us?

Answer 27

Individual variability!
A line doesn’t tell us what every individual in a group is doing. It is just telling us about the average of a group.

We are missing error bars.

Question 28

What is a way to see the individual in a line graph?

Answer 28

ERROR bars.
They provide some information on INDIVIDUAL VARIABILITY.
These are the standard deviation around the mean. You can read these too!

Question 29

What is an error bar?

Answer 29

Shows the standard deviation around the mean. Provides information on individual variability.

Question 30

What is a scatterplot?

Answer 30

Scatterplots are used to look at the relationship between 2 variables (like line graphs).
(what happens to the # on the y-axis as the # of the x-axis gets bigger?)
But it also provides information about every individual in a group!
This type of graph is used when both variables (1 on the x- and 1 on the y-axis) are CONTINOUS (in other words, no groups!)
This type of graph uses continuous data. To statistically ANALYZE it, we’ll need to do a REGRESSION or CORRELATION

Question 31

How do you statistically analyze a scatterplot?

Answer 31

With a REGRESSION or CORRELATION

Question 32

Benefits of scatterplots

Answer 32

They show ACTUAL individual variability!
From the sleep study example, we can now see that people vary in how much they change.

Question 33

Related to scatterplots, a spaghetti plot.

Answer 33

Same data as scatterplot, uses lines rather than dots to show all data (not just average)
- Good for when time is on x-axis
- Still shows variability, but now you see data by person.
Conclusions:
- People are different from one another.
- Change varies over time (it is not a straight line).

Question 34

What does it mean by continuous? What does this apply to?

Answer 34

A graph is continuous when there are no groups (we are looking at the relationship between two variables). This would be a line graph, scatterplot, or spaghetti plot.

Question 35

Sometimes it’s not a relationship, it’s a competition.

Answer 35

Graphs can help you compare one group to another
- The x-axis isn’t a continuum, it is either
- Bins of numbers, called intervals (histogram)
- Categories/groups (bar chart)

Question 36

When comparing one group to another, this is a __________ variable (Categorical or continuous)

Answer 36

Categorical

Question 37

When comparing one group to another, what type of graphs would we use and which would we not use? Why?

Answer 37

When comparing one group to another, we would use a histogram or a bar chart because comparison is categorical. We could not use a line graph, scatterplot or spaghetti spot because those are for continuous variables.

Question 38

What is a bar graph?

Answer 38

Bar graphs are used to look at differences between groups or times. The CATEGORICAL (group or binned variable) is on the x-axis and the CONTINUOUS variable is on the y-axis.

This type of graph uses a combination of categorical and continuous data. To statistically analyze it, we’ll need to do a T-TEST or ANOVA.

Question 39

How do you statistically analyze a bar graph?

Answer 39

With a T-TEST or ANOVA

Question 40

Where is the categorical and where is the continuous variable on a bar graph?

Answer 40

For bar graphs, they have both categorical and continuous data. The categorical (group or binned variable ex. NJ, PA) is on the x-axis and the continuous variable (numbers) is on the y-axis.

Question 41

Graphs that compare groups

Answer 41

Bar Graph
This bar graph compares average sick days/year among workers in different states.
- The x-axis is the groups.
- The y-axis shows sick days data.
- Error bars = variability from year to year.

Question 42

What is a histogram?

Answer 42

A histogram is a special type of BAR graph.
The y-axis is always FREQUENCY (the # of participants in the bin) and the data are always from 1 variable (nothing being compared).
It is a graph used for descriptive statistics (to describe data)
This is a different type of graph! What’s the major difference?
a) Bars are created by BINNING values on the x-axis
b) We are not looking at a RELATIONSHIP between x and y (no line), we are COMPARING the height of the bars.

Question 43

This is a histogram. Example

Answer 43

This histogram partitions grades into 5-point bins. It tells us that most students received a B (80-85) on the exam (10 out of 23). 9 more earned a B+.
There are no gaps between the bars because actually the data on the x-axis are CONTINUOUS, but BINNED into GROUPS
*Sometimes continuous data isn’t necessary. I might not care who got an 88 versus an 89; I just care how many B+s there were.

Question 44

Graphs that bin & measure how common something is

Answer 44

A histogram.

Question 45

Bar graphs are more common, but this one gives more detail!

Answer 45

A BOX & WHISKER (a fancy bar graph)

Question 46

What is a box and whisker graph?

Answer 46

A fancy bar graph. Still a combo of categorical and continuous data. To statistically analyze it, we’ll need to do a T-TEST or ANOVA.

Question 47

Quartiles

Answer 47

Order data, cut dataset into 4 parts. Sometimes the quarter spans more #s (tails)

Question 48

How does a box & whisker show outliers?

Answer 48

An asterisk is used to denote that a value is outside the expected range based on other values, and is likely to BIAS the results. It is an influential outlier.

A circle is used to denote that a value is outside the expected range based on other values but should be OK to keep.